Posted: February 26th, 2023

one page of answers

  1. Problem statement: what kind of problem is presented by the authors and why this problem is important?
  2. Approach & Design: briefly describe the approach designed by the authors
  3. Strengths and Weaknesses: list the strengths and weaknesses, in your opinion
  4. Evaluation: how did the authors evaluate the performance of the proposed scheme? What kind of workload was designed and used?
  5. Conclusion: by your own judgement.

A Machine-Checked Proof of Security for AWS Key Management Service

José Bacelar Almeida

University of Minho and


Manuel Barbosa

University of Porto (FCUP) and


Gilles Barthe

IMDEA Software Institute

MPI for Security and Privacy

Matthew Campagna

Amazon Web Services

Ernie Cohen

Amazon Web Services

Benjamin Gregoire

INRIA Sophia Antipolis

Vitor Pereira

University of Porto (FCUP) and INESC TEC

Bernardo Portela

University of Porto (FCUP) and INESC TEC

Pierre-Yves Strub

École Polytechnique

Serdar Tasiran

Amazon Web Services

ABSTRACT We present a machine-checked proof of security for the domain

management protocol of Amazon Web Services’ KMS (Key Man-

agement Service) a critical security service used throughout AWS

and by AWS customers. Domain management is at the core of

AWS KMS; it governs the top-level keys that anchor the security of

encryption services at AWS. We show that the protocol securely

implements an ideal distributed encryption mechanism under stan-

dard cryptographic assumptions. The proof is machine-checked in

the EasyCrypt proof assistant and is the largest EasyCrypt devel-

opment to date.

CCS CONCEPTS • Security and privacy → Key management; Logic and veri- fication.

KEYWORDS Provable-Security; Machine-Checked Proof; Key Management

ACM Reference Format: José Bacelar Almeida, Manuel Barbosa, Gilles Barthe, Matthew Campagna,

Ernie Cohen, Benjamin Gregoire, Vitor Pereira, Bernardo Portela, Pierre-

Yves Strub, and Serdar Tasiran. 2019. A Machine-Checked Proof of Security

for AWS Key Management Service. In 2019 ACM SIGSAC Conference on Computer & Communications Security (CCS ’19), November 11–15, 2019, London, United Kingdom. ACM, New York, NY, USA, 16 pages. https://doi.


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    1 INTRODUCTION Today’s cloud services use sophisticated distributed architectures

    and algorithms to make data highly available and durable. To im-

    prove security, data at rest is typically encrypted, and decrypted

    only when/where necessary. The encryption keys themselves must

    be similarly durable and available; however, directly providing all keys towhichever service needs to use them unnecessarily increases

    the attack surface. For the most sensitive keys, it is more prudent to

    encapsulate them within a separate distributed encryption service.

    Such a service allows the creation of new keys, and uses these

    keys to encrypt and decrypt data, but does not expose the keys

    themselves to clients.

    The subject of this paper is the AWS domain management proto-

    col (henceforth abbreviated DMP), a distributed encryption service

    underlying the Amazon Web Services (AWS) Key Management Ser-

    vice (KMS [5]). AWS KMS, a core component of the AWS cloud, lets

    AWS customers create and manage encryption keys, providing a

    consistent view of encryption/decryption operations across AWS

    services, and controlling their use through AWS Identity and Access

    Management (IAM). 1 The widespread usage of AWS KMS and the

    central role of the DMP justifies a high-assurance security proof,

    leveraging recent developments in computer-aided cryptography

    such as [3, 4, 7].

    In this paper, we present a fully mechanized, concrete proof of

    security of the DMP. Informally, the proof shows that the DMP

    provides an idealized encryption service.

    Security goal. The DMP is designed to protect the confidentiality

    of data encrypted under domain keys and guarantee the correct

    operation of the interface it provides, even in the presence of a

    malicious individual interfering with the inner workings of the sys-

    tem. In particular, we consider an adversary that can commission

    and decommission hosts and HSMs (Hardware Security Modules),

    assumed to be under adversarial control, and manipulate (insert,

    delete, modify) messages exchanged between system entities. Our

    1 Within AWS KMS, the DMP is used only to encrypt and decrypt customer master

    keys, the roots of the customer key hierarchies. The use of these master keys, and the

    design of KMS (outside of the DMP itself) is described in [5].

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    goal is to show that such an adversary cannot gain further advan-

    tage than possibly causing the system to go unresponsive.

    Formally, this security goal is defined using an ideal functionality

    and the real-vs-ideal world paradigm, similarly to the Universal

    Composability [14] framework. We prove that the DMP is indis-

    tinguishable from an idealized encryption service to an arbitrary

    external environment that can collude with a malicious insider

    adversary. This formalization captures precisely the security that

    the rest of AWS KMS needs from the DMP.

    Main Theorem. Our main theorem states that the DMP behaves

    like an ideal authenticated encryption service. The theorem rules

    out attacks from arbitrary computationally bounded adversaries,

    under standard cryptographic assumptions for digital signatures,

    hash-functions and encryption schemes. Formally, we prove that

    the probability of breaking the protocol is smaller than

    2 · ( (qops + qhid) · ϵsig + qdom · ϵaead + ϵcr + ϵmrpke + ϵcoll

    ) ,

    where qops and qhid are upper bounds on the number of human op-

    erators and HSMs in the system, respectively; qdom upper-bounds

    the number of domain keys; ϵsig, ϵaead and ϵcr denote the maxi-

    mum probabilities of breaking a standard signature, authenticated

    encryption and cryptographic hash function, respectively; ϵmrpke denotes the maximum probability of breaking a multi-recipient

    variant of public-key encryption; and ϵcoll is a small statistical term

    related to collisions of signature verification keys. The security of

    cryptographic signatures, hashes, and authenticated encryption im-

    plies that all of the epsilons above (and hence the total probability

    of breaking the protocol) are negligible. A more precise statement

    of the concrete cryptographic setting and bound can be found in

    Sections 4 and 5.

    Formalization. The proof is fully machine-checked in EasyCrypt [6],

    a proof assistant for cryptographic proofs. The development is

    15K lines of code (loc), of which 500 loc comprise the protocol

    specification. Besides being the largest EasyCrypt development

    to date, the proof combines game-hopping techniques that are

    standard in cryptographic proofs, and rich inductive reasoning that

    is standard in program verification. The machine-checked proof is

    novel for the following reasons:

    • We formalize a notion of key secrecy for KMS DMP in the style of

    cryptographic APIs [23] and extend prior work in this area by i.

    addressing a substantially more complex (distributed) API; and ii.

    making explicit which assumptions on the behaviour of human

    operators are necessary (as otherwise trivial breaks would be

    possible), whilst excluding all non-trivial breaks as in prior work

    by reducing to standard cryptographic assumptions.

    • We relate the above definition of security with a real-vs-ideal

    world security definition for encryption services, by proving

    a (reusable) general composition result for combining crypto-

    graphic key management APIs with AEAD schemes. Our result-

    ing top-level security theorem establishes that KMS DMP is as

    good as an ideal authenticated encryption service in the specified

    trust model.

    • The machine-checked proof follows best proof engineering prac-

    tices and favors reusable components, breaking down the verifi-

    cation effort in three types of steps:

    i. reusable results that lift standard cryptographic assumptions

    on signatures and hash functions to idealized versions that

    permit reasoning symbolically about complex invariants on

    authenticated data structures;

    ii. use rich inductive reasoning to prove that intricate authentica-

    tion invariants hold in the security experiments, and rewrite

    (slice) the code of the security games to make explicit the split

    between data which is under adversarial control (due to trivial

    strategies that do not contradict the security claim) and data

    which is outside of the adversary’s reach; and

    iii. build on the previous results to conduct a game hopping proof

    that, first, idealizes digital signatures and hash functions, accou-

    ting for concrete (negligible) security losses; then modularly

    uses the authentication invariants to perform security experi-

    ment slicing; and finally reduces the key-secrecy property to

    the security of multi-recipient encryption.

    Paper Structure. In Section 2 we give a bird’s eye view of our ap-

    proach and provide a road-map for the paper, before moving on to

    more technical sections. In Section 3 we give a detailed description

    of the DMP and of its formalization in EasyCrypt. Then, in Section 4

    we formalize the security model that we have adopted and in which

    we have proved security of the DMP. In Section 5 we describe the

    machine-checked security proof. Section 6 gives an overview of the

    improvements to EasyCrypt that were developed during the project.

    Section 8 contains a summary of related work, and Section 9 the

    concluding remarks.

    2 OVERVIEW In this section we present an overview of the DMP goals and inter-

    face, and then outline the structure and contents of the EasyCrypt

    model and proof (shown in Figure 1).

    DMP Concepts. The fundamental unit of security in the DMP is

    a domain. Each domain provides an independent distributed en-

    cryption functionality using a combination of machines and people

    (collectively referred to as entities) which may change over time.

    Each entity can participate in multiple domains.

    Concretely, a domain is given by its entities, the rules governing

    the domain, and a set of (symmetric) domain keys. The entities

    are of three types: HSMs, human operators, and front-end hosts. HSMs are the inner security boundary of the DMP, and have a

    limited web-based API and no other active physical interfaces to

    their operational state. Sensitive cryptographic materials of an HSM

    are stored only in volatile memory, and are erased when the HSM

    exits operational state, including shutdowns and resets. Domain

    keys likewise appear in the clear only in the volatile memory of

    HSMs in the domain.

    The goal of the DMP is to govern the operations on domain keys

    and to manage membership of HSMs in a domain, as well as au-

    thorizing operators to act on a domain. HSMs do not communicate

    directly with each other. Thus, a central function of the DMP is to

    synchronize the domain state between domain participants. For this

    purpose, all information about a domain state, including its domain

    keys, is transferred and stored in a domain token. A domain token

    contains encryptions of the domain keys, and is authenticated in

    order to bind these encryptions to the domain state.

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    Domain state is modified through quorum-authenticated com-

    mands issued by authorized operators for that domain. Changes

    to domain state include modifying the list of trusted participants

    in the domain, modifying the set of quorum rules, and periodi-

    cally rotating domain keys. Rules on quorum-signed commands

    are designed to mitigate attacks by colluding dishonest operators,

    namely attacks that might allow such operators to bypass the secu-

    rity protections provided by the HSMs. By requiring authorization

    from n operators from the domain, the security of operations that

    add new entities to a domain is anchored on the assumption that

    a quorum of n operators from the domain will always contain at

    least one honest operator that follows the protocol, where n is a

    security parameter for the domain. A more detailed description of

    the domain management operations is included in Section 3, along

    with their formalization in EasyCrypt.

    DMP Implementation. Not counting the crypto libraries, the imple-

    mentation of the DMP protocol is spread across some 16.5K lines

    of Java code. The conformance of this code to the protocol level

    design is checked via integration tests. Additionally, a formal code

    validation mechanism has been built using an extension to a taint

    tracking type system (the Checker Framework, [19]). The checked

    property is a necessary condition for conformance to the protocol:

    a domain key must not be returned as part of the return value of an

    API call without first being encrypted by another key. This check

    is performed continuously, every time the KMS codebase changes,

    and it required only 323 manual annotations to the codebase.

    DMP Functional Interface. The DMP provides an encryption func-

    tionality for each of its domains. Different domains can vary in the

    entities that they trust, their tolerance for dishonesty, and other

    security-related parameters. For each domain, the provided en-

    cryption functionality has the following interface 2 (formalized in

    Section 4):

    • New(hdl) creates a new domain key within the domain and as-

    sociates it to a key identifier hdl. The result indicates whether the operation was successful.

    • Enc(hdl,msg, ad) uses the domain key associated with identifier

    hdl to encrypt the payloadmsgwith associated data ad, returning the ciphertext.

    • Dec(hdl, cph, ad) uses the domain key associated with identifier

    hdl to decrypt ciphertext cph with associated data ad and, if

    successful, returns the recovered plaintext.

    The goal of the DMP security proof is to show that the DMP pro-

    vides an idealized version of this interface (with a small probability

    of error). This ideal interface is close to that of standard Authen-

    ticated Encryption with Associated Data (AEAD), as detailed in

    Section 4, except that operations might fail (with no effect), as one

    might expect in a distributed system.

    The EasyCrypt security proof consists of three layers. 3 The top

    layer gives a real-vs-ideal world security definition for the DMP

    and shows that security of a DMP domain in this model follows

    2 This interface mentions only domain keys, so the functionality gives a simple way

    to separate the security provided by the DMP from its use in the rest of AWS KMS.

    3 Note that the scale of the proof does not increase the trusted base, as it is fully

    machine-checked by EasyCrypt – indeed, this is the main motivation for machine-

    checked provable security; the guarantee that the proof justifies the formalized security

    theorem requires only trust in EasyCrypt itself.

    Sig (UF)

    SigService (Real-Ideal)

    Hash (CR)

    Hash Chain (Real-Ideal)

    Policy (Real-Ideal)

    Policy (Bad Event)

    AEADTag-Based MR-PKE

    ODH Group/KDF

    Crypto API (Ind-based)

    AEAD Service (Real-Ideal)

    Figure 1: Structure of the machine-checked proof

    from the secrecy of its domain keys. The next layer shows that the

    DMP does indeed preserve the secrecy of domain keys of so-called

    “honest" domains (described in Section 3), assuming the secure

    implementation of the low-level cryptographic constructions used

    to create domain tokens. The bottom layer shows the security of

    these low-level constructions.

    Proof: Real-vs-ideal World Security.At the top layer of the EasyCrypt proof lies a formal definition of security for encryption services

    supported by key management protocols such as the DMP (detailed

    in Section 5.1). The definition follows the real-vs-ideal paradigm of

    the UC framework (in fact, our proof can be seen as being carried out

    in a specific hybrid model in the UC framework, which we discuss

    in detail in Appendix A). Intuitively, the ideal functionality leaks

    nothing to the (adversarial) environment except the length of the

    data being encrypted, and implements decryption by maintaining a

    table mapping pairs (cph, ad) to messages. Ideal encryption always

    returns encryptions of 0 ℓ , where ℓ is the encrypted data length,

    and adds a new entry to this table; decryption simply does a lookup

    from the table (rather than calling the decryption function).

