Cryptology ePrint Archive: Report 2017/298

An Investigation of Sources of Randomness Within Discrete Gaussian Sampling

Séamus Brannigan and Neil Smyth and Tobias Oder and Felipe Valencia and Elizabeth O’Sullivan and Tim Güneysu and Francesco Regazzoni

Abstract: This paper presents a performance and statistical analysis of random number generators and discrete Gaussian samplers implemented in software. Most Lattice-based cryptographic schemes utilise discrete Gaussian sampling and will require a quality random source. We examine a range of candidates for this purpose, including NIST DRBGs, stream ciphers and well-known PRNGs. The performance of these random sources is analysed within 64-bit implementations of Bernoulli, CDT and Ziggurat sampling. In addition we perform initial statistical testing of these samplers and include an investigation into improper seeding issues and their effect on the Gaussian samplers. Of the NIST approved Deterministic Random Bit Generators (DRBG), the AES based CTR-DRBG produced the best balanced performance in our tests.

Category / Keywords: implementation / Lattice-based cryptography, Discrete Gaussian sampling, randomness, software

Date: received 31 Mar 2017, last revised 25 Apr 2017

Contact author: e osullivan at qub ac uk

Available format(s): PDF | BibTeX Citation

Note: Clarification of use of 64-bit precision. The author's would like to thank Michael Walter for his very helpful and insightful comments.

Version: 20170425:154731 (All versions of this report)

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