International Association
for Cryptologic Research

<p> X-Wing is a hybrid key-encapsulation mechanism based on X25519 and ML-KEM-768. It is designed to be the sensible choice for most applications. The concrete choice of X25519 and ML-KEM-768 allows X-Wing to achieve improved efficiency compared to using a generic KEM combiner. In this paper, we introduce the X-Wing hybrid KEM construction and provide a proof of security. We show (1) that X-Wing is a classically IND-CCA secure KEM if the strong Diffie-Hellman assumption holds in the X25519 nominal group, and (2) that X-Wing is a post-quantum IND-CCA secure KEM if ML-KEM-768 is itself an IND-CCA secure KEM and SHA3-256 is secure when used as a pseudorandom function. The first result is proved in the ROM, whereas the second one holds in the standard model. Loosely speaking, this means X-Wing is secure if either X25519 or ML-KEM-768 is secure. We stress that these security guarantees and optimizations are only possible due to the concrete choices that were made, and it may not apply in the general case. </p>

In the past three decades, an impressive body of knowledge has been built around secure and private password authentication. In particular, secure password-authenticated key exchange (PAKE) protocols require only minimal overhead over a classical Diffie-Hellman key exchange. PAKEs are also known to fulfill strong composable security guarantees that capture many password-specific concerns such as password correlations or password mistyping, to name only a few. However, to enjoy both round-optimality and strong security, applications of PAKE protocols must provide \emph{unique} session and participant identifiers. If such identifiers are not readily available, they must be agreed upon at the cost of additional communication flows, a fact which has been met with incomprehension among practitioners, and which hindered the adoption of provably secure password authentication in practice. In this work, we resolve this issue by proposing a new paradigm for truly \emph{password-only} yet securely composable PAKE, called \emph{bare} PAKE. We formally prove that two prominent PAKE protocols, namely CPace and EKE, can be cast as bare PAKEs and hence do not require pre-agreement of anything else than a password. Our bare PAKE modeling further allows us to investigate a novel ``reusability'' property of PAKEs, i.e., whether $n^2$ pairwise keys can be exchanged from only $n$ messages, just as the Diffie-Hellman non-interactive key exchange can do in a public-key setting. As a side contribution, this add-on property of bare PAKEs leads us to observe that some previous PAKE constructions relied on unnecessarily strong, ``reusable'' building blocks. By showing that ``non-reusable'' tools suffice for standard PAKE, we open a new path towards round-optimal post-quantum secure password-authenticated key exchange.

We present a formally verified proof of the correctness and IND-CCA security of ML-KEM, the Kyber-based Key Encapsulation Mechanism (KEM) undergoing standardization by NIST. The proof is machine-checked in EasyCrypt and it includes: 1) A formalization of the correctness (decryption failure probability) and IND-CPA security of the Kyber base public-key encryption scheme, following Bos et al. at Euro S&P 2018; 2) A formalization of the relevant variant of the Fujisaki-Okamoto transform in the Random Oracle Model (ROM), which follows closely (but not exactly) Hofheinz, Hovelmanns and Kiltz at TCC 2017; 3) A proof that the IND-CCA security of the ML-KEM specification and its correctness as a KEM follows from the previous results; 4) Two formally verified implementations of ML-KEM written in Jasmin that are provably constant-time, functionally equivalent to the ML-KEM specification and, for this reason, inherit the provable security guarantees established in the previous points. The top-level theorems give self-contained concrete bounds for the correctness and security of ML-KEM down to (a variant of) Module-LWE. We discuss how they are built modularly by leveraging various EasyCrypt features.

SPHINCS+ is a post-quantum signature scheme that, at the time of writing, is being standardized as SLH-DSA. It is the most conser- vative option for post-quantum signatures, but the original tight proofs of security were flawed — as reported by Kudinov, Kiktenko and Fe- dorov in 2020. In this work, we formally prove a tight security bound for SPHINCS+ using the EasyCrypt proof assistant, establishing greater confidence in the general security of the scheme and that of the param- eter sets considered for standardization. To this end, we reconstruct the tight security proof presented by Hülsing and Kudinov (in 2022) in a modular way. A small but important part of this effort involves a com- plex argument relating four different games at once, of a form not yet formalized in EasyCrypt (to the best of our knowledge). We describe our approach to overcoming this major challenge, and develop a general formal verification technique aimed at this type of reasoning. Enhancing the set of reusable EasyCrypt artifacts previously produced in the formal verification of stateful hash-based cryptographic construc- tions, we (1) improve and extend the existing libraries for hash func- tions and (2) develop new libraries for fundamental concepts related to hash-based cryptographic constructions, including Merkle trees. These enhancements, along with the formal verification technique we develop, further ease future formal verification endeavors in EasyCrypt, especially those concerning hash-based cryptographic constructions.