    At this level we reduce the real-vs-ideal world security of the

    DMP to an indistinguishability-based security property that cap-

    tures the secrecy of domain keys. This means that in the lower

    levels of the proof we do not need to reason about how domain

    keys are used; it suffices to prove that the DMP keeps domain keys

    hidden from the attacker’s view.

    Proof: Indistinguishability-based security. The second layer of results proves that the protocol hides all information about domain keys

    from the adversary’ view. This is formalized as a cryptographic

    API [23] that guarantees domain key secrecy. The model captures

    the actions of a malicious insider adversary by allowing the do-

    main management operations to consist of multiple adversarially

    orchestrated steps. The main challenge in this proof, formalized

    using the game-hopping technique, is to establish the invariants

    that govern the state of security experiments in each hop. These in-

    variants combine properties that arise from standard cryptographic

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    Figure 2: High-level view of the DMP. assumptions (e.g., absence of collisions and signature forgeries)

    with the inductive argument that justifies the soundness of the do-

    main update operations carried out by honest operators, HSMs and

    hosts. It is by the joint action of these two types of guarantees that

    the domain management policy excludes dishonest entities from

    explicitly obtaining information on domain keys. The proof at this

    layer reduces the security of the API to the security of lower-level

    abstractions, all of which are formalized in the indistinguishability

    style, in order to facilitate the game-hopping technique. The details

    are discussed in Section 5.3.

    Proof: Low-level abstractions. The lower layer of security results de-

    fines idealized versions of digital signature services, hash maps and

    certification of identity keys by human operators. It also contains

    proofs that these abstractions are indistinguishable from real-world

    instantiations down to standard cryptographic assumptions, which

    can then be used to make concrete the bounds in the theorems

    established at the higher layers in the development. At this level,

    we also formalize the specific flavor of (multi-recipient) public-key

    encryption that is used by the DMP.

    This lower layer in the proof is meant to modularize various

    components, for three purposes: 1) lifting assumptions formalized

    as bad events, such as unforgeability and collision resistance, to

    indistinguishability definitions, allowing the higher-level parts of

    the proof to be solely based on indistinguishability game hops; 2) al-

    lowing for reuse of the abstractions across the project (e.g., we reuse

    the signature abstraction for both operator signatures and HSM

    signatures); and 3) allow for multiple instantiations of the same

    underlying primitive (e.g., an encryption scheme with different

    constructions). This part of the proof is presented in Section 5.2.

    3 KMS DOMAIN MANAGEMENT PROTOCOL 3.1 Detailed Description A high-level operational view of the DMP is presented in Figure 2

    (reproduced from [5]). Operators issue commands, HSMs manipu-

    late the contents of domain tokens, and coordinator servers propa-

    gate updated domain tokens to each HSM in a domain to keep their

    domain states approximately synchronized (the latter are not shown

    and assumed for the purpose of the proof to be under adversarial


    We now describe the core concepts and mechanisms involved

    in the DMP at the level of the mathematical model of the protocol

    that forms the basis of the formal proof of security. We begin by

    introducing the notion of a domain state, the different entities in the

    system and what assumptions we make about their behavior; we

    then explain the roles of these entities in domain state transitions,

    and conclude with an intuitive explanation of the security rationale

    underlying the design.

    Protocol entities and assumed behavior. The DMP is implemented

    using three types of entities: HSMs, hosts, and operators. Each entity

    is identified with its identity (signature verification) key. A genuine entity is (the identity key of) anHSM/Host/Operator that behaves as

    specified by the DMP. A domain might include non genuine identity

    keys of any entity type, e.g. keys created by amalicious entity. HSMs

    perform the actual encryption and decryption operations, 45

    and are

    the only entities allowed to manipulate domain keys in cleartext.

    Operators are responsible for certifying identity keys: they sign

    statements claiming that a given identity key represents a genuine

    HSM, host or operator. 6 Honest operators only sign statements

    that are true, i.e. if an honest operator claims a key is that of a

    genuine HSM, the key is in fact genuine. Conversely, dishonest

    operators, while themselves genuine, might sign statements that

    are false. Note that we assume only that an honest operator can

    tell whether another operator is genuine, not whether he is honest.

    Genuine but dishonest operators model insider threats, possibly

    colluding with external adversaries. Non-genuine operators model

    arbitrary rogue identity keys that the adversary may also create in

    its attack. For the purpose of this paper, the quorum rule is defined

    by a security parameter n, which describes the minimum number

    of operators of the domain that must authorize an update over

    the domain state. Our security analysis is anchored on a global

    assumption that any set of n genuine operators contains at least

    one honest operator that follows the protocol. For example, a rule

    imposing that a quorum consists of a set of at least n = 2 operators

    from the domain guarantees that it requires at least two dishonest

    operators of the domain to break security.

    Finally, hosts are the service endpoints. Although the actions of

    hosts in AWS KMS are more complex, our analysis focuses on the

    crucial role of honest hosts in directing cryptographic operations

    to honest domains: 7 as entry points in the system, hosts keep track

    of domain states and check that they are updated consistently with

    the domain management rules by HSMs. (Although we have not

    formalized this, in Appendix B we discuss how our proof implies

    security in a model where corrupt hosts are considered.)

    4 What we call HSMs are, in AWS KMS, running instances of FIPS 140-2 certified

    hardware security modules. They generate fresh identity and agreement key pairs

    when they boot, and store them only in volatile memory; the instance is effectively

    destroyed when power is lost. This simplifies physical protection — it suffices to

    guarantee that the machine cannot be physically attacked without losing power.

    5 In our protocol model, HSMs are conceptually stateless beyond their identity and

    agreement key pairs. In AWS KMS, HSMs maintain the current domain state for each

    domain they operate on, allowing their behavior to be more tightly controlled. This

    provides defense in depth, and potentially allows the proof of additional security

    properties not described here.

    6 In AWS KMS, these statements are actually commands to perform particular actions,

    such as a command requesting an HSM to add or remove HSMs or operators from a

    domain; such a command implicitly carries with it the certification from the command

    signers that the added entities are genuine. Note also that operators represent human

    operators, which play many additional security roles in the system; we describe only

    as much as is needed to justify the presented

    security proof.

    7 Note that it is always safe to add domain-local secrets that appear only encrypted

    by keys of the domain. This can be done by allowing such secrets to only be created

    by an HSM of the domain (that immediately encrypts the new secret under a domain

    key), and to be re-encrypted from one domain key to another domain key of the same

    domain. For example, in AWS KMS, customer master keys are treated in this way, and

    hosts are also responsible for issuing the commands that manage the creation and

    usage of such keys.

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    Domain States, Tokens and Key Usage. A domain state logically

    consists of two parts: 1) a domain trust describing the administrative

    state of the domain—its entities and rules of operation—and 2) the

    actual domain keys. The trust components include a unique name

    of the domain, the set of entities of each type treated as genuine for

    the domain and the agreement keys for each HSM in the domain.

    The trust also includes a set of quorum rules defining what sets

    of operators (quorums) are considered trustworthy. Domain state

    modifications must be authorized by one of these quorums. Since

    the trust state of a domain can evolve over time (as operators, HSMs,

    and hosts are added and removed from the domain), the trust also

    includes the cryptographic fingerprint (hash) of the previous trust

    from which it was derived (by means of a trust update). Domain

    keys are kept secret from all entities other than the HSMs of the

    domain, whereas the domain trust only has to be authenticated.

    The concrete trust representation is signed by an HSM of the trust.

    To provide the encryption functionality of a domain, its HSMs

    need access to the domain keys, which should not be exposed to

    other entities. To allow this, the domain state is concretely repre-

    sented by a domain token signed by an HSM of the trust, which

    includes an encryption of the domain keys. This representation

    authenticates the state and binds the encrypted data to the trust;

    domain keys are decryptable only by the HSMs of the trust.

    To allow encryptions between HSMs of a domain, each HSM

    has a long-term Diffie-Hellman agreement key pair. It certifies its

    (public) agreement key as its own by signing it with its identity

    key. To encrypt the domain keys for the other HSMs in a domain,

    an HSM first encrypts them under an ephemeral symmetric key.

    It then generates an ephemeral Diffie-Hellman key pair, uses DH

    agreement with this key pair and each of the agreement keys of

    the domain HSMs to compute a shared secret with each HSM,

    uses a key derivation function (KDF) on each shared secret to pro-

    duce a set of symmetric keys, each of which is used to encrypt the

    ephemeral symmetric key. The result is a multi-recipient encryp-

    tion of the domain keys to all the other HSMs in the domain based

    on DHIES [1]. This scheme has performance advantages: cipher-

    texts to all the HSMs in the domain take less bandwidth and can

    be batch-generated faster. The final domain token includes all of

    these encryptions, the public ephemeral Diffie-Hellman key, and

    the domain trust, all signed by the HSM creating the token. When

    an HSM receives a command (other than to create a new domain),

    it also gets a domain token on which to operate 8 (see Figure 2); it

    decrypts the domain token, and uses it to process the request.

    Domain State Transitions. The security of a domain depends criti-

    cally on all of the HSMs of a domain being genuine. For example, if

    an adversary could somehow introduce an identity into a domain

    for which he holds the private signing key, he could use this identity

    to sign an agreement key for which he holds the private key, have

    another member update the domain, and use his fake agreement

    key to decrypt the new domain token, breaking security. How-

    ever, the HSMs performing the domain update operations (adding

    and removing entities) do not carry with them a state that allows

    them to recognize the identity keys of genuine entities. Domain

    8 In AWS KMS, these domain states are typically cached within the HSMs, rather

    than being explicitly provided as part of a command. This provides slightly stronger

    security guarantees, e.g. wrt state rollback.

    updates where HSMs modify trusts therefore rely on authorizations

    (attestations) of identity keys produced by operators, as follows.

    An HSMwill sign a new trust with any set of entities and quorum

    rules, if that trust is initial (i.e., has no predecessor fingerprint).9 To modify an existing trust to create a new trust, an HSM checks that 1)

    it is an HSM of the existing trust, and 2) every entity in the new trust

    is either in the old trust or is certified (for the domain) by a quorum

    of operators of the existing trust. If these checks are successful, it

    creates and signs a new trust with the updated information, with

    the fingerprint of the existing trust as predecessor of the new one.

    A host processing requests for a domain maintains in his state a

    trust for the domain; his commands can only be processed by HSMs

    in the trust. 10

    As the trust of a domain evolves, hosts update their

    version of the trust. A host of a domain is initially given the initial

    trust of the domain. A host updates to a new trust only if 1) the

    predecessor fingerprint of new trust is the fingerprint of its current

    trust, and 2) the new trust is signed by an HSM of its current trust.

    Invariant: an honest trust stays honest. A trust is honest if and only

    if its HSMs, hosts, and operators are all genuine, every quorum

    of operators (as defined by its quorum rules) contains an honest

    operator, and its predecessor trust (if any) is honest. A crucial

    property of the DMP is that, if a domain is initially created with

    an honest trust, then the domain will remain honest as updates

    are performed by HSMs. Note that this guarantee is enforced even

    though the HSM performing the updates keeps no state other than

    its own signing and agreement keys: 11

    such an HSM has no way

    of distinguishing genuine operators from non-genuine ones, and it

    depends on attestation by operators to identify genuine HSMs.

    Intuitively, the trust honesty property is preserved by the fol-

    lowing inductive reasoning, which we formalize in our machine-

    checked proof. The base case is trivial. In the inductive step, an HSM

    is asked to update an honest existing trust to a new trust, and it

    performs checks (1-2) described above. By the quorum requirement

    on honest trusts, any entity certified by a quorum in the existing

    trust is guaranteed to be genuine. By check 2) above, the HSM will

    therefore guarantee that all entities in the new trust are genuine. To

    show that honesty is preserved it remains to prove that the quorum

    requirement is satisfied by the new trust. This is guaranteed by

    the global assumption on the security parameter n: since we just proved all operators in the new trust must be genuine, it must be

    the case that any subset of operators of size at least n contains at

    least one honest operator. Thus, if the current trust is honest, the

    successor trust (once signed by an HSM of the predecessor trust) is

    also honest. By the observation of the last paragraph, the actions

    of a host guarantee that if the host starts out with an honest trust,

    the host trust will remain honest.

    Allowing Dishonest Domains. The DMP presented here allows dis-

    honest domains to share entities with honest domains. In AWS

    KMS, this is prevented by having HSMs cache domain states, and

    9 This corresponds to a domain creation request in AWS KMS.

    10 Commands are in fact issued by first obtaining an ephemeral symmetric key token

    generated by an HSM of the trust, with the plaintext key decryptable only using

    either a domain key or by the host requesting the token. We do not describe this

    communication mechanism in this paper.

    11 Again, AWS KMS caches domain tokens, rather than them being explicitly provided

    for updates; the DMP proof shows that this caching is not needed for the current

    security proof. Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom 67

    type HId. (∗ Identities of HSMs ∗) type OpId. (∗ Identities of Operators ∗) type HstId. (∗ Identities of Hosts ∗) type DomId. (∗ Identities of Domains ∗)

    (∗ Trust data (genuine HSMs) and metadata ∗) type Fpr. typeQuorum = OpId fset ∗ int. typeMetadata =Quorum ∗ Fpr option ∗ HstId fset ∗ DomId. type Trust = (HId fset) ∗Metadata.

    (∗ Domain keys in plaintext and encrypted form ∗) type Keys = (Handle,Key) fmap. type EKeys = MCTxt.

    (∗ Unwrapped domain token ∗) type TkData = { td_inst: bool; td_trust: Trust; td_skeys: Keys;


    (∗Wrapped domain token and trust ∗) type TkWrapped = { tkw_ekeys: EKeys; tkw_signer: HId; tkw_sig: signature; }. type Token = { tk_inst: bool; tk_trust: Trust; tk_wdata: TkWrapped; }.

    Figure 3: EasyCrypt Definitions for Domain Tokens

    using additional commands by which an HSM attests to its current

    domains. This allows operators to check that an HSM is loaded

    up with honest domain tokens, and so will never process requests

    using dishonest domain tokens. The current proof shows that lock-

    ing down the HSMs in this way is not needed to achieve domain

    security. Note that the current proof nevertheless still applies to

    the security of AWS KMS, since the latter’s stricter rules simply

    restrict adversarial action.

