Cryptology ePrint Archive: Report 2015/483

Improved security proofs in lattice-based cryptography: using the Rényi divergence rather than the statistical distance

Shi Bai and Adeline Langlois and Tancrède Lepoint and Amin Sakzad and Damien Stehle and Ron Steinfeld

Abstract: The Rényi divergence is a measure of closeness of two probability distributions. We show that it can often be used as an alternative to the statistical distance in security proofs for lattice-based cryptography. Using the Rényi divergence is particularly suited for security proofs of primitives in which the attacker is required to solve a search problem (e.g., forging a signature). We show that it may also be used in the case of distinguishing problems (e.g., semantic security of encryption schemes), when they enjoy a public sampleability property. The techniques lead to security proofs for schemes with smaller parameters, and sometimes to simpler security proofs than the existing ones.

Category / Keywords: public-key cryptography /

Date: received 21 May 2015, last revised 31 Aug 2016

Contact author: damien stehle at gmail com

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Version: 20160831:074931 (All versions of this report)

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