Sampling from Arbitrary Centered Discrete Gaussians for Lattice-Based Cryptography

Carlos Aguilar Melchor (1) , Martin R. Albrecht (2) , Thomas Ricosset (1, 3)

1 IRIT-RMESS - Réseaux, Mobiles, Embarqués, Sans fil, Satellites
2 RHUL - Royal Holloway [University of London]
3 THALES COMMUNICATIONS & SECURITY

Non-Centered Discrete Gaussian sampling is a fundamental building block in many lattice-based constructions in cryptography, such as signature and identity-based encryption schemes. On the one hand, the center-dependent approaches, e.g. cumulative distribution tables (CDT), Knuth-Yao, the alias method, discrete Zigurat and their variants, are the fastest known algorithms to sample from a discrete Gaussian distribution. However, they use a relatively large precomputed table for each possible real center in [0,1) making them impracticable for non-centered discrete Gaussian sampling. On the other hand, rejection sampling allows to sample from a discrete Gaussian distribution for all real centers without prohibitive precomputation cost but needs costly floating-point arithmetic and several trials per sample. In this work, we study how to reduce the number of centers for which we have to precompute tables and propose a non-centered CDT algorithm with practicable size of precomputed tables as fast as its centered variant. Finally, we provide some experimental results for our open-source C++ implementation indicating that our sampler increases the rate of Peikert’s algorithm for sampling from arbitrary lattices (and cosets) by a factor 3 with precomputation storage up to 6.2 MB.

Mots clés: Non-centered CDT algorithm; Cryptography; Lattice-based constructions; Discrete Gaussian distribution

Domaines: Réseaux et télécommunications [cs.NI]; Système d'exploitation [cs.OS]; Architectures Matérielles [cs.AR]; Systèmes embarqués

Carlos Aguilar Melchor, Martin R. Albrecht, Thomas Ricosset. Sampling from Arbitrary Centered Discrete Gaussians for Lattice-Based Cryptography. International Conference on Applied Cryptography and Network Security (ACNS 2017), Jul 2017, Kanazawa, Japan. pp.3-19. ⟨hal-02548105⟩