    3.2 Formalization in EasyCrypt

    Background on EasyCrypt. EasyCrypt is an interactive proof assis-

    tant for verifying the security of cryptographic constructions in the

    computational model. EasyCrypt adopts the code-based approach,

    in which primitives, security goals and hardness assumptions are

    expressed as probabilistic programs. EasyCrypt uses formal tools

    from program verification and programming languages to justify

    cryptographic reasoning, providing several program logics. We now

    describe the formalization of the DMP in EasyCrypt. 12

    Trusts and Domain Tokens. Figure 3 shows the EasyCrypt declara- tions for domain tokens. The HId type is a pair holding the signing

    key of the HSM and its public agreement key. The OpId type is simply

    the signing key for the human operator. Type TkWrapped corresponds

    to signed data structures, which we reuse both for signed trusts and

    signed domain tokens. Technically, this simplifies the writing of

    invariants, as we only need to deal with one encoding function into

    the domain of signature schemes. We then syntactically distinguish

    (using bit tk_inst) installable signed trusts—only these can be installed

    in hosts—from signed domain tokens that also carry domain keys.

    Wrapping and Unwrapping. Figure 4 shows how we formalize in

    EasyCrypt the operations carried out by HSMs to wrap (i.e., creat-

    ing a data structure that is digitally signed and contains encrypted

    domain keys) and unwrap (verifying authenticity and recover clear-

    text domain keys) domain tokens. Operator checkToken performs con-

    sistency checks on tokens and performs signature verification; in

    particular, it also checks that the encrypted keys cph are encrypted

    12 Notation: In EasyCrypt tup.1 denotes the first element of a tuple; notation is over-

    loaded for fields in records, as in rec.field.

    op proj_pks (hids: HId fset) : MPk = image snd hids.

    (∗ Operator used for both unwrap and trust updates ∗) op checkToken(inst : Installable, old new : Trust, tkw : TkWrapped)


    let (cphs, sid, sig) = (tkw.tkw_ekeys, tkw.tkw_signer, tkw.tkw_sig) in let msg = encode_msg (new,cphs,sid,inst) in verify(sid.1, msg, sig) ∧ proj_pks (tr_mems old) = fdom cphs ∧ sid ∈ tr_mems old.

    proc wrap(hid : HId,td : TkData) : Token = { (inst, trust, keys)← (td.td_inst, td.td_trust, td.td_skeys); mem← tr_mems trust; tag← encode_tag trust; ptxt← encode_ptxt keys; ekeys←$ mencrypt (proj_pks mem) tag ptxt; msg← encode_msg (trust, ekeys, hid, inst); sig← SigSch.sign(hid.1, msg); tkw← { tkw_ekeys = ekeys; tkw_signer = hid; tkw_sig = sig }; return { tk_inst = inst; tk_trust = trust; tk_wdata = tkw; };


    proc unwrap(hid : HId, tk : Token) : TkData option = { rtd← None; (inst, trust, data)← (tk.tk_inst, tk.tk_trust, tk.tk_wdata); (∗ Signer must be in trust: so we call check with trust as old ∗) if (checkToken inst trust tk.tk_wdata ∧

    hid ∈ tr_mems trust ∧ hid_in hid benc_keys) { (ekey, dkey)← benc_keys[hid.1]; (tag, cphs)← (encode_tag trust, data.tkw_ekeys); cph← cphs[ekey]; optxt← decrypt dkey tag cph; if (optxt,None) skeys← decode_ptxt optxt; rtd← Some { td_inst = inst; td_trust = trust; td_skeys = skeys; };

    } return rtd;


    Figure 4: HSM Operations for Domain Token (un)wrapping.

    to all HSM members of the trust (proj_pks(tr_mems old)=fdom cphs), and that

    the signer is a member of the trust (sid ∈ tr_mems old).13

    Encryption is formalized as tag-based multi-recipient public-

    key encryption [8, 22]. Intuitively, this is a variant of public-key

    encryption where one can provide multiple agreement keys to

    the encryption algorithm, so that the resulting ciphertext can be

    decrypted independently by multiple recipients using only their

    individual private agreement keys. Encryption therefore takes a set

    of public keys (type MPk), and we model ciphertexts as a map from

    public keys to sub-ciphertexts that contain only the parts of the full

    ciphertext that each recipient needs to decrypt. This abstraction

    permits capturing the specific flavor of public-key encryption used

    in the DMP: the multi-recipient syntax permits modeling schemes

    that minimize bandwidth and encryption time via the reuse of

    randomness across multiple ciphertexts. The construction is tag-

    based, because it binds the ciphertext to the meta-data of the token

    (parameter tag) thereby preventing an adversary from porting such

    a ciphertext from a domain token associated to an honest trust

    to a domain token that is under its control. We describe how we

    formalized the proof of security for the encryption scheme used

    in AWS KMS in Section 5, and how we showed that the security

    model it satisfies is sufficient for the purposes of the DMP.

    Trust management operations. Figure 5 shows the modeling of host

    operations. This consists of checking a signed trust (token) for

    consistency and its relation to its predecessor. The latter means

    checking that the signer is in the predecessor trust, and that the

    13 When this operator is used in unwrap we have old=trust. The same operator is used

    for checking updates by both hosts and HSMs; in that case, the signer must be an HSM

    of the predecessor trust as well.

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    op tr_initial(trust : Trust) = tfpr trust = None. op checkTrustProgress(old new : Trust) = old = tfpr new.

    proc installUpdatedTrust(hstid : HstId, tk : Token) : bool = { b← false; if (hstid ∈ HstPolSrv.hosts_tr) { old← hosts_tr[hstid]; (∗ Signer must be in old trust and trust must be installable ∗) b← tk.tk_inst ∧ checkToken tk.tk_inst old tk.tk_trust tk.tk_wdata ∧

    hstid ∈ hosts_tr ∧ ¬tr_initial (tr_data tk.tk_trust) ∧ checkTrustProgress hosts_tr[hstid] tk.tk_trust;

    if (b) hosts_tr[hstid]← tk.tk_trust; } return b; }

    Figure 5: Host Trust Update Operation

    op checkTrustUpdate(old : Trust, new : Trust, auth : Authorizations) : bool = (∗ Check threshold n preserved ∗) tthr old = tthr new ∧ (∗ Signers are a quorum ∗) fdom auth \subset tops old ∧ (∗ Signers are a quorum of correct size ∗) (tthr old) ≤ card (fdom auth) ∧ (∗ Check hash consistency ∗) tfpr new = hash old ∧ (∗ Check all new members signed ∗) let newmems = tmems new \ tmems old in let newops = tops new \ tops old in (∗ Verify all signatures ∗) let msg = encode (newmems,newops) in all (fun o⇒ o ∈ auth ∧ verify (o, msg, oget auth[o])) (fdom auth).

    Figure 6: HSM Trust Update Validation

    predecessor fingerprint contained in the new trust is the finger-

    print of the predecessor trust (so the new trust can also not be an

    initial/root trust, and must actually have a fingerprint). Note that,

    for each host, we keep track of which trust is installed using a map


    Finally, Figure 6 shows the behavior of an HSM when checking a

    request for a trust update after successful unwrapping of the domain

    token containing the old trust. This ensures that an HSM member

    of the old trust has signed it. The update request is formalized by

    providing the new trust and a set of authorizations, which are just

    signatures by operators on the members of the new trust, who are

    not in the old trust. The check enforces that the minimum quorum

    size (tthr old) is preserved, and that a quorum of at least this size of

    operators in the old trust have signed the request. This is computed

    by a fold over the list of operators auth that signed the request.

    4 REAL-VS-IDEAL SECURITY FOR KMS DMP In this section we describe and justify the security definition we

    adopted for the DMP, corresponding to the AEAD-service layer

    as shown in Figure 1. We begin by defining a general syntax for

    (possibly distributed) cryptographic keymanagement APIs, inspired

    by the work of Shrimpton, Stam andWarinschi [23]. This formalism

    abstracts away all the details of the protocol that are not directly

    related to key operations, and we believe it to be of independent

    interest to analyse the security of other key management APIs.

    This allows us to reason about different security models using

    simpler definitions, and later refine the results for the concrete

    case of the DMP. With this refinement in mind, we clarify how

    the introduced abstract notions map to DMP features in various

    remarks throughout the text.

    type KMS_Oracles = { proc newOp(badOp : bool) : OpId option ∗ OpSk option proc requestAuthorization(request : Request, opid : OpId)

    : Authorization option proc newHst() : HstId proc installInitialTrust(hstid : HstId, tk : Token) : bool proc installUpdatedTrust(hstid : HstId, tk : Token) : bool proc newHSM() : HId proc newToken(hid : HId, new : Trust) : Token option proc updateTokenTrust(hid : HId, new_trust : Trust, auth : Authorizations,

    tk : Token) : Token option proc addTokenKey(hid : HId, hdl : Handle, tk : Token) : Token option · · · }.

    Figure 7: KMS TkManage and TkNewKey Operations

    4.1 Key Management APIs Key management APIs store keys in tokens. In the real world, a

    token can be implemented by using trusted hardware (e.g., an HSM

    or a SIM card) to store and perform computations with the keys,

    in which case keys may never leave the trusted boundaries of the

    hardware device. In other settings, for example in the cases where

    the underlying hardware cannot store the key material in its inter-

    nal state, tokens are implemented as cryptographically hardened

    data structures, which guarantee that only trusted devices can (tem-

    porarily) access the key material. Our formalization abstracts these

    details and applies to both cases.

    A token tk is a data structure mapping handles (key identifiers)

    to keys key, together with some meta-data that is used by the API

    for management operations. The basic operations on tokens are:

    • TkManage(tk, cmd): a generic interface that captures all man-

    agement operations that can be carried out on tokens, including

    creating a new empty token, changing meta-data, and all other

    operations that do not affect the keys stored in the token. 14


    input a token tk and a command description, it returns a (possibly

    updated) token.

    • TkNewKey(tk, hdl, cmd): samples a new key from the appro-

    priate distribution and adds it to the token under the relation

    hdl→ key and following the API-specific instructions described

    in cmd. The success of this operation may depend on the consis-

    tency of the input token itself and on the command cmd, e.g. the command might violate a check on permissions for generating

    keys in a particular token. 15

    • TkReveal(tk, hdl, cmd): exposes the key associatedwith hdlwithin tk, following the API-specific instructions described in cmd. As before, the success of this operation may depend on the command

    details cmd. The TkReveal operation is a modeling artifact. It is used to make

    explicit that any cryptographic API will contain as part of its in-

    ternal mechanisms a procedure to recover keys contained within

    tokens, so that they can be used to provide cryptographic services.

    This serves two purposes: i. to define what correctness of an API

    means, and ii. to obtain keys managed by the API in the security

    games that define API security—in some cases these keys are simply

    given to the adversary in order to model security breaches and, in

    other cases, they are used to construct challenges for the adversary.

    Relation to the DMP.We show in Figure 7 the EasyCrypt declarations

    matching the notions of TkNewKey (addTokenKey) and TkManage (the 14 I.e., these commands may change the state of the API and even the meta-data

    associated with keys, but the handle-to-key map will not change.

    15 We do not model key deletion operations; including them in the model does not

    affect the proof rationale, but it adds complexity to invariants.

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    remaining proc declarations) for the DMP. addTokenKey simply takes

    the identity of the HSM that shall carry out the operation of adding

    a key to the token.

    In token management (TkManage), we include procedures to create new genuine operators (the model allows both honest and

    dishonest ones, in which case the adversary gets the signing key)

    and genuine hosts and HSMs. The requestAuthorization procedure models

    the actions of honest operators signing attestation requests for

    genuine entity identities, in which case this management operation

    is really not operating on tokens, but only on the global state of the

    API. The body of this procedure just checks that all entities in the

    request are indeed genuine and signs the request with the key for

    honest operator OpId.

    Two procedures model the operations on hosts: installing an

    initial trust in host hstid, and updating the installed trust. In the first

    case, the body of the procedure ensures that the installed trust is

    honest and initial. This captures the global assumption that we

    are focusing our analysis on hosts that were initially configured

    with honest trusts (there is nothing one can guarantee otherwise).

    In the latter case, the procedure executes the operations for hosts

    shown in Figure 5. Finally, the newToken and updateTokenTrust procedures

    model the actions of HSMs when they are called upon to create

    empty tokens, or to update a trust based on authorizations issued

    by operators.

    Crucially our model enforces that, as in the DMP, the states of

    genuine HSMs, operators and hosts are totally disjoint, and that the

    only communication between the different entities in the model

    must be explicitly performed using calls to this API.

    It remains to explain the semantics of the TkReveal operation within AWS KMS. Recall that the purpose of the operation in the

    syntax of key management APIs is to allow defining security exper-

    iments that explicitly have access to API-protected keys in order

    to express the goal of an adversary (e.g., to formalize that a key

    is indistinguishable from random, the experiment needs to have

    access to the key in order to construct a real-or-random oracle). In

    our model of the DMP, TkReveal is simply the operation that asks

    a genuine HSM to unwrap a domain token and return the key for a

    particular handle 16 .

    Correctness. A natural requirement for key management APIs is

    that, subject to an API-specific set of restrictions over calls, they

    reliably store secret keys. To define correctness we introduce a pred-

    icate valid over traces of calls to TkManage and TkNewKey, which for a given token-handle-command input (tk, hdl, cmd) indicates whether a reveal operation should successfully return a key. In the

    AWS KMS model, valid simply requires that the command is placed

    on a genuine HSM, and the trust of the domain token is installed in

    a genuine host. Correctness requires that, if the HSM validates the

    domain token and a key with to hdl is stored within, then TkReveal must successfully recover it.

    4.2 Defining Security of Encryption Services Cryptographic key management APIs such as the DMP are used to

    build cryptographic services. In this section we follow the approach

    adopted in Universal Composability to formalizing this notion, by

    16 TkReveal is of course not an actual operation of the DMP; it is only used as part of

    the proof.

