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1. Randomized Half-Ideal Cipher on Groups with Applications to UC (a)PAKE

   Santos, Bruno Freitas ; Gu, Yanqi ; Jarecki, Stanislaw ( April 2023 , Lecture notes in computer science: Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023)

   Hazay, Carmit ; Stam, Martin (Ed.)

   An Ideal Cipher (IC) is a cipher where each key defines a random permutation on the domain. Ideal Cipher on a group has many attractive applications, e.g., the Encrypted Key Exchange (EKE) protocol for Password Authenticated Key Exchange (PAKE) [8], or asymmetric PAKE (aPAKE) [31, 33]. However, known constructions for IC on a group domain all have drawbacks, including key leakage from timing information [12], requiring 4 hash-onto-group operations if IC is an 8-round Feistel [22], and limiting the domain to half the group [9] or using variable-time encoding [39, 47] if IC is implemented via (quasi-) bijections from groups to bitstrings [33]. We propose an IC relaxation called a (Randomized) Half-Ideal Cipher (HIC), and we show that HIC on a group can be realized by a modified 2-round Feistel (m2F), at a cost of 1 hash-onto-group operation, which beats existing IC constructions in versatility and computational cost. HIC weakens IC properties by letting part of the ciphertext be non-random, but we exemplify that it can be used as a drop-in replacement for IC by showing that EKE [8] and aPAKE of [33] realize respectively UC PAKE and UC aPAKE even if they use HIC instead of IC. The m2F construction can also serve as IC domain extension, because m2F constructs HIC on domain D from an RO-indifferentiable hash onto D and an IC on 2k-bit strings, for k a security parameter. One application of such extender is a modular lattice-based UC PAKE using EKE instantiated with HIC and anonymous lattice-based KEM. 

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2. Asymmetric PAKE with Low Computation and communication

   Dos Santos, Bruno Freitas ; Gu, Yanqi. ; Jarecki, Stanislaw. ; Krawczyk, Hugo ( May 2022 , Lecture Notes in Computer Science (LNCS))

   Dunkelman, O. ; Dziembowski, S (Ed.)

   In Crypto’21 Gu, Jarecki, and Krawczyk [25] showed an asymmetric password authenticated key exchange protocol (aPAKE) whose computational cost matches (symmetric) password authenticated key exchange (PAKE) and plain (i.e. unauthenticated) key exchange (KE). However, this minimal-cost aPAKE did not match prior aPAKE’s in round complexity, using 4 rounds assuming the client initiates compared to 2 rounds in an aPAKE of Bradley et al. [13]. In this paper we show two aPAKE protocols (but not strong aPAKEs like [13, 30]), which achieve optimal computational cost and optimal round complexity. Our protocols can be seen as variants of the Encrypted Key Exchange (EKE) compiler of Bellovin and Merritt [7], which creates password-authenticated key exchange by password-encrypting messages in a key exchange protocol. Whereas Bellovin and Merritt used this method to construct a PAKE by applying password-encryption to KE messages, we construct an aPAKE by password-encrypting messages of a unilaterally authenticated Key Exchange (ua-KE). We present two versions of this compiler. The first uses salted password hash and takes 2 rounds if the server initiates. The second uses unsalted password hash and takes a single simultaneous flow, thus simultaneously matching the minimal computational cost and the minimal round complexity of PAKE and KE. We analyze our aPAKE protocols assuming an Ideal Cipher (IC) on a group, and we analyze them as modular constructions from ua-KE realized via a universally composable Authenticated Key Exchange where the server uses one-time keys (otk-AKE). We also show that one-pass variants of 3DH and HMQV securely realize otk-AKE in the ROM. Interestingly, the two resulting concrete aPAKE’s use the exact same protocol messages as variants of EKE, and the only difference between the symmetric PAKE (EKE) and asymmetric PAKE (our protocols) is in the key derivation equation. 

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3. Password-Authenticated TLS via OPAQUE and Post-Handshake Authentication

   Hesse, Julia ; Jarecki, Stanislaw ; Krawczyk, Hugo ; Wood, Christopher ( April 2023 , Lecture notes in computer science: Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023)

   Hazay, Carmit ; Stam, Martin (Ed.)

