Lattice signatures and bimodal Gaussians

Leo Ducas 1 Alain Durmus 2 Tancrede Lepoint 1, 3 Vadim Lyubashevsky 4
4 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : Our main result is a construction of a lattice-based digital signature scheme that represents an improvement, both in theory and in practice, over today's most efficient lattice schemes. The novel scheme is obtained as a result of a modification of the rejection sampling algorithm that is at the heart of Lyubashevsky's signature scheme (Eurocrypt, 2012) and several other lattice primitives. Our new rejection sampling algorithm which samples from a bimodal Gaussian distribution, combined with a modified scheme instantiation, ends up reducing the standard deviation of the resulting signatures by a factor that is asymptotically square root in the security parameter. The implementations of our signature scheme for security levels of 128, 160, and 192 bits compare very favorably to existing schemes such as RSA and ECDSA in terms of efficiency. In addition, the new scheme has shorter signature and public key sizes than all previously proposed lattice signature schemes. As part of our implementation, we also designed several novel algorithms which could be of independent interest. Of particular note, is a new algorithm for efficiently generating discrete Gaussian samples over ℤ n . Current algorithms either require many high-precision floating point exponentiations or the storage of very large pre-computed tables, which makes them completely inappropriate for usage in constrained devices. Our sampling algorithm reduces the hard-coded table sizes from linear to logarithmic as compared to the time-optimal implementations, at the cost of being only a small factor slower.
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Communication dans un congrès
Canetti, Ran and Garay, Juan A. CRYPTO 2013 - 33rd Annual Cryptology Conference, Aug 2013, Santa Barbara, United States. Springer, 8042, pp.40-56, 2013, Lecture Notes in Computer Science. 〈10.1007/978-3-642-40041-4_3〉
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https://hal.inria.fr/hal-00864298
Contributeur : Vadim Lyubashevsky <>
Soumis le : vendredi 20 septembre 2013 - 17:25:24
Dernière modification le : vendredi 25 mai 2018 - 12:02:05

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Leo Ducas, Alain Durmus, Tancrede Lepoint, Vadim Lyubashevsky. Lattice signatures and bimodal Gaussians. Canetti, Ran and Garay, Juan A. CRYPTO 2013 - 33rd Annual Cryptology Conference, Aug 2013, Santa Barbara, United States. Springer, 8042, pp.40-56, 2013, Lecture Notes in Computer Science. 〈10.1007/978-3-642-40041-4_3〉. 〈hal-00864298〉

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