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    TkManage(tk, cmd) AAACFHicbZBNS8NAEIY39avWr6hHL4tFqCglEUGPRS9ehAr9gjaUzWbTLtlswu5GKCE/wot/xYsHRbx68Oa/cZumoNWBgYd3ZpiZ140ZlcqyvozS0vLK6lp5vbKxubW9Y+7udWSUCEzaOGKR6LlIEkY5aSuqGOnFgqDQZaTrBtfTeveeCEkj3lKTmDghGnHqU4yUlobmySBEaiz9tBXcIo5GJKvNFRVkp3PGoZcdD82qVbfygH/BLqAKimgOzc+BF+EkJFxhhqTs21asnBQJRTEjWWWQSBIjHOi1fY0chUQ6af5UBo+04kE/Ejq5grn6cyJFoZST0NWd+ZGLtan4X62fKP/SSSmPE0U4ni3yEwZVBKcOQY8KghWbaEBYUH0rxGMkEFbax4o2wV58+S90zuq25rvzauOqsKMMDsAhqAEbXIAGuAFN0AYYPIAn8AJejUfj2Xgz3metJaOY2Qe/wvj4Bhnan3Y=AAACFHicbZBNS8NAEIY39avWr6hHL4tFqCglEUGPRS9ehAr9gjaUzWbTLtlswu5GKCE/wot/xYsHRbx68Oa/cZumoNWBgYd3ZpiZ140ZlcqyvozS0vLK6lp5vbKxubW9Y+7udWSUCEzaOGKR6LlIEkY5aSuqGOnFgqDQZaTrBtfTeveeCEkj3lKTmDghGnHqU4yUlobmySBEaiz9tBXcIo5GJKvNFRVkp3PGoZcdD82qVbfygH/BLqAKimgOzc+BF+EkJFxhhqTs21asnBQJRTEjWWWQSBIjHOi1fY0chUQ6af5UBo+04kE/Ejq5grn6cyJFoZST0NWd+ZGLtan4X62fKP/SSSmPE0U4ni3yEwZVBKcOQY8KghWbaEBYUH0rxGMkEFbax4o2wV58+S90zuq25rvzauOqsKMMDsAhqAEbXIAGuAFN0AYYPIAn8AJejUfj2Xgz3metJaOY2Qe/wvj4Bhnan3Y=AAACFHicbZBNS8NAEIY39avWr6hHL4tFqCglEUGPRS9ehAr9gjaUzWbTLtlswu5GKCE/wot/xYsHRbx68Oa/cZumoNWBgYd3ZpiZ140ZlcqyvozS0vLK6lp5vbKxubW9Y+7udWSUCEzaOGKR6LlIEkY5aSuqGOnFgqDQZaTrBtfTeveeCEkj3lKTmDghGnHqU4yUlobmySBEaiz9tBXcIo5GJKvNFRVkp3PGoZcdD82qVbfygH/BLqAKimgOzc+BF+EkJFxhhqTs21asnBQJRTEjWWWQSBIjHOi1fY0chUQ6af5UBo+04kE/Ejq5grn6cyJFoZST0NWd+ZGLtan4X62fKP/SSSmPE0U4ni3yEwZVBKcOQY8KghWbaEBYUH0rxGMkEFbax4o2wV58+S90zuq25rvzauOqsKMMDsAhqAEbXIAGuAFN0AYYPIAn8AJejUfj2Xgz3metJaOY2Qe/wvj4Bhnan3Y=AAACFHicbZBNS8NAEIY39avWr6hHL4tFqCglEUGPRS9ehAr9gjaUzWbTLtlswu5GKCE/wot/xYsHRbx68Oa/cZumoNWBgYd3ZpiZ140ZlcqyvozS0vLK6lp5vbKxubW9Y+7udWSUCEzaOGKR6LlIEkY5aSuqGOnFgqDQZaTrBtfTeveeCEkj3lKTmDghGnHqU4yUlobmySBEaiz9tBXcIo5GJKvNFRVkp3PGoZcdD82qVbfygH/BLqAKimgOzc+BF+EkJFxhhqTs21asnBQJRTEjWWWQSBIjHOi1fY0chUQ6af5UBo+04kE/Ejq5grn6cyJFoZST0NWd+ZGLtan4X62fKP/SSSmPE0U4ni3yEwZVBKcOQY8KghWbaEBYUH0rxGMkEFbax4o2wV58+S90zuq25rvzauOqsKMMDsAhqAEbXIAGuAFN0AYYPIAn8AJejUfj2Xgz3metJaOY2Qe/wvj4Bhnan3Y=

    New(hdl) AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUlE0GXRjSupYB/QhjKZ3LRDJw9mJkoJATf+ihsXirj1J9z5N07TCNp6YODMOfdy7z1uzJlUlvVlLCwuLa+sltbK6xubW9vmzm5LRomg0KQRj0THJRI4C6GpmOLQiQWQwOXQdkeXE799B0KyKLxV4xicgAxC5jNKlJb65n4vIGoo/fQa7rPqz2fo8ey4b1asmpUDzxO7IBVUoNE3P3teRJMAQkU5kbJrW7FyUiIUoxyyci+REBM6IgPoahqSAKST5jdk+EgrHvYjoV+ocK7+7khJIOU4cHVlvuSsNxH/87qJ8s+dlIVxoiCk00F+wrGK8CQQ7DEBVPGxJoQKpnfFdEgEoUrHVtYh2LMnz5PWSc3W/Oa0Ur8o4iihA3SIqshGZ6iOrlADNRFFD+gJvaBX49F4Nt6M92npglH07KE/MD6+AYVTmBA=AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUlE0GXRjSupYB/QhjKZ3LRDJw9mJkoJATf+ihsXirj1J9z5N07TCNp6YODMOfdy7z1uzJlUlvVlLCwuLa+sltbK6xubW9vmzm5LRomg0KQRj0THJRI4C6GpmOLQiQWQwOXQdkeXE799B0KyKLxV4xicgAxC5jNKlJb65n4vIGoo/fQa7rPqz2fo8ey4b1asmpUDzxO7IBVUoNE3P3teRJMAQkU5kbJrW7FyUiIUoxyyci+REBM6IgPoahqSAKST5jdk+EgrHvYjoV+ocK7+7khJIOU4cHVlvuSsNxH/87qJ8s+dlIVxoiCk00F+wrGK8CQQ7DEBVPGxJoQKpnfFdEgEoUrHVtYh2LMnz5PWSc3W/Oa0Ur8o4iihA3SIqshGZ6iOrlADNRFFD+gJvaBX49F4Nt6M92npglH07KE/MD6+AYVTmBA=AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUlE0GXRjSupYB/QhjKZ3LRDJw9mJkoJATf+ihsXirj1J9z5N07TCNp6YODMOfdy7z1uzJlUlvVlLCwuLa+sltbK6xubW9vmzm5LRomg0KQRj0THJRI4C6GpmOLQiQWQwOXQdkeXE799B0KyKLxV4xicgAxC5jNKlJb65n4vIGoo/fQa7rPqz2fo8ey4b1asmpUDzxO7IBVUoNE3P3teRJMAQkU5kbJrW7FyUiIUoxyyci+REBM6IgPoahqSAKST5jdk+EgrHvYjoV+ocK7+7khJIOU4cHVlvuSsNxH/87qJ8s+dlIVxoiCk00F+wrGK8CQQ7DEBVPGxJoQKpnfFdEgEoUrHVtYh2LMnz5PWSc3W/Oa0Ur8o4iihA3SIqshGZ6iOrlADNRFFD+gJvaBX49F4Nt6M92npglH07KE/MD6+AYVTmBA=AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUlE0GXRjSupYB/QhjKZ3LRDJw9mJkoJATf+ihsXirj1J9z5N07TCNp6YODMOfdy7z1uzJlUlvVlLCwuLa+sltbK6xubW9vmzm5LRomg0KQRj0THJRI4C6GpmOLQiQWQwOXQdkeXE799B0KyKLxV4xicgAxC5jNKlJb65n4vIGoo/fQa7rPqz2fo8ey4b1asmpUDzxO7IBVUoNE3P3teRJMAQkU5kbJrW7FyUiIUoxyyci+REBM6IgPoahqSAKST5jdk+EgrHvYjoV+ocK7+7khJIOU4cHVlvuSsNxH/87qJ8s+dlIVxoiCk00F+wrGK8CQQ7DEBVPGxJoQKpnfFdEgEoUrHVtYh2LMnz5PWSc3W/Oa0Ur8o4iihA3SIqshGZ6iOrlADNRFFD+gJvaBX49F4Nt6M92npglH07KE/MD6+AYVTmBA=

    F AAAB8nicbVDLSsNAFL2pr1pfVZdugkVwVRIRdFkUxGUF+4A2lMl00g6dzISZG6GEfoYbF4q49Wvc+TdO2iy09cDA4Zx7mXNPmAhu0PO+ndLa+sbmVnm7srO7t39QPTxqG5VqylpUCaW7ITFMcMlayFGwbqIZiUPBOuHkNvc7T0wbruQjThMWxGQkecQpQSv1+jHBMSUiu5sNqjWv7s3hrhK/IDUo0BxUv/pDRdOYSaSCGNPzvQSDjGjkVLBZpZ8alhA6ISPWs1SSmJkgm0eeuWdWGbqR0vZJdOfq742MxMZM49BO5hHNspeL/3m9FKPrIOMySZFJuvgoSoWLys3vd4dcM4piagmhmtusLh0TTSjaliq2BH/55FXSvqj7lj9c1ho3RR1lOIFTOAcfrqAB99CEFlBQ8Ayv8Oag8+K8Ox+L0ZJT7BzDHzifP3fpkVw=AAAB8nicbVDLSsNAFL2pr1pfVZdugkVwVRIRdFkUxGUF+4A2lMl00g6dzISZG6GEfoYbF4q49Wvc+TdO2iy09cDA4Zx7mXNPmAhu0PO+ndLa+sbmVnm7srO7t39QPTxqG5VqylpUCaW7ITFMcMlayFGwbqIZiUPBOuHkNvc7T0wbruQjThMWxGQkecQpQSv1+jHBMSUiu5sNqjWv7s3hrhK/IDUo0BxUv/pDRdOYSaSCGNPzvQSDjGjkVLBZpZ8alhA6ISPWs1SSmJkgm0eeuWdWGbqR0vZJdOfq742MxMZM49BO5hHNspeL/3m9FKPrIOMySZFJuvgoSoWLys3vd4dcM4piagmhmtusLh0TTSjaliq2BH/55FXSvqj7lj9c1ho3RR1lOIFTOAcfrqAB99CEFlBQ8Ayv8Oag8+K8Ox+L0ZJT7BzDHzifP3fpkVw=AAAB8nicbVDLSsNAFL2pr1pfVZdugkVwVRIRdFkUxGUF+4A2lMl00g6dzISZG6GEfoYbF4q49Wvc+TdO2iy09cDA4Zx7mXNPmAhu0PO+ndLa+sbmVnm7srO7t39QPTxqG5VqylpUCaW7ITFMcMlayFGwbqIZiUPBOuHkNvc7T0wbruQjThMWxGQkecQpQSv1+jHBMSUiu5sNqjWv7s3hrhK/IDUo0BxUv/pDRdOYSaSCGNPzvQSDjGjkVLBZpZ8alhA6ISPWs1SSmJkgm0eeuWdWGbqR0vZJdOfq742MxMZM49BO5hHNspeL/3m9FKPrIOMySZFJuvgoSoWLys3vd4dcM4piagmhmtusLh0TTSjaliq2BH/55FXSvqj7lj9c1ho3RR1lOIFTOAcfrqAB99CEFlBQ8Ayv8Oag8+K8Ox+L0ZJT7BzDHzifP3fpkVw=AAAB8nicbVDLSsNAFL2pr1pfVZdugkVwVRIRdFkUxGUF+4A2lMl00g6dzISZG6GEfoYbF4q49Wvc+TdO2iy09cDA4Zx7mXNPmAhu0PO+ndLa+sbmVnm7srO7t39QPTxqG5VqylpUCaW7ITFMcMlayFGwbqIZiUPBOuHkNvc7T0wbruQjThMWxGQkecQpQSv1+jHBMSUiu5sNqjWv7s3hrhK/IDUo0BxUv/pDRdOYSaSCGNPzvQSDjGjkVLBZpZ8alhA6ISPWs1SSmJkgm0eeuWdWGbqR0vZJdOfq742MxMZM49BO5hHNspeL/3m9FKPrIOMySZFJuvgoSoWLys3vd4dcM4piagmhmtusLh0TTSjaliq2BH/55FXSvqj7lj9c1ho3RR1lOIFTOAcfrqAB99CEFlBQ8Ayv8Oag8+K8Ox+L0ZJT7BzDHzifP3fpkVw=

    TkNewKey(tk, hdl, cmd) AAACIXicbZBLS8NAEMc39VXrK+rRS7AIFaQkIthj0YsgSIW+oC1ls5m0SzcPdjdKCPkqXvwqXjwo0pv4ZdymLWrrwMJv/zPDzPztkFEhTfNTy62srq1v5DcLW9s7u3v6/kFTBBEn0CABC3jbxgIY9aEhqWTQDjlgz2bQskfXk3zrAbiggV+XcQg9Dw986lKCpZL6eqXrYTkUblIf3cHjLcRpaa7IUXo256HDfj7Ec9LTvl40y2YWxjJYMyiiWdT6+rjrBCTywJeEYSE6lhnKXoK5pIRBWuhGAkJMRngAHYU+9kD0kuzC1DhRimO4AVfPl0am/u5IsCdE7NmqMltyMTcR/8t1IulWegn1w0iCT6aD3IgZMjAmdhkO5UAkixVgwqna1SBDzDGRytSCMsFaPHkZmudlS/H9RbF6NbMjj47QMSohC12iKrpBNdRABD2hF/SG3rVn7VX



    CorruptR(tk, hdl, cmd) AAACIXicbZBLS8NAEMc39VXrK+rRS7AIFaQkIthjsRePVewD2lA2m027dPNgdyKUkK/ixa/ixYMivYlfxm2aorYOLPz2PzPMzN+JOJNgmp9aYW19Y3OruF3a2d3bP9APj9oyjAWhLRLyUHQdLClnAW0BA067kaDYdzjtOOPGLN95pEKyMHiASURtHw8D5jGCQUkDvdb3MYyklzRCIeII7tPKQoFxerHgkct/PsR30/OBXjarZhbGKlg5lFEezYE+7bshiX0aAOFYyp5lRmAnWAAjnKalfixphMkYD2lPYYB9Ku0kuzA1zpTiGl4o1AvAyNTfHQn2pZz4jqrMllzOzcT/cr0YvJqdsCCKgQZkPsiLuQGhMbPLcJmgBPhEASaCqV0NMsICE1CmlpQJ1vLJq9C+rFqK



