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

### Shi Bai, Adeline Langlois, Tancrède Lepoint, Damien Stehlé, Ron Steinfeld

Abstract: The Rényi divergence is a mean to measure the
closeness of two 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.
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