Oblivious Transfer (OT) is a central primitive in secure computation. To limit the number of communications, random OT-correlated pairs can be generated silently, i.e., non-interactively, notably using Pseudorandom Correlation Functions (PCFs). While some of these constructions rely on group-based assumptions, notoriously broken by Shor's algorithm, several others are believed to be quantum-secure. In this talk, we present a work that leverages an existing CPRF-to-PCF compiler to obtain a post-quantum PCF for OT from isogeny-based assumptions. This yields the most compact post-quantum silent OT construction to date, and the first whose security is rigorously proven in the QROM. Along the way, we use this result to illustrate a general principle: many classical group-based protocols can be systematically translated into post-quantum ones by re-expressing them via group actions and instantiating them with isogenies. The remaining core challenge is then to establish the security of the resulting scheme in this new setting.
Arthur Herlédan Le Merdy is a postdoctoral researcher at COSIC, KU Leuven, Belgium. His research focuses on post-quantum cryptography, with a particular emphasis on isogeny-based cryptography, including the relationships between the various hard problems underlying the field, and the design of new cryptographic protocols built from them.