    $\mathsf{Enc}(\mathsf{hdl},\mathsf{msg},\mathsf{ad}) $\mathsf{Dec}(\mathsf{hdl},\mathsf{cph},\mathsf{ad})

    Enc(hdl, msg, ad) 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

    Dec(hdl, cph, ad) AAACHHicbVDLSsNAFJ34rPUVdelmsAgVpCQq6LKoC5cV7APaUCaTSTN0MgkzE6GEfIgbf8WNC0XcuBD8G6dpitp6YOCcc+9l7j1uzKhUlvVlLCwuLa+sltbK6xubW9vmzm5LRonApIkjFomOiyRhlJOmooqRTiwICl1G2u7walxv3xMhacTv1CgmTogGnPoUI6WtvnnaC5EKpJ9eE5xVpyLwWHY8FTgOfgTysqO+WbFqVg44T+yCVECBRt/86HkRTkLCFWZIyq5txcpJkVAUM5KVe4kkMcJDNCBdTTkKiXTS/LgMHmrHg34k9OMK5u7viRSFUo5CV3fmO87WxuZ/tW6i/AsnpTxOFOF48pGfMKgiOE4KelQQrNhIE4QF1btCHCCBsNJ5lnUI9uzJ86R1UrOtmn17VqlfFnGUwD44AFVgg3NQBzegAZoAgwfwBF7Aq/FoPBtvxvukdcEoZvbAHxif36fbovI=AAACHHicbVDLSsNAFJ34rPUVdelmsAgVpCQq6LKoC5cV7APaUCaTSTN0MgkzE6GEfIgbf8WNC0XcuBD8G6dpitp6YOCcc+9l7j1uzKhUlvVlLCwuLa+sltbK6xubW9vmzm5LRonApIkjFomOiyRhlJOmooqRTiwICl1G2u7walxv3xMhacTv1CgmTogGnPoUI6WtvnnaC5EKpJ9eE5xVpyLwWHY8FTgOfgTysqO+WbFqVg44T+yCVECBRt/86HkRTkLCFWZIyq5txcpJkVAUM5KVe4kkMcJDNCBdTTkKiXTS/LgMHmrHg34k9OMK5u7viRSFUo5CV3fmO87WxuZ/tW6i/AsnpTxOFOF48pGfMKgiOE4KelQQrNhIE4QF1btCHCCBsNJ5lnUI9uzJ86R1UrOtmn17VqlfFnGUwD44AFVgg3NQBzegAZoAgwfwBF7Aq/FoPBtvxvukdcEoZvbAHxif36fbovI=AAACHHicbVDLSsNAFJ34rPUVdelmsAgVpCQq6LKoC5cV7APaUCaTSTN0MgkzE6GEfIgbf8WNC0XcuBD8G6dpitp6YOCcc+9l7j1uzKhUlvVlLCwuLa+sltbK6xubW9vmzm5LRonApIkjFomOiyRhlJOmooqRTiwICl1G2u7walxv3xMhacTv1CgmTogGnPoUI6WtvnnaC5EKpJ9eE5xVpyLwWHY8FTgOfgTysqO+WbFqVg44T+yCVECBRt/86HkRTkLCFWZIyq5txcpJkVAUM5KVe4kkMcJDNCBdTTkKiXTS/LgMHmrHg34k9OMK5u7viRSFUo5CV3fmO87WxuZ/tW6i/AsnpTxOFOF48pGfMKgiOE4KelQQrNhIE4QF1btCHCCBsNJ5lnUI9uzJ86R1UrOtmn17VqlfFnGUwD44AFVgg3NQBzegAZoAgwfwBF7Aq/FoPBtvxvukdcEoZvbAHxif36fbovI=AAACHHicbVDLSsNAFJ34rPUVdelmsAgVpCQq6LKoC5cV7APaUCaTSTN0MgkzE6GEfIgbf8WNC0XcuBD8G6dpitp6YOCcc+9l7j1uzKhUlvVlLCwuLa+sltbK6xubW9vmzm5LRonApIkjFomOiyRhlJOmooqRTiwICl1G2u7walxv3xMhacTv1CgmTogGnPoUI6WtvnnaC5EKpJ9eE5xVpyLwWHY8FTgOfgTysqO+WbFqVg44T+yCVECBRt/86HkRTkLCFWZIyq5txcpJkVAUM5KVe4kkMcJDNCBdTTkKiXTS/LgMHmrHg34k9OMK5u7viRSFUo5CV3fmO87WxuZ/tW6i/AsnpTxOFOF48pGfMKgiOE4KelQQrNhIE4QF1btCHCCBsNJ5lnUI9uzJ86R1UrOtmn17VqlfFnGUwD44AFVgg3NQBzegAZoAgwfwBF7Aq/FoPBtvxvukdcEoZvbAHxif36fbovI=

    Figure 8: Diagram of the UC-style ideal functionality.

    focusing on a service that provides authenticated encryption on

    client-chosen payloads, as described in Section 2.

    The central component in our definition of correctness and se-

    curity for such cryptographic service is an ideal functionality that

    describes how the service is expected to behave if it were provided

    as a monolithic self-contained block by a trusted-third-party. The

    ideal functionality provides both a functional specification of the

    service and a precise bound on the flow of information from the ser-

    vice to the (possibly adversarial) environment. We will define this

    functionality for the encryption service interface presented in Sec-

    tion 3.1, but the approach extends naturally to other cryptographic

    mechanisms providing confidentiality and authentication.

    Our ideal functionality has two interfaces: the external interface

    accessible to an arbitrary environment 𝒵 , and an adversarial inter-

    face that captures whatever influence a malicious insider adversary

    𝒜 is allowed with the underlying cryptographic API. The inter-

    face accessible to 𝒜 is the same in the real and ideal worlds. We

    show this pictorially in Figure 8. As expected, we let the adversary

    𝒜 and the environment 𝒵 communicate freely. The execution is

    controlled by 𝒵 , which may choose to interact with the outward

    facing encryption service interface or pass control to 𝒜. In other

    words, the goal of 𝒵 is to distinguish the real world encryption

    service from an ideal authenticated encryption functionality. 𝒜 is

    an insider colluding with the environment𝒵 , and helping it achieve

    this goal.

    Our ideal AEAD functionality follows the standard UC approach:

    for each key hdl, calls to Enc(hdl,msg, ad) return encryptions of

    a fixed constant, rather than msg; and Dec(hdl, cph, ad) returns the original msg if and only if cph was previously given to 𝒵 as the result of a call to Enc(hdl,msg, ad). However, we need to

    consider the underlying distributed protocol that manages access

    to encryption keys, and the possibility that the adversary disrupts

    its operation, e.g., by not allowing the API to complete a request.

    Therefore, before answering requests placed by environment 𝒵 ,

    we let adversary 𝒜 interact with the cryptographic API and lead it

    into a configuration of its choice.

    We now describe in more detail the real-world and ideal-world

    experiments of our security model. The functionality keeps track

    of a list of corrupted key handles and a list of key handles that

    have been used in encryption and decryption. 17

    In what follows,

    ℰ and 𝒟 represent the encryption and decryption operations of a

    standard AEAD scheme.

    17 These lists will always be disjoint, as we do not allow corrupted keys to be used for

    encryption operations. Fully removing this restriction would lead to a non-committing

    encryption level of security, not a goal for AWS KMS. However, in Appendix B we

    describe how our proof extends to a simple relaxation where corrupt keys can be used

    after corruption.

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom 70

    Real World. In the real world, the interface offered to environment

    𝒵 behaves as follows:

    • New(hdl) passes control to 𝒜, indicating that 𝒵 requested the

    generation of a new domain key under handle hdl. • Enc(hdl,msg, ad) passes control to𝒜, indicating that𝒵 requested

    the AEAD encryption of payload msg with associated data ad, under the secret key corresponding to handle hdl. Adversary 𝒜 is expected to eventually return a tuple (tk, cmd) and, if pred- icate valid(trace, tk, hdl, cmd) holds and the key with hdl has not been corrupted by 𝒜, the functionality computes sk ← TkReveal(tk, hdl, cmd) and cph← ℰ (sk,msg, ad), returning the

    result to 𝒵 . Otherwise, an error

    symbol is re


    • Dec(hdl, cph, ad) passes control to𝒜, indicating that𝒵 requested

    the decryption of ciphertext cph with associated data ad, under the key corresponding to handle hdl. Adversary𝒜 is expected to

    eventually return a tuple (tk, cmd) and, if valid(trace, tk, hdl, cmd) holds and the key with hdl has not been corrupted by 𝒜, the

    functionality computes sk← TkReveal(tk, hdl, cmd) andmsg← 𝒟(sk, cph, ad), returning the result to 𝒵 . Otherwise, an error

    symbol is returned.

    Note that, as in the previous section, our definition of security keeps

    track of calls placed by𝒜 to the TkManage and TkNewKey oracles

    and relies on the valid predicate to determine whether the service

    is required to produce a correct output to the environment 𝒵 . Ad-

    versary𝒜 may therefore prevent the service from answering client

    requests by simply not executing the required API calls. Indeed,

    valid will naturally exclude sequences of API calls where a secret

    key with handle hdl is used before it is created, either because 𝒵 did not request its creation, or because 𝒜 decided against carrying

    out this request. However, and crucially for our result, the valid predicate is totally oblivious of the honesty of trusts and tokens,

    so that any adversary that succeeds in leading the system into a

    dishonest configuration is not restricted in its actions: as shown

    below, it requires only that the selected host and HSM exist, and

    that the host is configured with the trust in the selected token.

    op valid (t : Trace, tk : Token, hdl : Hdl, c : Cmd) : bool = (∗ · · · ∗) with c = Creveal hstid hid⇒ let (hstmap,hids,tklist) = t in ((hid ∈ hids) && (hstmap[hstid] = Some tk.tk_trust)).

    Ideal World. In the ideal world, the interface offered to environment

    𝒵 behaves identically to what we presented for the real world, with

    the following exceptions. The ideal functionality keeps a tableT as-

    sociating handle-ciphertext-authenticated data tuples (hdl, cph, ad) to payload (msg) values, which is initially empty. When 𝒵 places

    a call to one of its oracles, the following occurs:

    • There is no change in oracle New(hdl). • Enc(hdl,msg, ad) passes control to𝒜, indicating that𝒵 requested

    the AEAD encryption of payload msg with associated data ad, under the secret key corresponding to handle hdl. Adversary 𝒜 is expected to eventually return a tuple (tk, cmd) and, if pred- icate valid(trace, tk, hdl, cmd) holds and the key with hdl has not been corrupted by 𝒜, the functionality first computes sk← TkReveal(tk, hdl, cmd) and cph ← ℰ (sk, 0 |msg | , ad). It then up-

    dates the table with (hdl, cph, ad) → msg and returns cph to 𝒵 .

    Otherwise, an error symbol is returned.

    • Dec(hdl, cph, ad) passes control to𝒜, indicating that𝒵 requested the decryption of ciphertext cph with associated data ad, under the key corresponding to handle hdl. Adversary𝒜 is expected to

    eventually return a tuple (tk, cmd) and, if valid(trace, tk, hdl, cmd) holds and the key with hdl has not been corrupted by 𝒜, then

    𝒵 receives T [(hdl, cph, ad)]. Otherwise, an error symbol is re-


    This ends the presentation of the interface offered to 𝒵 .

    Adversarial interface. The oracles available to𝒜 reflect precisely the

    capabilities of a malicious insider adversary with direct access to the

    cryptographic API. As a worst case scenario, we let this adversary

    control the scheduling of API management and key generation

    operations, which in particular means that such an adversary may

    decide not to allow the API to answer the environment’s requests.

    We follow common practice in cryptographic API security defini-

    tions and allow𝒜 to corrupt keys using a CorruptR oracle, through

    which it can explicitly learn any secret key with handle hdl, even if such a key would otherwise be hidden from its view, i.e. even if

    such a key is meant to be protected by the API. Importantly, this

    captures a common real-world issue where keys are (maliciously

    or inadvertently) leaked, and ensures that non-leaked keys remain

    secret under those circumstances. To prevent the adversary from

    trivially distinguishing the real world from the ideal world, we

    never allow 𝒜 to corrupt a key that is used by the environment 𝒵 for encryption/decryption operations.

    Security goal. We say a cryptographic service is secure if, for all

    (𝒵,𝒜), the views of 𝒵 in the real and ideal worlds are computa-

    tionally indistinguishable. This means that the real-world system is

    not allowed to leak more than the ideal-world functionality, which

    reveals nothing about client payloads to insider adversaries inter-

    acting with the API.

    5 MACHINE-CHECKED SECURITY PROOF We describe the machine-checked proof in EasyCrypt in three steps,

    corresponding to the three layers introduced in Section 2. We first

    describe the formalization of indistinguishability-based security,

    and show that this can be used as a convenient stepping stone in

    the analysis of the DMP, as it implies our real-vs-ideal world notion

    of security. This corresponds to the top layer in Figure 1. Then,

    we describe a set of low-level abstractions that we constructed in

    order to tame the complexity of the proof of indistinguishability-

    based security. We also discuss how we proved that the security

    guarantees that we modularly obtain from these abstractions follow

    from standard cryptographic assumptions, which allows us to state

    our main result in concrete terms. This corresponds to the lower-

    level layer in Figure 1. Finally we describe the core theorem that

    establishes the indistinguishability-based security of the DMP, and

    highlight the most interesting technical aspects of its proof. This

    corresponds to the intermediate layer shown in Figure 1.

