PolarSig: An efficient digital signature based on polar codes

Abstract

Code-based digital signatures suffer from two main drawbacks: large public key size and slow signature generation. Large public key size is inherent in almost all the code-based cryptosystems and other post-quantum alternatives; however, slow signature generation is due to their specific structure. Most of the current code-based signature schemes are constructed based on Courtois, Finiasz, and Sendrier (CFS) signature. CFS uses a counter to produce decodable syndromes or the complete decoding technique that imposes some extra computational cost to the signing algorithm for many choices of codes. In this study, the authors propose an efficient digital signature, PolarSig, which can reduce both public key size and signing time simultaneously. PolarSig uses some specific instances of polar codes that enable us to decode every random syndrome. Moreover, they apply puncturing and randomised omitting of frozen bits to protect the authors’ scheme from commonplace attacks targeting former cryptosystems based on polar codes. Besides, they prove that their signature is existentially unforgeable under a chosen message attack secure in the random oracle model.