Post-quantum secure signature schemes from isogenies

Most public-key cryptography that is deployed in today’s systems is susceptible to attacks by quantum computers. With increasing investment in the development of large-scale quantum computers, it is important to develop cryptography that is secure against both classical and quantum attacks. Considering this, in 2016, NIST began an effort to standardise post-quantum secure key exchange mechanisms and signature schemes. In this talk, we will focus on signature schemes, and introduce SQIsign, the only isogeny-based signature scheme that was submitted to NISTs recent alternate call for signatures and boasts the smallest combined signature and public key sizes. We will discuss the benefits and drawbacks of SQIsign compared to other post-quantum secure signatures, and present joint work (with Jonathan Komada Eriksen, Michael Meyer and Krijn Reijnders) to obtain faster verification for SQIsign.