    5.1 From key hiding to real-vs-ideal security The indistinguishability-based security of a cryptographic API [23]

    guarantees that cryptographic keys managed by the API remain

    hidden from the adversary. We adapt this notion to our formalism

    via a game where, in addition to interacting with the API to create

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    game Sec𝒜 (1λ ) :

    Tested← [ ];

    Corrupted← [ ];

    b $

    ←− {0, 1};

    b′ ← 𝒜𝒪 (1λ ); return b = b′;

    CorruptR(tk, hdl, cmd) : key←⊥; if hdl < Tested∧

    valid(tk, hdl, cmd) key← TkReveal(tk, hdl, cmd); Corrupted← hdl : Corrupted;

    return key;

    Test(tk, hdl, cmd) :

    key 1 ← 𝒦(1λ ); key0 ←⊥;

    if hdl < Corrupted ∧ valid(tk, hdl, cmd)

    key 0 ← TkReveal(tk, hdl, cmd);

    if hdl ∈ Tested key

    1 ← Tested[hdl];

    else Tested[hdl]← key 1 ;

    key← keyb ; return key;

    InsideR(tk, hdl, cmd) : key←⊥; if ¬(honest(tk, hdl, cmd)) key← TkReveal(tk, hdl, cmd);

    return key;

    𝒪 = {TkManage, TkNewKey, Test, InsideR, CorruptR}

    Figure 9: Indistinguishability-based security.

    and manage tokens, the adversary gets access to three oracles that

    capture the key hiding property. The Test oracle internally uses

    the TkReveal operator in order to model a real-or-random style

    challenge oracle on keys. The CorruptR and InsideR oracles use

    TkReveal to model explicit leakage of secret keys via corruption

    and execution traces recognized as dishonest by the security def-

    inition (note that such queries only strengthen the definition, as

    they state that domain keys will be protected even if one specific

    key is leaked by some external means). In particular, the CorruptR oracle allows the adversary to expose keys that it might otherwise

    be challenged on, and the InsideR oracle permits capturing CCA-

    style attacks. The game is shown in Figure 9. In this experiment,

    the adversary interacts with a set of oracles, which it can use to

    test valid, non-corrupt handles, receiving either the real key or a

    randomly generated one (depending on bit b). We require that no

    adversary can win this game other than with small probability over

    the random guess.

    The following theorem, formalized and proved in EasyCrypt, im-

    plies that any cryptographic API that satisfies indistinguishability-

    based security will give rise to an encryption service that achieves

    our notion of UC-style security, when used together with an AEAD

    scheme satisfying the standard notions of correctness and security.

    Theorem 5.1 (Informal). If a cryptographic API satisfies indis-

    tinguishability-based security, and (ℰ ,𝒟) satisfy the standard no-

    tions of AEAD security then, for all adversaries (𝒵,𝒜) the views of 𝒵 in the real world and ideal worlds are indistinguishable.

    The proof proceeds as follows. One first uses the indistinguisha-

    bility-based security of the API to show that Dec is effectively

    operating on a consistent secret key for each hdl, which are all

    hidden from the adversary. Note that consistency is implied by

    the indistinguishability definition, as the random branch b = 1

    enforces that the same key is always returned for the same handle.

    Consistency is essential to ensure that standard AEAD security

    suffices in the next step of the proof, as otherwise one would need

    robust-encryption-level guarantees to ensure that operations with

    different keys on the same ciphertext do not leak information or

    allow forgeries.

    The second step is to use AEAD correctness and unforgeability to

    switch to the table-like computation of Dec performed by the ideal

    functionality. Note that, when reducing to the security of the API,

    the validity predicate on traces enforced by the ideal functionality

    directly matches identical conditions in the oracles available in

    the indistinguishability-based definition. In particular, the corrupt

    oracles exactly match.

    In EasyCrypt, the theorem is stated as follows. Notice that the

    reduction is tight, even though the bound includes the advantage of

    correctness and indistinguishability-security twice. This is because

    the proof requires symmetric game hops that first replace API

    managed keys with random ones using the IND-property and, after

    using AEAD security, restore the correct keys in order to match

    the ideal functionality exactly.

    lemma IndImpliesUC:

    AdvZ ,A RI

    ≤ AdvB (Z ,A) API

    + AdvC (API,Z ,A) AEAD

    + AdvB1 (Z ,A) API

    . where

    AdvZ ,A RI =

    |Pr[Real(Z , A, API).main():res] − Pr[Ideal(Z , A, API).main():res]| AdvD

    API =

    |Pr[Ind(D, API).main(false):¬res] − Pr[Ind(D, API).main(true):res]| AdvD

    AEAD =

    |Pr[AEAD_LoRCondProb(D).game(false):¬res] − Pr[AEAD_LoRCondProb(D).game(true):res]|

    In the above statement, B, B1 and C are constructed adversaries.

    This theorem allows us to focus on the main result proven in Easy-

    Crypt in the rest of this section, namely that the KMS Domain

    Management API satisfies indistinguishability-based security.

    5.2 Low-level abstractions We now describe the lower layer in the EasyCrypt development,

    which defines and instantiates three reusable abstractions that are

    then used as black-box modules in the proof of indistinguishability-

    based security. The first abstraction is a generic signature service,

    which we use multiple times in the proof and can be reused in future

    EasyCrypt developments. The second abstraction is specific to AWS

    KMS, and it was created for managing the complexity of the proof

    by black-boxing the guarantees provided by the combined actions

    of HSMs and human operators in domain management. The third

    abstraction is the multi-recipient public-key encryption scheme,

    which is only used once in the main proof of security, but is meant

    for reuse in future EasyCrypt developments.

    The ideal signature service abstraction. A central component in our

    modeling of the protocol and its proof of security (in both ver-

    sions) is the signature service abstraction. We introduce a module

    called RealSignatureServ with an external interface that permits creating

    stateless signers, each with an independent signing key.

    This service offers a signature verification procedure that works

    as a pure operator based on the public key and uses the signature

    verification algorithm for the underlying signature scheme. This

    means that any protocol using a digital signature with multiple

    signers and arbitrary verifiers that have access to the public keys

    can be described as a client to the real signature service. We then

    show that the standard property of unforgeability implies that this

    service is indistinguishable from an ideal one in which signature

    verification is now carried out by checking a list of signed messages.

    The proof of security of the protocol relies on two instances of

    this abstraction, one for operator signatures and another one for

    HSM signatures. When using this abstraction, one first rewrites the

    description of the protocol as a function of the RealSignatureServ, which

    is always possible. Then we can use the fact that no adversary

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    can distinguish this service from its ideal counterpart to modify

    the protocol into another one that uses a table-based idealized

    representation for signatures. From that point on, we can write

    invariants that refer to these idealized tables, which contain domain

    tokens/trusts (resp. identity attestations) if and only if they have

    been signed by genuine HSMs (resp. operators).

    Domain Management Abstraction.We define a general notion of a

    domain management policy, for which we specify security in terms

    of distinguishing a real policy enforcement mechanism from an

    ideal policy enforcement mechanism.

    Figure 10 details the module which captures the notion of a

    domain management policy based on the actions of hosts, operators

    and HSMs we have introduced in Section 3. This module maintains

    two data structures that keep track of the trusts manipulated by

    the system: protectedTrusts and parentTrust. Protected trusts are those that

    contain only genuine parties; this can happen because the trust is

    directly checked by operators in the isGoodInitialTrust operation to be a

    good initial trust, or because an HSM has checked that it is a valid

    descendant of a protected trust in checkTrustUpdate. The descendant

    relation is maintained using the parentTrust map.

    The idealized version of the abstraction, which we omit for

    brevity, offers the same functionality as the real one, but ensures

    the following invariants:

    i. All protected trusts contain only genuine HSM members and

    they descend from a protected trust.

    ii. The descendant relation computed by HSMs behaves like an in-

    jective function—any trust has at most one valid parent through-

    out the lifetime of the system. This relation can be checked by

    hosts, if it has been computed by HSMs.

    Intuitively this proof follows in the lines of the invariant described

    in Section 3. Note that this abstraction does not require genuine

    hosts or HSMs to be able to tell whether a trust was previously

    checked by a genuine HSM: it only speaks about trusts that have

    been tagged as protected. More precisely, the ideal policy says

    that, if a trust was previously tagged as protected, then the honest

    property is propagated and a genuine host will have the same view

    of the descendant relation; otherwise no guarantee is given.

    In the main proof, which we discuss in the next subsection, we

    strengthen the security guarantee provided by this abstraction,

    relying on the authentication guarantees inherent to the signed

    trust data structure: looking ahead, we will use the fact that any

    trust for which the honesty property has been established must

    have been signed by a genuine HSM.

    The following EasyCrypt theorem provides a concrete bound for

    any adversary distinguishing the real policy management module

    from its idealized version for the KMS Domain Management policy

    enforced by operators andHSMs. The bound is given by the collision

    resistance property of the hash function used to compute trust

    fingerprints, and the unforgeability advantage against the signature

    scheme used by operators to certify identity keys, scaled up by the

    maximum number of operators in the system q_ops.18

    18 We note that our formalization relies on a unkeyed hash function. As we give

    concrete security reductions, our results are meaningful for unkeyed cryptographic

    hash functions used in practice, as discussed for example in [20]. Modifying the proof

    to support a keyed hash function would be straightforward, but would require the

    assumption that every entity in the system can be set-up with the same key.

    module RealTrustService(OA : OperatorActions) : TrustService = { var protectedTrusts : Trust fset var parentTrust : (Trust,Trust) fmap proc newOp = OpPolSrv(OA).newOp proc addHId = OpPolSrv(OA).addHId proc requestAuthorization = OpPolSrv(OA).requestAuthorization proc newHst = HstPolSrv.newHst proc installInitialTrust = HstPolSrv.installInitialTrust proc installUpdatedTrust = HstPolSrv.installUpdatedTrust proc isInstalledTrust = HstPolSrv.isInstalledTrust

    proc isGoodInitialTrust(trust: Trust) = { b← OpPolSrv(OA).isGoodInitialTrust(tr_data trust); if (b) protectedTrusts← protectedTrusts | fset1 trust; return b; }

    proc checkTrustUpdate(old:Trust, new:Trust, auth:Authorizations) : bool = { c← HSMPolSrv.checkTrustUpdate(old,new,auth); protected← old ∈ protectedTrusts; if (c) { if (¬new ∈ parentTrust) parentTrust[new]← old; if (protected) protectedTrusts← protectedTrusts | fset1 new;

    } return c; }

    proc isProtectedTrust(trust : Trust) : bool = { return trust ∈ protectedTrusts; } · · ·


    Figure 10: Domain management policy abstraction.

    lemma domain_management: |Pr[TrustSecInd(A,IdealTrustService(OAR)).main():res] − Pr[TrustSecInd(A,RealTrustService(OAR)).main():res]| ≤

    Pr[CR(AdvCR(A)).main():res] + q_ops ∗ Pr[UF1(AdvUF1(A)).main():res]. where OAR=OA(RealSigServ)

    Multi-recipient PKE Abstraction. The security proof of the main the-

    orem relies on a tag-based multi-recipient public-key encryption

    abstraction. As a contribution of independent interest, we show

    that the variant of DHIES [2] used by the DMP to create domain

    tokes satisfies this notion of security. The IND-CCA security of this

    construction follows from the results in [2], together with the gen-

    eral results on multi-recipient encryption in [8]. We also extend the

    result to the tag-based setting of Shoup [21], in which encryption

    takes a tag t and the decryption oracle permits decrypting any pair

    (t , c ) , (t∗, cph∗), where (t∗, cph∗) was returned from the left-or-

    right oracle. This extension is crucial to show that a malicious HSM

    cannot modify an honest token to change the trust, in a way that

    decrypts successfully.

    5.3 Main Theorem The proof of indistinguishability security is carried out using the

    game-hopping technique. The first hop shows that the KMSDomain

    Management protocol can be re-expressed using the signature ser-

    vice and policymanagement abstractions introduced in the previous

    subsection. This hop is conservative, and introduces no additional

    terms in the security bound. The second and third hops consist

    of replacing the signature abstraction and the policy management

    abstraction with their ideal counterparts. These hops show that

    any adversary distinguishing the two games in the hop can be used

    to break the real-ideal indistinguishability guarantee for the low

    level abstractions, which we showed in the previous subsection

    can be, in turn, reduced to the security of standard cryptographic


    At this point we perform a conservative hop that entails the

    most innovative part of the entire security proof. Here we combine

    two types of reasoning: 1) the inductive argument that establishes

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom 73

    the propagation of trust honesty as discussed above; and 2) the

    global invariants guaranteeing the absence of collisions between

    trust fingerprints, and of signature forgeries. Together, these justify

    a game hop that slices the entire code of the indistinguishability

    game, isolating protected (honest) trusts from the remaining ones

    and enforces that the Test oracle can only be called by the adversary on protected trusts.

    Furthermore, the game no longer relies on public-key decryption

    to recover domain-keys when dealing with protected trusts; instead,

    it keeps a table of domain keys to answer the adversary’s challenge

    queries (i.e., at this point the domain keys are still encrypted in

    domain tokens, but domain tokens for protected trusts are never

    explicitly decrypted). To prove this hop we formalize an invariant

    (c.f. Appendix C) that establishes an equivalence between hon-

    est trusts and protected trusts occurring in the game, and further

    demonstrates that all trusts installed in genuine hosts are protected.

    This invariant also implies consistent management of the same key

    for each handle, which is necessary for indistinguishability-based

    security as mentioned above. 19

    At this point in the proof we can rely on the security of the multi-

    recipient encryption scheme to replace the domain keys encrypted

    in protected domain tokens with fixed constants. It is crucial that

    there is a strict separation between protected trusts and dishon-

    est trusts, since the reduction to the security of the encryption

    scheme critically relies on the fact that one can use the left-or-

    right challenge oracle for public-key encryption to emulate the

    encryption of domain keys in protected domain tokens in both

    games. Intuitively, genuine HSMs map to the (honest) public keys

    in the multi-recipient public-key encryption game. CCA security of

    the underlying encryption scheme permits dealing with arbitrary

    InsideR queries, where one needs to decrypt ciphertexts contained

    in domain tokens mauled by the adversary.

    The final step in the proof shows that, at this point, the adver-

    sary’s view is independent of the domain key values and hence it

    has no advantage in winning the last game.

