Implementing the Castryck-Decru SIDH Key Recovery Attack in SageMath

Editor’s note: since the publication of this blog post, an expanded and more technical discussion of the implementation process has been written, and is available on eprint: https://eprint.iacr.org/2022/1283. Introduction Last weekend (July 30th) a truly incredible piece of mathematical/cryptanalysis research was put onto eprint. Wouter Castryck and Thomas Decru of KU Leuven published a paper "An … Continue reading Implementing the Castryck-Decru SIDH Key Recovery Attack in SageMath

Estimating the Bit Security of Pairing-Friendly Curves

Introduction The use of pairings in cryptography began in 1993, when an algorithm developed by Menezes, Okamoto and Vanstone, now known as the MOV-attack, described a sub-exponential algorithm for solving the discrete logarithm problem for supersingular elliptic curves.1 It wasn't until the following decade that efficient pairing-based algorithms were used constructively to build cryptographic protocols … Continue reading Estimating the Bit Security of Pairing-Friendly Curves