International Association
for Cryptologic Research

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.

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.

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.

In this paper we revisit the problem of erasing sensitive data from memory and registers during return from a cryptographic routine. While the problem and related attacker model is fairly easy to phrase, it turns out to be surprisingly hard to guarantee security in this model when implementing cryptography in common languages such as C/C++ or Rust. We revisit the issues surrounding zeroization and then present a principled solution in the sense that it guarantees that sensitive data is erased and it clearly defines when this happens. We implement our solution as extension to the formally verified Jasmin compiler and extend the correctness proof of the compiler to cover zeroization. We show that the approach seamlessly integrates with state-of-the-art protections against microarchitectural attacks by integrating zeroization into Libjade, a cryptographic library written in Jasmin with systematic protections against timing and Spectre-v1 attacks. We present benchmarks showing that in many cases the overhead of zeroization is barely measurable and that it stays below 2% except for highly optimized symmetric crypto routines on short inputs.

Recently, numerous physical attacks have been demonstrated against lattice-based schemes, often exploiting their unique properties such as the reliance on Gaussian distributions, rejection sampling and FFT-based polynomial multiplication. As the call for concrete implementations and deployment of postquantum cryptography becomes more pressing, protecting against those attacks is an important problem. However, few countermeasures have been proposed so far. In particular, masking has been applied to the decryption procedure of some lattice-based encryption schemes, but the much more difficult case of signatures (which are highly nonlinear and typically involve randomness) has not been considered until now. In this paper, we describe the first masked implementation of a lattice-based signature scheme. Since masking Gaussian sampling and other procedures involving contrived probability distributions would be prohibitively inefficient, we focus on the GLP scheme of Güneysu, Lyubashevsky and Pöppelmann (CHES 2012). We show how to provably mask it in the Ishai–Sahai–Wagner model (CRYPTO 2003) at any order in a relatively efficient manner, using extensions of the techniques of Coron et al. for converting between arithmetic and Boolean masking. Our proof relies on a mild generalization of probing security that supports the notion of public outputs. We also provide a proof-of-concept implementation to assess the efficiency of the proposed countermeasure.

We propose a new approach for building efficient, provably secure, and practically hardened implementations of masked algorithms. Our approach is based on a Domain Specific Language in which users can write efficient assembly implementations and fine-grained leakage models. The latter are then used as a basis for formal verification, allowing for the first time formal guarantees for a broad range of device-specific leakage effects not addressed by prior work. The practical benefits of our approach are demonstrated through a case study of the PRESENT S-Box: we develop a highly optimized and provably secure masked implementation, and show through practical evaluation based on TVLA that our implementation is practically resilient. Our approach significantly narrows the gap between formal verification of masking and practical security.

We initiate the study of principled, automated methods for analyzing hardness assumptions in generic group models, following the approach of symbolic cryptography. We start by defining a broad class of generic and symbolic group models for different settings—symmetric or asymmetric (leveled) k -linear groups—and by proving “computational soundness” theorems for the symbolic models. Based on this result, we formulate a very general master theorem that formally relates the hardness of a (possibly interactive) assumption in these models to solving problems in polynomial algebra. Then, we systematically analyze these problems. We identify different classes of assumptions and obtain decidability and undecidability results. Next, we develop and implement automated procedures for verifying the conditions of master theorems, and thus the validity of hardness assumptions in generic group models. The concrete outcome of this work is an automated tool which takes as input the statement of an assumption and outputs either a proof of its generic hardness or shows an algebraic attack against the assumption.