    We conclude this section with the statement in EasyCrypt of the

    resulting security theorem. The indistinguishability advantage is

    upper-bounded by the probability that an adversary can break the

    domain management policy invariant (upper-bounded in lemma

    domain_management in the previous subsection), the probability that

    an adversary breaks the underlying signature scheme, and the

    probability that an adversary breaks the underlying multi-recipient

    public-key encryption scheme. Additional negligible terms account

    for the probability that the signing keys of honest parties collide

    with keys that an adversary generates itself and uses as identities

    for adversarially controlled operators and HSMs.

    Pr[KMS_RoR(A).main():res] ≤ 1 / 2 + AdvAdvMRPKE(A)

    MRPKE + Pr[CR(AdvCR(A)).main():res] +

    q_ops ∗ Pr[UF1op(AdvUF1op(A)).main():res] + q_hid ∗ Pr[UF1hsm(AdvUF1hsm(A)).main():res] + ϵ

    where AdvD

    MRPKE =

    Pr[MRPKE.Sec(D).main(false):¬res] − Pr[MRPKE.Sec(D).main(true):res] ϵ = q_hid ∗ ((q_hid + q_tkmng + q_tkmng) ∗ max_size) / n_keygen +

    19 To complete this hop wemade explicit a property that is implied by the unforgeability

    of digital signatures, and which states that no adversary can guess the signing key of

    a genuine entity before it is generated. This allowed us to show that any trust that

    was declared by the game to be dishonest remains dishonest even after a new identity

    key is generated.

    q_ops ∗ (((q_tkmng + q_installinitial) ∗ 2 ∗ max_size) / n_keygen)

    6 EASYCRYPT USAGE AND EXTENSIONS The EasyCrypt development consists of 15K lines of code (loc),

    where 500 loc correspond to the protocol specification. Additionally,

    2.5K loc establish reusable definitions and supporting lemmas on

    standard cryptographic primitives and EasyCrypt data structures;

    5.5K loc contain definitions and general results on KMS-specific

    security models; and 6.5K loc is the approximate size of the main

    security proof.

    The core logics of EasyCrypt proved to be expressive enough and

    no exensions to these logics were needed to complete the proofs.

    However, for convenience during the development, we introduced

    a few new features that helped reduce the proof effort resulting

    from the unprecedented scale of this project. These new features

    do not enlarge the Trusted Computing Base (TCB) of EasyCrypt,

    which is composed of a set of base tactics defining the EasyCrypt

    core logics. Indeed, all the added features generate internal proof

    trees that only rely on the core tactics. Hence, no bug in the added

    features could lead to the acceptance of an invalid proof tree: this

    would be rejected by the TCB.

    Management of pre- and post-conditions. Several core tactics re- quire users to provide intermediate assertions, e.g. loop invariants.

    When dealing with complex programs and specifications, writ-

    ing such intermediate assertions becomes cumbersome and error-

    prone. However, in a majority of cases, these assertions can be ex-

    pressed with little work from the current pre- and post-conditions

    (which tend to grow in size). We added the possibility to match

    sub-formulas that appear in the current proof goal and use these

    sub-formulas for new assertions. Doing this greatly decreases the

    proof writing effort and makes the proof script more robust, as the

    new assertion is given as a delta from the active proof goals. It also

    provides more readable proof goals.

    Proof automation. Several core tactics of EasyCrypt generate

    proof obligations that code is lossless, i.e. that it terminates with

    probability 1. We have implemented heuristics to deal with such

    goals automatically.

    We have also improved existing automation to chain applications

    of core tactics, and tuned the implementation of some core tactics. In

    particular we have integrated an automatic version of the frame rule,

    which removes parts of the post-condition that are immediately

    implied by the pre-condition.

    7 LESSONS LEARNED In addition to producing the machine-checked specifications and

    security proofs for KMS DMP that we described in this paper,

    this project was also an oportunity to better understant the chal-

    lenges posed by larger-scale developments to computer-aided cryp-

    tographic provable security, and particularly when using EasyCrypt. We now give an overview of the main take-away lessons we got

    from the project.

    Imperative vs Functional specification. One of the strong points of EasyCrypt is that there is a great deal of freedom in choosing

    how to formalize cryptographic primitives and security games. As

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom 74

    security models become more intricate, a crucial decision is how to

    model the keeping of state, as there is usually a tension between

    game readability and the complexity of proof goals/invariants.

    Favouring game readability means using EasyCrypt’s imperative

    language as much as possible to describe the step-by-step actions

    that occur in each oracle call. This means using a dedicated Easy- Crypt module to syntactically distinguish the behaviour of each

    entity (or type of entity) in the system, keeping each part of the

    game state as a separate local variable in the correct submodule,

    and using if and while statements to deal with control-flow. The

    consequence of this is that the top-level program that describes the

    security experiment displays a very complex control-flow, which

    makes proving the equivalences required for game-hopping harder

    (in particular because game hops typically require addressing par-

    ticular cases that introduce additional branching points).

    The alternative is to flatten the specificacions of security exper-

    iments by collapsing the module structure and moving as much

    of the detail as possible to EasyCrypt operators (functional speci- fications of deterministic state transitions). This makes the speci-

    fications less readable, but it naturally provides a slicing between

    probabilistic statements, which model the cryptographic opera-

    tions and associated control-flow (e.g., branching on a signature

    verification result) that are usually the crucial program actions in in-

    distinguishability and bad-event hops, from branching and iteration

    statements that are only modeling state management operations

    (e.g., checking syntactic validity of a message and deciding where

    it should be dispatched).

    In this project we have used both approaches and, in hindsight,

    the conclusion is that starting with a readable model that can be

    checked for soundness more easily and then flattening it as a first

    game hop is often the best choice.

    Modular proofs using global invariants. A related issue in manag-

    ing proof complexity is identifying early on the abstraction bound-

    aries that allow decomposing the proof into treatable self-contained

    intermediate goals. For some cases this is straightforward to do,

    namely for sub-components in the protocol that cryptographers

    naturally see as building-blocks (e.g., a signature service or a global

    hash function) that give rise to simple and well-understood global

    invariants in the security games. However, in this project we en-

    countered protocol-specific semantically rich global invariants that

    permit (once correctly identified and formalized) not only to break

    the proof down into manageable subgoals, but also to simplify the

    top-level proof. Intuitively, we achieved this by: i. first specifying

    invariant I = I1 ∧ I2 ∧ I3 . . . globally in, say gameGi ; then ii. reduc-

    ing the preservation of I in game Gi to a bad event occurring in a

    simpler flattened game, where the probability of bad is bounded at

    much lower cost; and iii. jumping to game Gi+1 where the preser-

    vation of I is hardwired as checks of (and sometimes branching

    on) some sub-formula Ik directly in the code, where needed. The

    challenge here is to pin down the minimal use of Ik in the new

    game, so that the invariant does not need to be reproved, while

    keeping Gi+1 as simple as possible in order to complete the proof

    more easily. As a side result of this design pattern, which we believe

    it is interesting to generalize in future work, gameGi+1 now syntac-

    tically displays only the relevant parts of the established invariant

    in its code, which makes it easier to understand the context for

    each proof goal.

    Proof effort. Overall, from a rough analysis of the proof effort

    involved in this project our intuition is that the resources required

    to complete game hopping proofs by experienced EasyCrypt users, once the games and security invariants are correctly specified (and

    following good practices, some of which were highlighted above)

    scales “linearly with the complexity” of the programs/games, sim-

    ilarly to functional equivalence proofs between programs with a

    reasonably close, if not identical, control-flow.

    8 RELATEDWORK There has been significant work on the formal verification of cryp-

    tographic API, and in particular on PKCS tokens.

    Delaune, Kremer, and Steel [16] model tokens as security pro-

    tocols with a sole party, and apply Dolev-Yao verification meth-

    ods to analyze their security. Bortolozzo, Centenaro, Focardi and

    Steel [12] build an automated tool for model checking the security

    and functionality of tokens, and evaluate commercially available

    PKCS tokens. They discover several security issues and validate


    Cachin and Chandran [13] formalize computational security of

    cryptographic APIs, and show security of PKCS tokens in their

    model. Kremer, Steel and Warinschi [18] define another model de-

    signed to provide more genericity and to support more powerful

    corruptions. Kremer, Künnemann and Steel [17] define a UC func-

    tionality for key management, and use their model for proving the

    security of a minimal example. The model imposes constraints on

    the interactions between key management and key usage.

    Shrimpton, Stam and Warinschi [23] also show that the indistin-

    guishability definition of security for cryptographic APIs composes

    with a natural class of symmetric-key primitives, such as AEAD

    and MAC in order to provide cryptographic services. The security

    of these cryptographic services was defined by extending the attack

    vectors of standard AEAD and MAC security with all the oracles

    available to the cryptographic API adversary. We depart from this

    approach and adopt an alternative formulation for the security of

    cryptographic services, which is inspired by the Universal Compos-

    ability framework (UC). As discussed in Appendix A, from UC we

    inherit two important advantages: i. clear composition guarantees

    of cryptographic services with other systems; and ii. a clean and

    intuitive view of correctness and security guarantees for the clients

    of cryptographic services.

    Blanchet and Chaudhuri [11] use ProVerif to analyze a protocol

    for secure file sharing, which includes distributed key management

    features. Their analysis is conducted in the symbolic model of

    cryptography, which provides weaker guarantees, but allows for a

    higher degree of automation.

    CryptoVerif [9] was among the first tools to support crypto-

    graphic security proofs in the computational model. It uses prob-

    abilistic process algebra as a modelling language and leverages

    different notions of equivalence to support proofs of equivalence,

    equivalence up to failure events, as well as simple forms of hybrid

    arguments. CryptoVerif has been used for verifying primitives, as

    well as protocols; it was recently applied to TLS 1.3 [10].

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom


    9 CONCLUSION We proved a concrete security bound for the DMP of AWS KMS,

    down to standard cryptographic assumptions. The bound is tight,

    increasing linearly with the number of entities in the system, and

    it is machine-checked in EasyCrypt. For practical purposes, our

    work gives strong evidence that the DMP is as good as an ideal

    encryption service, under the assumption that any quorum of AWS

    operators that authorizes a domain update operation includes at

    least one honest operator.

    ACKNOWLEDGEMENTS Manuel Barbosa was supported by grant SFRH/BSAB/143018/2018

    awarded by the Portuguese Foundation for Science and Technology

    (FCT). Vitor Pereira was supported by grant FCT-PD/BD/113967/201

    awarded by FCT. This work was partially funded by national funds

    via FCT in the context of project PTDC/CCI-INF/31698/2017.

    REFERENCES [1] Michel Abdalla, Mihir Bellare, and Phillip Rogaway. 1998. DHIES: An Encryption

    Scheme Based On The Diffie-Hellman Problem. Contributions to IEEE P1363a.

    (Sept. 1998).

    [2] Michel Abdalla, Mihir Bellare, and Phillip Rogaway. 2001. The Oracle Diffie-

    Hellman Assumptions and an Analysis of DHIES. In CT-RSA 2001 (LNCS), David Naccache (Ed.), Vol. 2020. Springer, Heidelberg, 143–158.


    [3] José Bacelar Almeida, Manuel Barbosa, Gilles Barthe, and François Dupres-

    soir. 2016. Verifiable Side-Channel Security of Cryptographic Implementations:

    Constant-Time MEE-CBC. In FSE 2016 (LNCS), Thomas Peyrin (Ed.), Vol. 9783.

    Springer, Heidelberg, 163–184.

    [4] José Bacelar Almeida, Manuel Barbosa, Gilles Barthe, François Dupressoir,

    Benjamin Grégoire, Vincent Laporte, and Vitor Pereira. 2017. A Fast and

    Verified Software Stack for Secure Function Evaluation. In Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, CCS 2017, Dallas, TX, USA, October 30 - November 03, 2017, Bhavani M. Thurais-

    ingham, David Evans, Tal Malkin, and Dongyan Xu (Eds.). ACM, 1989–2006.

    [5] Amazon Web Services (AWS). 2018. AWS Key Management Service Crypto-

    graphic Details. (August 2018).

    Cryptographic-Details .

    [6] Gilles Barthe, François Dupressoir, Benjamin Grégoire, César Kunz, Benedikt

    Schmidt, and Pierre-Yves Strub. 2013. EasyCrypt: A Tutorial. In Foundations of Security Analysis and Design VII - FOSAD 2012/2013 Tutorial Lectures (Lecture Notes in Computer Science), Alessandro Aldini, Javier López, and Fabio Martinelli

    (Eds.), Vol. 8604. Springer, 146–166.

    [7] Gilles Barthe, Benjamin Grégoire, Sylvain Heraud, and Santiago Zanella Béguelin.

    2011. Computer-Aided Security Proofs for the Working Cryptographer. In

    CRYPTO 2011 (LNCS), Phillip Rogaway (Ed.), Vol. 6841. Springer, Heidelberg,


    [8] Mihir Bellare, Alexandra Boldyreva, and Jessica Staddon. 2003. Randomness Re-

    use in Multi-recipient Encryption Schemeas. In PKC 2003 (LNCS), Yvo Desmedt

    (Ed.), Vol. 2567. Springer, Heidelberg, 85–99.


    [9] Bruno Blanchet. 2006. A Computationally Sound Mechanized Prover for Security

    Protocols. In 2006 IEEE Symposium on Security and Privacy. IEEE Computer

    Society Press, 140–154.

    [10] Bruno Blanchet. 2018. Composition Theorems for CryptoVerif and Application

    to TLS 1.3. In 31st IEEE Computer Security Foundations Symposium, CSF 2018, Oxford, United Kingdom, July 9-12, 2018. IEEE Computer Society, 16–30. https:


    [11] Bruno Blanchet and Avik Chaudhuri. 2008. Automated Formal Analysis of a

    Protocol for Secure File Sharing on Untrusted Storage. In 2008 IEEE Symposium on Security and Privacy (S&P 2008), 18-21 May 2008, Oakland, California, USA. IEEE Computer Society, 417–431.

    [12] Matteo Bortolozzo, Matteo Centenaro, Riccardo Focardi, and Graham Steel. 2010.

