Description
In this talk, I will present a new zero-knowledge proof of knowledge for the syndrome decoding (SD) problem on random linear codes. Instead of using permutations like most of the existing protocols, we rely on the MPC-in-the-head paradigm in which we reduce the task of proving the low Hamming weight of the SD solution to proving some relations between specific polynomials. Specifically, we propose a 5-round zero-knowledge protocol that proves the knowledge of a vector x such that y=Hx and wt(x)<= w and which achieves a soundness error closed to 1/N for an arbitrary N.<br/> While turning this protocol into a signature scheme, we achieve a signature size of 11-12 KB for 128-bit security when relying on the hardness of the SD problem on binary fields. Using larger fields (like F_{256}), we can produce fast signatures of around 8 KB. This allows us to outperform Picnic3 and to be competitive with SPHINCS+, both post-quantum signature candidates in the ongoing NIST standardization effort. Since the security relies on the hardness of the syndrome decoding problem for random linear codes which is known to be NP-hard and for which the cryptanalysis state of the art has been stable for many years, it results in a conservative signature scheme. Moreover, our scheme outperforms all the existing code-based signature schemes for the common « signature size + public key size » metric.<br/> Joint work with Antoine Joux and Matthieu Rivain.<br/> lien: https://seminaire-c2.inria.fr/
Prochains exposés
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Efficient zero-knowledge proofs and arguments in the CL framework
Orateur : Agathe Beaugrand - Institut de Mathématiques de Bordeaux
The CL encryption scheme, proposed in 2015 by Castagnos and Laguillaumie, is a linearly homomorphic encryption scheme, based on class groups of imaginary quadratic fields. The specificity of these groups is that their order is hard to compute, which means it can be considered unknown. This particularity, while being key in the security of the scheme, brings technical challenges in working with CL,[…] -
Constant-time lattice reduction for SQIsign
Orateur : Sina Schaeffler - IBM Research
SQIsign is an isogeny-based signature scheme which has recently advanced to round 2 of NIST's call for additional post-quantum signatures. A central operation in SQIsign is lattice reduction of special full-rank lattices in dimension 4. As these input lattices are secret, this computation must be protected against side-channel attacks. However, known lattice reduction algorithms like the famous[…] -
Circuit optimisation problems in the context of homomorphic encryption
Orateur : Sergiu Carpov - Arcium
Fully homomorphic encryption (FHE) is an encryption scheme that enables the direct execution of arbitrary computations on encrypted data. The first generation of FHE schemes began with Gentry's groundbreaking work in 2019. It relies on a technique called bootstrapping, which reduces noise in FHE ciphertexts. This construction theoretically enables the execution of any arithmetic circuit, but[…] -
TBD
Orateur : Maria Corte-Real Santos - ENS Lyon
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Cryptography
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