Speaker: 

Travis Scholl

Institution: 

UCI

Time: 

Tuesday, October 9, 2018 - 3:00pm to 4:00pm

Host: 

Location: 

RH 340P

Elliptic curve cryptography (ECC) is a widely used public key cryptosystem. The security of ECC relies on the difficulty of the elliptic curve discrete log problem (ECDLP). Isogenies are morphisms of curves that can be used to transfer instances of ECDLP between elliptic curves. Suppose that we suspect that some proportion of curves are "weak" in the sense that the ECDLP can be solved quickly. To avoid an attacker moving the ECDLP to a weak curve, we would want to use curves for which it difficult to transfer the ECDLP. In this talk we will introduce the notion of an "isolated" curve. These are curves which do not admit many computable isogenies which obstructs the transferring of the ECDLP.