Simon Lundborg: A study of SQIsign

Abstract: Classical cryptographic schemes are widely used in secure digital communication. Essential to the security of many digital communication protocols are cryptographic signatures, which authorize digital messages. The most common classical cryptographic schemes are vulnerable to algorithms preformed by quantum computers and may need to be replaced. SQIsign (Short Quaternion and Isogeny Signature) is a recently proposed post-quantum cryptographic digital signature scheme based on isogenies between supersingular elliptic curves. In this thesis we present the SQIsign 1.0 protocol, outline the security of the scheme, prove parts of the scheme's soundness, and discuss the scheme in the context of post-quantum cryptography. Lastly we discuss SQIsign 2.0 and recent improvements to the protocol.