Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn
as the foundation for secure cryptographic systems. Attractive features of lattice cryptography …

Quantum computers can execute algorithms that dramatically outperform classical
computation. As the best-known example, Shor discovered an efficient quantum algorithm …

Abstract The National Institute of Standards and Technology is in the process of selecting
one or more public-key cryptographic algorithms through a public, competition-like process …

Rapid advances in quantum computing, together with the announcement by the National
Institute of Standards and Technology (NIST) to define new standards for digitalsignature …

Post-quantum cryptosystems should be prepared before the advent of powerful quantum
computers to ensure information secure in our daily life. In 2016 a post-quantum …

We present a new tensoring technique for LWE-based fully homomorphic encryption. While
in all previous works, the ciphertext noise grows quadratically (B → B^ 2 ⋅ poly (n)) with …

We propose the first fully homomorphic encryption scheme, solving an old open problem.
Such a scheme allows one to compute arbitrary functions over encrypted data without the …

We construct a simple fully homomorphic encryption scheme, using only elementary
modular arithmetic. We use Gentry's technique to construct a fully homomorphic scheme …

We show that the Learning with Errors (LWE) problem is classically at least as hard as
standard worst-case lattice problems. Previously this was only known under quantum …

Our main result is a reduction from worst-case lattice problems such as GapSVP and SIVP to
a certain learning problem. This learning problem is a natural extension of the “learning from …