A Supersingular Elliptic Curve Isogeny-Based Quantum Resistant Cryptographic Key Exchange Scheme

Abstract

In the past decades, cryptographers tried to validate that a cryptographic universe exists by instantiating its components from concrete computational assumptions. Presently, a large set of public key primitives is built from Deffie Hellman (DH), factorization and lattice-based assumptions. Unfortunately, no corresponding amount of progress is made in building such a large set of crypto primitives from quantum cryptosystem derivatives including code based, multi-variate based, or isogeny-based assumptions. This retarded progress is attributed to the quantum-based primitives not being mainstream assumptions yet. This is not good for the security requirement of the future as the DH or factorization assumptions are not post-quantum secure. Additionally, it is unwise to trust one single post-quantum solution given the recent advances in lattices cryptanalysis. Therefore, it is wise to diversify the set of possible post-quantum secure assumptions to build rich crypto primitives. In readiness for a possible cryptographic tsunami in the next couple of years, we propose a post quantum key exchange scheme based on supersingular elliptic curve isogeny known as Quantum Resistant Supersingular Isogeny Key Exchange scheme, which is based on eSIDH. The scheme employs Montgomery and Edward models that allow performing arithmetic operations faster.