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**2015/483**

**Title:**

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

**Authors:**
Shi Bai, Adeline Langlois, Tancrëde Lepoint, Amin Sakzad, Damien Stehle, 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.

**ePrint:**
https://eprint.iacr.org/2015/483

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