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An introduction to lattice-based post-quantum cryptography

Seminario: venerdì 31 maggio 2019 alle 13:45
Aula beta - Via Celoria 18
Speaker: Nadir Murru, Università degli Studi di Torino
Responsabile scientifico: Andrea Visconti

Abstract

The development of quantum computers is a great threat for the public key cryptosystems, like RSA, which are based on the difficulty of the factorization of an integer and the evaluation of the discrete logarithm. Indeed, in 1994 Shor exhibited a quantum algorithm that is able to efficiently factorize large integer numbers. Thus, the cryptographic community is working on the study of new asymmetric schemes whose security is based on problems which are "difficult" to solve also using quantum computers. Some of these schemes are based on the properties of lattices and in particular on the problem of finding the shortest vector and on the so called "Ring Learning with Errors" problem. In this talk, we will see all the mathematical basis for understanding these problems on lattices. Moreover, we will see in details one of the main public key scheme developed on lattices, which is NTRU.

Short bio:

Nadir Murru is researcher at the Department of Mathematics of the Turin University. He received his PhD in 2011 with a thesis about periodic representations and rational approximations of algebraic irrationalities. Afterwards, he was research fellow at the CNR of Pisa and at the University of Turin, studying topic of algebra and its applications, and at the Politecnico of Turin in a project regarding post quantum cryptography. His research topics concern Diophantine approximation, continued fractions and their generalizations, combinatorial transformation of sequences in rings, applications of number theory in cryptography with a special focus on RSA-like schemes. He is author or co-author of more than 40 research papers in these fields.

29 maggio 2019
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