Microsoft Launch SEAL

It is not just the HEAT project which is working on trying to find applications of Somewhat Homomorphic Encryption in practice; others around the world are also doing this. In particular Microsoft Research Labs have just announced a project called SEAL(Simple Encrypted Arithmetic Library) which is detailed in the following paper: http://research.microsoft.com/pubs/258435/ManualHE.pdf with code available here http://sealcrypto.codeplex.com/

The Microsoft work is aimed at medical information, in particular bioinfomatics algorithms related to genomic data. The SEAL project is built around the YASHE SHE scheme based on the cyclotomic ring defined by $X^n+1$, for $n$ a power of two. The associated paper explains how large integers and floating point operations can be encoded within the YASHE scheme.

Using the Rényi divergence rather than the statistical distance in lattice-based cryptography

To analyze the efficiency of the homomorphic encryption schemes at the core of the HEAT project, we studied how the Rényi divergence can be used instead of the statistical distance. The Rényi divergence is a measure of closeness of two probability distributions. In the HEAT project, we obtained that the latter divergence can often be used as an alternative to the statistical distance in security proofs for lattice-based cryptography, and therefore in homomorphic encryption schemes.

Our contributions are as follows:

• Smaller signatures for the Hash-and-Sign Gentry-Peikert-Vaikuntanathan signature scheme
• Smaller storage requirement for the Fiat-Shamir BLISS signature scheme
• Alternative proof that the Learning With Errors problem with noise chosen uniformly in an interval is no easier than the Learning With Errors problem with Gaussian noise (and tighter reduction!)
• Smaller parameters for the dual-Regev encryption scheme

and are described in the article

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

Shi Bai and Adeline Langlois and Tancrède Lepoint and Damien Stehlé and Ron Steinfeld

This article has been accepted for publication at ASIACRYPT 2015 and will receive the Best Paper Award.

ASIACRYPT 2015 is one of the top-tier conference of cryptography, organized by the IACR, and will take place in December 2015 in New Zealand.