   OPAQUE is an Asymmetric Password-Authenticated Key Exchange (aPAKE) protocol being standardized by the IETF (Internet Engineering Task Force) as a more secure alternative to the traditional “password-over-TLS” mechanism prevalent in current practice. OPAQUE defends against a variety of vulnerabilities of password-over-TLS by dispensing with reliance on PKI and TLS security, and ensuring that the password is never visible to servers or anyone other than the client machine where the password is entered. In order to facilitate the use of OPAQUE in practice, integration of OPAQUE with TLS is needed. The main proposal for standardizing such integration uses the Exported Authenticators (TLS-EA) mechanism of TLS 1.3 that supports post-handshake authentication and allows for a smooth composition with OPAQUE. We refer to this composition as TLS-OPAQUE and present a detailed security analysis for it in the Universal Composability (UC) framework. Our treatment is general and includes the formalization of components that are needed in the analysis of TLS-OPAQUE but are of wider applicability as they are used in many protocols in practice. Specifically, we provide formalizations in the UC model of the notions of post-handshake authentication and channel binding. The latter, in particular, has been hard to implement securely in practice, resulting in multiple protocol failures, including major attacks against prior versions of TLS. Ours is the first treatment of these notions in a computational model with composability guarantees. We complement the theoretical work with a detailed discussion of practical considerations for the use and deployment of TLS-OPAQUE in real-world settings and applications. 

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4. Universal Composition with Global Subroutines: Capturing Global Setup within plain UC

   Badertscher, Christian ; Canetti, Ran ; Hesse, Julia ; Tackmann, Björn ; Zikas, Vassilis ( November 2021 , Theory of Cryptography Conference)

   null (Ed.)

   The Global and Externalized UC frameworks [Canetti-Dodis-Pass-Walfish, TCC 07] extend the plain UC framework to additionally handle protocols that use a "global setup", namely a mechanism that is also used by entities outside the protocol. These frameworks have broad applicability: Examples include public-key infrastructures, common reference strings, shared synchronization mechanisms, global blockchains, or even abstractions such as the random oracle. However, the need to work in a specialized framework has been a source of confusion, incompatibility, and an impediment to broader use. We show how security in the presence of a global setup can be captured within the plain UC framework, thus significantly simplifying the treatment. This is done as follows: - We extend UC-emulation to the case where both the emulating protocol π and the emulated protocol ϕ make subroutine calls to protocol γ that is accessible also outside π and ϕ. As usual, this notion considers only a single instance of ϕ or π (alongside γ). - We extend the UC theorem to hold even with respect to the new notion of UC emulation. That is, we show that if π UC-emulates ϕ in the presence of γ, then ρϕ→π UC-emulates ρ for any protocol ρ, even when ρ uses γ directly, and in addition calls many instances of ϕ, all of which use the same instance of γ. We prove this extension using the existing UC theorem as a black box, thus further simplifying the treatment. We also exemplify how our treatment can be used to streamline, within the plain UC model, proofs of security of systems that involve global set-up, thus providing greater simplicity and flexibility. 

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5. EasyUC: Using EasyCrypt to Mechanize Proofs of Universally Composable Security

   Canetti, Ran ; Stoughton, Alley ; Varia, Mayank ( July 2019 , 32nd IEEE Computer Security Foundations Symposium (CSF 2019))

   We present a methodology for using the EasyCrypt proof assistant (originally designed for mechanizing the generation of proofs of game-based security of cryptographic schemes and protocols) to mechanize proofs of security of cryptographic protocols within the universally composable (UC) security framework. This allows, for the first time, the mechanization and formal verification of the entire sequence of steps needed for proving simulation-based security in a modular way: * Specifying a protocol and the desired ideal functionality. * Constructing a simulator and demonstrating its validity, via reduction to hard computational problems. * Invoking the universal composition operation and demonstrating that it indeed preserves security. We demonstrate our methodology on a simple example: stating and proving the security of secure message communication via a one-time pad, where the key comes from a Diffie-Hellman key-exchange, assuming ideally authenticated communication. We first put together EasyCrypt-verified proofs that: (a) the Diffie-Hellman protocol UC-realizes an ideal key-exchange functionality, assuming hardness of the Decisional Diffie-Hellman problem, and (b) one-time-pad encryption, with a key obtained using ideal key-exchange, UC-realizes an ideal secure-communication functionality. We then mechanically combine the two proofs into an EasyCrypt-verified proof that the composed protocol realizes the same ideal secure-communication functionality. Although formulating a methodology that is both sound and workable has proven to be a complex task, we are hopeful that it will prove to be the basis for mechanized UC security analyses for significantly more complex protocols. 

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