Description
Lattice signature schemes generally require particular care when it comes to preventing secret information from leaking through signature transcript. For example, the Goldreich-Goldwasser-Halevi (GGH) signature scheme and the NTRUSign scheme were completely broken by the parallelepiped-learning attack of Nguyen and Regev (Eurocrypt 2006). Several heuristic countermeasures were also shown vulnerable to similar statistical attacks.<br/> At PKC 2008, Plantard, Susilo and Win proposed a new variant of GGH, informally arguing resistance to such attacks. Based on this variant, Plantard, Sipasseuth, Dumondelle and Susilo proposed a concrete signature scheme, called DRS, that has been accepted in the round 1 of the NIST post-quantum cryptography project. In this work, we propose yet another statistical attack and demonstrate a weakness of the DRS scheme: one can recover some partial information of the secret key from sufficiently many signatures. One difficulty is that, due to the DRS reduction algorithm, the relation between the statistical leak and the secret seems more intricate. We work around this difficulty by training a statistical model, using a few features that we designed according to a simple heuristic analysis.<br/> While we only recover partial information on the secret key, this information is easily exploited by lattice attacks, significantly decreasing their complexity. Concretely, we claim that, provided that 100,000 signatures are available, the secret key may be recovered using BKZ-138 for the first set of DRS parameters submitted to the NIST. This puts the security level of this parameter set below 80-bits (maybe even 70-bits), to be compared to an original claim of 128-bits. lien: rien
Next sessions
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Efficient zero-knowledge proofs and arguments in the CL framework
Speaker : 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
Speaker : 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
Speaker : 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[…] -
Cycles of pairing-friendly abelian varieties
Speaker : Maria Corte-Real Santos - ENS Lyon
A promising avenue for realising scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. More specifically, such a cycle consists of two elliptic curves E/Fp and E’/Fq that both have a low embedding degree and also satisfy q = #E(Fp) and p = #E’(Fq). These constraints turn out to be rather restrictive; in the decade that has passed since 2-cycles were first[…]-
Cryptography
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