Paper 2015/483
Improved security proofs in lattice-based cryptography: using the Rényi divergence rather than the statistical distance
Shi Bai, Adeline Langlois, Tancrëde Lepoint, Amin Sakzad, 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.
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.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Contact author(s)
- ron steinfeld @ monash edu
- History
- 2018-02-25: last of 4 revisions
- 2015-05-21: received
- See all versions
- Short URL
- https://ia.cr/2015/483
- License
-
CC BY
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} }