Driven by the NIST's post-quantum standardization efforts and the selection of Kyber as a lattice-based Key-Encapsulation Mechanism (KEM), several Password Authenticated Key Exchange (PAKE) protocols have been recently proposed that leverage a KEM to create an efficient, easy-to-implement and secure PAKE. In two recent works, Beguinet et al. (ACNS 2023) and Pan and Zeng (ASIACRYPT 2023) proposed generic compilers that transform KEM into PAKE, relying on an Ideal Cipher (IC) defined over a group. However, although IC on a group is often used in cryptographic protocols, special care must be taken to instantiate such objects in practice, especially when a low-entropy key is used. To address this concern, Dos Santos et al. (EUROCRYPT 2023) proposed a relaxation of the IC model under the Universal Composability (UC) framework called Half-Ideal Cipher (HIC). They demonstrate how to construct a UC-secure PAKE protocol, EKE-KEM, from a KEM and a modified 2-round Feistel construction called m2F. Remarkably, the m2F sidesteps the use of an IC over a group, and instead employs an IC defined over a fixed-length bitstring domain, which is easier to instantiate. In this paper, we introduce a novel PAKE protocol called CHIC that improves the communication and computation efficiency of EKE-KEM, by avoiding the HIC abstraction. Instead, we split the KEM public key in two parts and use the m2F directly, without further randomization. We provide a detailed proof of the security of CHIC and establish precise security requirements for the underlying KEM, including one-wayness and anonymity of ciphertexts, and uniformity of public keys. Our findings extend to general KEM-based EKE-style protocols and show that a passively secure KEM is not sufficient. In this respect, our results align with those of Pan and Zeng (ASIACRYPT 2023), but contradict the analyses of KEM-to-PAKE compilers by Beguinet et al. (ACNS 2023) and Dos Santos et al. (EUROCRYPT 2023). Finally, we provide an implementation of CHIC, highlighting its minimal overhead compared to the underlying KEM -- Kyber. An interesting aspect of the implementation is that we reuse the rejection sampling procedure in Kyber reference code to address the challenge of hashing onto the public key space. As of now, to the best of our knowledge, CHIC stands as the most efficient PAKE protocol from black-box KEM that offers rigorously proven UC security.

We extend and consolidate the security justification for the Dilithium signature scheme. In particular, we identify a subtle but crucial gap that appears in several ROM and QROM security proofs for signature schemes that are based on the Fiat-Shamir with aborts paradigm, including Dilithium. The gap lies in the CMA-to-NMA reduction and was uncovered when trying to formalize a variant of the QROM security proof by Kiltz, Lyubashevsky, and Schaffner (Eurocrypt 2018). The gap was confirmed by the authors, and there seems to be no simple patch for it. We provide new, fixed proofs for the affected CMA-to-NMA reduction, both for the ROM and the QROM, and we perform a concrete security analysis for the case of Dilithium to show that the claimed security level is still valid after addressing the gap. Furthermore, we offer a fully mechanized ROM proof for the CMA-security of Dilithium in the EasyCrypt proof assistant. Our formalization includes several new tools and techniques of independent interest for future formal verification results.

This work presents a novel machine-checked tight security proof for XMSS --- a stateful hash-based signature scheme that is (1) standardized in RFC 8391 and NIST SP 800-208, and (2) employed as a primary building block of SPHINCS+, one of the signature schemes recently selected for standardization as a result of NIST's post-quantum competition. In 2020, Kudinov, Kiktenko, and Fedoro pointed out a flaw affecting the tight security proofs of SPHINCS+ and XMSS. For the case of SPHINCS+, this flaw was fixed in a subsequent tight security proof by Hülsing and Kudinov. Unfortunately, employing the fix from this proof to construct an analogous tight security proof for XMSS would merely demonstrate security with respect to an insufficient notion. At the cost of modeling the message-hashing function as a random oracle, we complete the tight security proof for XMSS and formally verify it using the EasyCrypt proof assistant. (Note that this merely extends the use of the random oracle model, as this model is already required in other parts of the security analysis to justify the currently standardized parameter values). As part of this endeavor, we formally verify the crucial step common to the security proofs of SPHINCS+ and XMSS that was found to be flawed before, thereby confirming that the core of the aforementioned security proof by Hülsing and Kudinov is correct. As this is the first work to formally verify proofs for hash-based signature schemes in EasyCrypt, we develop several novel libraries for the fundamental cryptographic concepts underlying such schemes --- e.g., hash functions and digital signature schemes --- establishing a common starting point for future formal verification efforts. These libraries will be particularly helpful in formally verifying proofs of other hash-based signature schemes such as LMS or SPHINCS+.