    Attacking and fixing PKCS#11 security tokens. In ACM CCS 10, Ehab Al-Shaer, Angelos D. Keromytis, and Vitaly Shmatikov (Eds.). ACM Press, 260–269. https:


    [13] Christian Cachin and Nishanth Chandran. 2009. A Secure Cryptographic Token

    Interface. In Proceedings of the 22nd IEEE Computer Security Foundations Sym- posium, CSF 2009, Port Jefferson, New York, USA, July 8-10, 2009. IEEE Computer

    Society, 141–153.

    [14] Ran Canetti. 2001. Universally Composable Security: A New Paradigm for

    Cryptographic Protocols. In 42nd FOCS. IEEE Computer Society Press, 136–145.

    [15] Ran Canetti, Yevgeniy Dodis, Rafael Pass, and Shabsi Walfish. 2007. Universally

    Composable Security with Global Setup. In TCC 2007 (LNCS), Salil P. Vadhan (Ed.), Vol. 4392. Springer, Heidelberg, 61–85.


    [16] Stéphanie Delaune, Steve Kremer, and Graham Steel. 2008. Formal Analysis of

    PKCS#11. In Proceedings of the 21st IEEE Computer Security Foundations Sympo- sium, CSF 2008, Pittsburgh, Pennsylvania, USA, 23-25 June 2008. IEEE Computer

    Society, 331–344.

    [17] Steve Kremer, Robert Künnemann, and Graham Steel. 2013. Universally Com-

    posable Key-Management. In ESORICS 2013 (LNCS), Jason Crampton, Sushil

    Jajodia, and Keith Mayes (Eds.), Vol. 8134. Springer, Heidelberg, 327–344. https:


    [18] Steve Kremer, Graham Steel, and Bogdan Warinschi. 2011. Security for Key Man-

    agement Interfaces. In Proceedings of the 24th IEEE Computer Security Foundations Symposium, CSF 2011, Cernay-la-Ville, France, 27-29 June, 2011. IEEE Computer

    Society, 266–280.

    [19] Matthew M. Papi, Mahmood Ali, Telmo Luis Correa, Jr., Jeff H. Perkins, and

    Michael D. Ernst. 2008. Practical Pluggable Types for Java. In Proceedings of the 2008 International Symposium on Software Testing and Analysis (ISSTA ’08). ACM,

    New York, NY, USA, 201–212.

    [20] Phillip Rogaway. 2006. Formalizing Human Ignorance. In Progress in Cryptology - VIETCRYPT 06 (LNCS), Phong Q. Nguyen (Ed.), Vol. 4341. Springer, Heidelberg,


    [21] Victor Shoup. 2001. A Proposal for an ISO Standard for Public Key Encryption

    (version 2.1). (2001). .

    [22] Victor Shoup. 2001. A Proposal for an ISO Standard for Public Key Encryption.

    Cryptology ePrint Archive, Report 2001/112. (2001).


    [23] Thomas Shrimpton, Martijn Stam, and Bogdan Warinschi. 2016. A Modular

    Treatment of Cryptographic APIs: The Symmetric-Key Case. In CRYPTO 2016, Part I (LNCS), Matthew Robshaw and Jonathan Katz (Eds.), Vol. 9814. Springer,

    Heidelberg, 277–307.


    Although we have not formalized it (syntactically) in this way,

    our security model and proof can be recast in terms of Universal

    Composability with global setup [15]. This is a framework that

    extends Universal Composability to enable set-up assumptions

    such as common reference strings, or public-key infrastructures

    (PKI). In this setting we would consider three types of parties.

    • Hosts, which provide the environment 𝒵 with the high-level

    interface of AEAD encryption and decryption and enable 𝒜 to

    install trusts.

    • HSMs, which enable 𝒜 to update trusts and manage keys, as

    well as perform encryption and decryption operations based on

    requests placed by hosts.

    • Operators, which enable𝒵 to generate key attestation statements

    for operators and HSMs.

    The proof assumes static-corruptions, whereby some parties are

    known to be corrupt from the beginning of computation.

    The proof of security in the UC framework would be carried out

    in a hybrid model. The first hybrid functionality is a confidential

    and authenticated channel through which hosts place encryption

    and decryption requests to HSMs. We emphasise that this hybrid

    functionality is not used by the KMS DMP protocol in any of the do-

    main management operations, which are the focus of our analysis;

    it captures only the architectural choice that KMS hosts collect end-

    user encryption/decryption requests and forward them to HSMs

    (see footnote 7). Future work will extend the proof to consider the

    specific secure channel used by KMS for this purpose, which builds

    on top of the DMP itself.

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom 76

    Additionally the hybrid model includes two set-up assumptions.

    The first set-up assumption is a standard PKI functionality that is

    used only by operators, and which registers the identity keys of

    genuine entities in the system; this models the real world operation

    of KMS DMP in which operators are assumed to know the set of

    genuine entities. A crucial aspect of the security guarantees we

    prove for KMS DMP is precisely that this resource is restricted to

    operators, and still it suffices to guarantee that trust honesty is

    preserved by host and HSM actions.

    The second set-up assumption captures the global quorum in-

    variant that in any group of n genuine operators, there exists at

    least one non-corrupt operator. This assumption can be modeled via

    a simple hybrid functionality that is used only by hosts and HSMs.

    This functionality takes a set of operator identities and returns a

    single bit; the bit will be true if either the set contains a non-genuine

    operator or, if this is not the case, if the invariant is satisfied. By

    accessing this functionality, the description of the DMP protocol

    executed by hosts and HSMs can be instrumented (as a modeling

    artefact) to truncate execution traces where the global invariant is


    While the PKI set-up assumption is standard for many real-world

    systems, the second set-up assumption reflects a different kind of

    trust assumption that arises in modeling the actions of human

    operators in the UC setting.

    The implication of recasting our result in the gUC framework is

    that we obtain composability: any higher-level protocol that can be

    proved secure by relying on the ideal encryption functionality we

    defined in the main body of the paper will still be secure when this

    functionality is replaced by the DMP protocol, assuming of course

    that the set-up assumptions described above are satisfied and that

    the deployed cryptographic schemes are secure.

    B EXTENSIONS TO THE SECURITY PROOF B.1 Access to keys in dishonest tokens The security model in the main body of the paper underspecifies

    what happens if an attacker is able to maul a non-genuine identity

    into an honest trust, or convince an honest host to accept a dishon-

    est trust: what it states is that, even if that were possible, the attacker should not be able to break the secrecy of domain keys associated

    with that trust. This is somewhat counterintuitive and, indeed, our

    security proof establishes the stronger result that no honest trust

    will ever be successfully updated to another one inhabitted by non-

    genuine identities. For this reason, our machine-checked proof is

    actually carried out in a stronger security model.

    In this model we extend the adversarial interface in the ideal

    functionality to make it explicit that, whenever the adversary suc-

    ceeds in causing any of the events above, it can successfully launch

    a distinguishing attack separating the real world from the ideal

    world. We model this by extending the ideal functionality with

    two oracles (BadEnc and BadDec) that check if a trace satisfies a

    predicate honest(trace, tk, hdl, cmd) and, if this is not the case, they execute TkReveal to obtain secret key key and answer the adver-

    sary’s request by encrypting or decrypting the provided payload.

    Note that, if the honest predicate is trivially true, then theBadEnc and BadDec oracles are useless to an adversary. Conversely, exclud-

    ing traces from the honest predicate explicitly rules out protocols

    that allow non-honest traces to occur, as the attacker can trivially

    distinguish the world from the ideal world by decrypting the ci-

    phertext provided to the environment by the ideal functionality.

    Our strenghthening maps to the indistinguishability definition,

    where we introduced the InsideR oracle; this works as a CCA-style

    oracle on dishonest tokens: it allows an attacker to reveal all keys

    in tokens associated with dishonest trusts and, technically, it maps

    to the CCA security of the multi-recipient encryption scheme used

    by the KMS DMP. In the reduction from the UC-style definition to

    the indistinguishability definition, the BadEnc and BadDec oracles can be simulated using InsideR to obtain the key and then perform

    the encryption and decryption operations.

    B.2 Stronger corruption models Although we have not formalized these extensions, it is easy to see

    that our proof can be easily adapted to deal with two (apparently)

    stronger corruption models. The first strengthening refers to the

    possibility of using corrupt keys, i.e., allowing an attacker to re-

    quest encryptions and decryptions on keys it has corrupted (prior

    to legitimate usage, of course). In this case, the ideal functionality

    would provide an encryption/decryption of the actual payload/ci-

    phertext provided by the attacker. This has no impact in the proof

    of security, as the reduction to indistinguishability can be extended

    to cache corrupted keys and use them to simulate these extra calls.

    The second strenghtening refers to dealing with corrupted hosts,

    which might be accepting dishonest trusts and/or revealing client

    payloads to the attacker; this case is similar to the previous one,

    in that the ideal functionality would need to be extended to keep

    track of whether these corrupt hosts were dealing with honest or

    dishonest trusts, and provide ideal or real encryption accordingly.

    C EXAMPLE INVARIANT IN DMP PROOF We present here the core invariant that supports the intermediate

    step in the proof of KMS DMP security, where global invariants

    stemming from cryptographic security guarantees provided by low-

    level components are combined with inductive properties related to

    trust honesty. This invariant permits separating honest (protected)

    trusts from those whomay be under adversarial control and proving

    that the adversary cannot gain control over domain keys that are

    initially associated to an honest trust.

    The invariant relies on signedTr and signedTk predicates that allow

    leveraging the authentication guarantee provided by the signature

    scheme used by HSMs. Similarly, the properties of the parentTrust rela-

    tion permit relying on the injectivity of trust fingerprints, which is

    (computationally) guaranteed by a collision-resistant hash function.

    (∗ if a trust is installed, then it is protected ∗) (∀ hstid, hstid ∈ HstPolSrv.hosts_tr⇒

    oget HstPolSrv.hosts_tr[hstid] ∈ RealTrustService.protectedTrusts){2} ∧

    (∗ if a trust is protected, all its members are genuine ∗) (∀ t, t ∈ RealTrustService.protectedTrusts⇒

    all_genuine OpPolSrv.genuine t){2} ∧ (∗ if a trust has a parent, then it is not initial ∗) (∀ t, t ∈ RealTrustService.parentTrust⇒

    ¬tr_initial t){2} ∧ (∗ all signed installable non initial tokens have a parent ∗) (∀ (tk : Token), ¬tr_initial tk.tk_trust⇒

    tk.tk_inst⇒ signedTk tk RealSigServ.qs⇒ tk.tk_trust ∈ RealTrustService.parentTrust){2} ∧

    (∗ all signed tokens with genuine trusts have signed trusts ∗) (∀ tk, signedTk tk RealSigServ.qs⇒

    all_genuine OpPolSrv.genuine tk.tk_trust⇒ signedTr tk.tk_trust RealSigServ.qs){2} ∧

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom 77

    (∗ if a trust has a parent that is all genuine, then the parent was signed in an installable token ∗)

    (∀ t, t ∈ RealTrustService.parentTrust⇒ all_genuine OpPolSrv.genuine (oget RealTrustService.parentTrust[t])⇒

    signedTr (oget RealTrustService.parentTrust[t]) RealSigServ.qs){2} ∧

    (∗ if a trust is protected, then it was signed in an installable token ∗)

    (∀ t, t ∈ RealTrustService.protectedTrusts⇒ signedTr t RealSigServ.qs){2} ∧

    (∗ if a trust was signed in an installable token, all its members are genuine and has an initial trust, then it is protected ∗)

    (∀ t, tr_initial t⇒ signedTr t RealSigServ.qs⇒ all_genuine OpPolSrv.genuine t⇒ t ∈ IOperatorActions.trusts⇒ oget IOperatorActions.trusts[t]⇒ t ∈ RealTrustService.protectedTrusts){2} ∧

    (∗ if a token is signed with a trust where all its members are genuine and has an initial trust, then this trust was installable signed. ∗)

    (∀ (tk : Token), tr_initial tk.tk_trust⇒ signedTk tk RealSigServ.qs⇒

    all_genuine OpPolSrv.genuine tk.tk_trust⇒ tk.tk_trust ∈ IOperatorActions.trusts⇒ oget IOperatorActions.trusts[tk.tk_trust]⇒ signedTr tk.tk_trust RealSigServ.qs){2} ∧

    (∗ if a trust is protected and is not initial then it has a parent and this protected as well ∗)

    (∀ t, ¬tr_initial t⇒ t ∈ RealTrustService.protectedTrusts⇒

    (t ∈ RealTrustService.parentTrust ∧ oget RealTrustService.parentTrust[t] ∈

    RealTrustService.protectedTrusts)){2} ∧ (∗ if a trust has a protected parent then it is protected as well ∗) (∀ t, t ∈ RealTrustService.parentTrust⇒

    oget RealTrustService.parentTrust[t] ∈ RealTrustService.protectedTrusts⇒ t ∈ RealTrustService.protectedTrusts){2} ∧

    (∗ Encryptions ∗) (∀ (tk : Token), signedTk tk RealSigServ.qs{2}⇒

    tk.tk_trust ∈ RealTrustService.protectedTrusts{2}⇒ tk ∈ KMS_Procedures3.wrapped_keys{2} ∧ tk.tk_wdata.tkw_ekeys ∈

    mencrypt (proj_pks (tr_mems tk.tk_trust)) (encode_tag tk.tk_trust) (encode_ptxt (oget KMS_Procedures3.wrapped_keys{2}[tk])))

    Session 1C: Cloud Security I CCS ’19, November 11–15, 2019, London, United Kingdom 78
    • 1 Introduction
    • 2 Overview
    • 3 KMS Domain Management Protocol
    • 3.1 Detailed Description 3.2 Formalization in EasyCrypt
    • 4 Real-vs-Ideal security for KMS DMP
    • 4.1 Key Management APIs 4.2 Defining Security of Encryption Services
    • 5 Machine-checked Security Proof
    • 5.1 From key hiding to real-vs-ideal security 5.2 Low-level abstractions 5.3 Main Theorem
    • 6 EasyCrypt usage and extensions
    • 7 Lessons learned
    • 8 Related Work
    • 9 Conclusion
    • References
    • A Relation to Universal Composability
    • B Extensions to the security proof
    • B.1 Access to keys in dishonest tokens B.2 Stronger corruption models
    • C Example invariant in DMP proof

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