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 Tancrëde 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 25 Feb 2018

Contact author: ron steinfeld at monash edu

Available format(s): PDF | BibTeX Citation

Note: Added a correction to our claims in a previous version regarding the first dimension-preserving reduction for LWR: we have recently become aware that [BGM+16] already gave a dimension-preserving reduction for prime modulus q. Our reduction works for composite q.

Version: 20180225:082611 (All versions of this report)

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