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