Simple Lattice Trapdoor Sampling from a Broad Class of Distributions

Vadim Lyubashevsky (1, 2) , Daniel Wichs (3)

1 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
2 LIENS - Laboratoire d'informatique de l'école normale supérieure
3 CSS - College of Computer and Information Science [Boston]

At the center of many lattice-based constructions is an algorithm that samples a short vector s, satisfying [A|AR − HG]s = t mod q where A, AR, H, G are public matrices and R is a trapdoor. Although the algorithm crucially relies on the knowledge of the trapdoor R to perform this sampling efficiently, the distribution it outputs should be independent of R given the public values. We present a new, simple algorithm for performing this task. The main novelty of our sampler is that the distribution of s does not need to be Gaussian, whereas all previous works crucially used the properties of the Gaussian distribution to produce such an s. The advantage of using a non-Gaussian distribution is that we are able to avoid the high-precision arithmetic that is inherent in Gaussian sampling over arbitrary lattices. So while the norm of our output vector s is on the order of √ n to n-times larger (the representation length, though, is only a constant factor larger) than in the samplers of Gentry, Peikert, Vaikuntanathan (STOC 2008) and Micciancio, Peikert (EUROCRYPT 2012), the sampling itself can be done very efficiently. This provides a useful time/output trade-off for devices with constrained computing power. In addition, we believe that the conceptual simplicity and generality of our algorithm may lead to it finding other applications.

Domaines: Cryptographie et sécurité [cs.CR]

Vadim Lyubashevsky, Daniel Wichs. Simple Lattice Trapdoor Sampling from a Broad Class of Distributions. Public Key Cryptography 2015, IACR, Mar 2015, Gaithersburgh, United States. ⟨10.1007/978-3-662-46447-2_32⟩. ⟨hal-01235177⟩