Abstract

Computational problems from elliptic curve isogeny graphs were recent recognized as the new source of hardness in building post-quantum cryptography. In this work we explore more hard problems from isogeny graphs by looking at the isogeny graphs defined over RSA moduli. Although the problems are no longer hard against quantum computers, they provide more interesting cryptographic capabilities secure against classical computers. In particular, based on the conjectured hardness of these new problems, we provide candidate constructions of groups with infeasible inversion.

Recall that in a group with infeasible inversion, computing the inverse of a group element is required to be hard, while performing the group operation is easy. Motivated by the potential cryptographic application of building a directed transitive signature scheme, the search for a group with infeasible inversion was initiated in the theses of Hohenberger and Molnar (2003). Later it was also shown to provide a broadcast encryption scheme by Irrer et al. (2004). However, to date the only case of a group with infeasible inversion is implied by the strong assumption of indistinguishability obfuscation (iO). Our construction gives a candidate without using the heavy machinery of iO.

In the talk I will give an introduction of the basic application of isogeny graphs in cryptography. No background of elliptic curve is required.

Based on the joint work with Salim Ali Altug from Boston University.

Time

11月19日  14:00--15:00

Speaker

Yilei joined Visa Research in June 2018. Prior to joining Visa, he received his PhD in March 2018 from Boston University under the supervision of Professor Ran Canetti and Professor Leonid Reyzin.

His research area is cryptography and cryptanalysis, specifically in lattice-based cryptography, multilinear maps and program obfuscation. During his PhD he interned at SRI International, and visited Tel Aviv University, IST Austria, IBM Research, and ENS.

Venue

信息管理与工程学院602室

上海财经大学（第三教学楼西侧）

上海市杨浦区武东路100号