In this paper we present the first formally verified implementations of Kyber and, to the best of our knowledge, the first such implementations of any post-quantum cryptosystem. We give a (readable) formal specification of Kyber in the EasyCrypt proof assistant, which is syntactically very close to the pseudocode description of the scheme as given in the most recent version of the NIST submission. We present high-assurance open-source implementations of Kyber written in the Jasmin language, along with machine-checked proofs that they are functionally correct with respect to the EasyCrypt specification. We describe a number of improvements to the EasyCrypt and Jasmin frameworks that were needed for this implementation and verification effort, and we present detailed benchmarks of our implementations, showing that our code achieves performance close to existing hand-optimized implementations in C and assembly.

We carry out the first provable security analysis of the new FIDO2 protocols, the promising FIDO Alliance’s proposal for a standard for passwordless user authentication. Our analysis covers the core components of FIDO2: the W3C’s Web Authentication (WebAuthn) specification and the new Client-to-Authenticator Protocol (CTAP2). Our analysis is modular. For WebAuthn and CTAP2, in turn, we propose appropriate security models that aim to capture their intended security goals and use the models to analyze their security. First, our proof confirms the authentication security of WebAuthn. Then, we show CTAP2 can only be proved secure in a weak sense; meanwhile, we identify a series of its design flaws and provide suggestions for improvement. To withstand stronger yet realistic adversaries, we propose a generic protocol called sPACA and prove its strong security; with proper instantiations, sPACA is also more efficient than CTAP2. Finally, we analyze the overall security guarantees provided by FIDO2 and WebAuthn+sPACA based on the security of their components. We expect that our models and provable security results will help clarify the security guarantees of the FIDO2 protocols. In addition, we advocate the adoption of our sPACA protocol as a substitute for CTAP2 for both stronger security and better performance.

The algebraic-group model (AGM), which lies between the generic group model and the standard model of computation, provides a means by which to analyze the security of cryptosystems against so-called algebraic adversaries. We formalize the AGM within the framework of universal composability, providing formal definitions for this setting and proving an appropriate composition theorem. This extends the applicability of the AGM to more-complex protocols, and lays the foundations for analyzing algebraic adversaries in a composable fashion. Our results also clarify the meaning of composing proofs in the AGM with other proofs and they highlight a natural form of independence between idealized groups that seems inherent to the AGM and has not been made formal before---these insights also apply to the composition of game-based proofs in the AGM. We show the utility of our model by proving several important protocols universally composable for algebraic adversaries, specifically: (1) the Chou-Orlandi protocol for oblivious transfer, and (2) the SPAKE2 and CPace protocols for password-based authenticated key exchange.

Protocols for password authenticated key exchange (PAKE) allow two parties who share only a weak password to agree on a cryptographic key. We revisit the notion of PAKE in the universal composability (UC) framework, and propose a relaxation of the PAKE functionality of Canetti et al. that we call lazy-extraction PAKE (lePAKE). Our relaxation allows the ideal-world adversary to postpone its password guess until after a session is complete. We argue that this relaxed notion still provides meaningful security in the password-only setting. As our main result, we show that several PAKE protocols that were previously only proven secure with respect to a ``game-based'' definition of security can be shown to UC-realize the lePAKE functionality in the random-oracle model. These include SPEKE, SPAKE2, and TBPEKE, the most efficient PAKE schemes currently known.

We study Authenticated Encryption with Associated Data (AEAD) from the viewpoint of composition in arbitrary (single-stage) environments. We use the indifferentiability framework to formalize the intuition that a “good” AEAD scheme should have random ciphertexts subject to decryptability. Within this framework, we can then apply the indifferentiability composition theorem to show that such schemes offer extra safeguards wherever the relevant security properties are not known, or cannot be predicted in advance, as in general-purpose crypto libraries and standards.We show, on the negative side, that generic composition (in many of its configurations) and well-known classical and recent schemes fail to achieve indifferentiability. On the positive side, we give a provably indifferentiable Feistel-based construction, which reduces the round complexity from at least 6, needed for blockciphers, to only 3 for encryption. This result is not too far off the theoretical optimum as we give a lower bound that rules out the indifferentiability of any construction with less than 2 rounds.