| Speaker: Jason LeGrow Affiliation: The University of Auckland Time: 15:00 Thursday, 12 August, 2021 Location: 303-257 |
| Key establishment is a fundamental cryptographic method that allows two parties communicating over an authenticated but public channel to establish a high-entropy shared secret value, called a key. The vast majority of key establishment protocols in widespread use today are based on the Diffie-Hellman problem; such schemes will be vulnerable to attacks by large-scale quantum computers. To counteract this looming threat, cryptographers are developing so-called post-quantum schemes: schemes for which the underlying computational problem is not known to be easily solved on a quantum computer. Post-quantum schemes can be coarsely divided into classes based on the “mathematical domain” of their underlying computational problems. One such class is that of supersingular isogeny-based schemes, whose security is based on the quantum hardness of finding isogenies between pairs of supersingular elliptic curves. There are essentially two varieties of isogeny-based key establishment protocols: those based on the Supersingular Isogeny Diffie-Hellman (SIDH) protocol, and those based on the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) protocol. In recent years, isogeny-based protocols have been the subject of much attention due to their extremely small communication requirements. There have been many works optimizing the protocol specifications and the algorithms used to perform the required computations in both SIDH and CSIDH. In this talk I will discuss some recent developments on optimizing and enhancing SIDH and CSIDH; in particular, methods to construct improved class group action evaluation algorithms and global parameter sets for CSIDH, fault attack countermeasures for CSIDH, and translating some techniques from CSIDH to SIDH to make SIDH faster on single-core devices. |