## La Trobe-Kyushu Joint Seminar on Mathematics for Industry (11)

Jan. 12, 2016

**La Trobe-Kyushu Joint Seminar on Mathematics for Industry (11)**

**Date & Time : Jan. 12, 2016 14:00(Australian time) / 12:00(Japan time)****Venue: IMI Australia Branch in La Trobe University / C512 Middle Lecture Room, IMI, Kyushu University****Title: Security Evaluation of Public-Key Cryptography****Speaker: Professor Tsuyoshi Takagi, Institute of Mathematics for Industry, Kyushu University**

Abstract:

The security of public-key cryptography is based on the hardness of some mathematical problems such as the integer factorization problem (IFP), the discrete logarithm problem (DLP). However, some efficient algorithms for solving the problems have been developed in 80's such as number

field sieve and elliptic curve method. In 1994, Shor proposed a quantum polynomial time algorithm for solving the IFP and DLP, and thus the widely used public-key cryptography (RSA cryptosystem and elliptic curve cryptography) become vulnerable eventually. In this talk, we give an overview of the recent research on the post-quantum cryptography (PQC), which is still secure in the era of quantum computer. Interestingly, PQC is constructed by some new mathematical problems such as the shortest vector problem over lattices, the problem of solving multivariate polynomial system, the isogney problem of elliptic curve cryptography.