Paper 2015/483 Original: eprint.iacr.org/2015/483 ↗
Improved security proofs in lattice-based cryptography: using the Rényi divergence rather than the statistical distance
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.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2018-02-25: last updated
- 2015-05-21: published
- Short URL
- https://ia.cr/2015/483
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2015/483,
author = {Shi Bai and Adeline Langlois and Tancrëde Lepoint and Amin Sakzad and Damien Stehle and Ron Steinfeld},
title = {Improved security proofs in lattice-based cryptography: using the Rényi divergence rather than the statistical distance},
howpublished = {Cryptology {ePrint} Archive, Paper 2015/483},
year = {2015},
url = {https://eprint.iacr.org/2015/483}
}