International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Olivier Blazy

Publications

Year
Venue
Title
2020
ASIACRYPT
Public-Key Generation with Verifiable Randomness 📺
We revisit the problem of proving that a user algorithm selected and correctly used a truly random seed in the generation of her cryptographic key. A first approach was proposed in 2002 by Juels and Guajardo for the validation of RSA secret keys. We present a new security model and general tools to efficiently prove that a private key was generated at random according to a prescribed process, without revealing any further information about the private key. We give a generic protocol for all key-generation algorithms based on probabilistic circuits and prove its security. We also propose a new protocol for factoring-based cryptography that we prove secure in the aforementioned model. This latter relies on a new efficient zero-knowledge argument for the double discrete logarithm problem that achieves an exponential improvement in communication complexity compared to the state of the art, and is of independent interest.
2019
EUROCRYPT
Durandal: A Rank Metric Based Signature Scheme 📺
We describe a variation of the Schnorr-Lyubashevsky approach to devising signature schemes that is adapted to rank based cryptography. This new approach enables us to obtain a randomization of the signature, which previously seemed difficult to derive for code-based cryptography. We provide a detailed analysis of attacks and an EUF-CMA proof for our scheme. Our scheme relies on the security of the Ideal Rank Support Learning and the Ideal Rank Syndrome problems and a newly introduced problem: Product Spaces Subspaces Indistinguishability, for which we give a detailed analysis. Overall the parameters we propose are efficient and comparable in terms of signature size to the Dilithium lattice-based scheme, with a signature size of 4 kB for a public key of size less than 20 kB.
2018
PKC
Hash Proof Systems over Lattices Revisited
Hash Proof Systems or Smooth Projective Hash Functions (SPHFs) are a form of implicit arguments introduced by Cramer and Shoup at Eurocrypt’02. They have found many applications since then, in particular for authenticated key exchange or honest-verifier zero-knowledge proofs. While they are relatively well understood in group settings, they seem painful to construct directly in the lattice setting.Only one construction of an SPHF over lattices has been proposed in the standard model, by Katz and Vaikuntanathan at Asiacrypt’09. But this construction has an important drawback: it only works for an ad-hoc language of ciphertexts. Concretely, the corresponding decryption procedure needs to be tweaked, now requiring q many trapdoor inversion attempts, where q is the modulus of the underlying Learning With Errors (LWE) problem.Using harmonic analysis, we explain the source of this limitation, and propose a way around it. We show how to construct SPHFs for standard languages of LWE ciphertexts, and explicit our construction over a tag-IND-CCA2 encryption scheme à la Micciancio-Peikert (Eurocrypt’12). We then improve our construction and our analysis in the case where the tag is known in advance or fixed (in the latter case, the scheme is only IND-CPA) with a super-polynomial modulus, to get a stronger type of SPHF, which was never achieved before for any language over lattices.Finally, we conclude with applications of these SPHFs: password-based authenticated key exchange, honest-verifier zero-knowledge proofs, and a relaxed version of witness encryption.
2016
ASIACRYPT
2016
ASIACRYPT
2015
EPRINT
2015
EPRINT
2015
EPRINT
2015
EPRINT
2015
PKC
2014
CRYPTO
2014
EPRINT
2013
PKC
2013
CRYPTO
2013
ASIACRYPT
2012
TCC
2011
PKC
2010
EPRINT
Batch Groth-Sahai
In 2008, Groth and Sahai proposed a general methodology for constructing non-interactive zero-knowledge (and witness-indistinguishable) proofs in bilinear groups. While avoiding expensive NP-reductions, these proof systems are still inefficient due to a number of pairing computations required for verification. We apply recent techniques of batch verification to the Groth-Sahai proof systems and manage to improve significantly the complexity of proof verification. We give explicit batch verification formulas for generic Groth-Sahai equations (whose cost is less than a tenth of the original) and also for specific popular protocols relying on their methodology (namely Groth's group signatures and Belenkiy-Chase-Kohlweiss-Lysyanskaya's P-signatures).

Program Committees

Asiacrypt 2020
Asiacrypt 2019