Key Exchange Protocol Based on Permuted Goppa Syndrome Decoding Problem

Abstract

Code-based cryptography has been one of the main approaches of post-quantum cryptography and primitives that are based on the hardness of Permuted Goppa Syndrome Decoding Problem is still the mainstream of code-based primitives construction. However, code-based key exchange protocols introduced such as Ouroboros that restrict the structure of the error pattern lacks flexibility when used in association with such primitives. Thus, in this paper, we introduce a new code-based key exchange protocol that is constructed based on the hardness of Permuted Goppa Syndrome Decoding Problem. The proposed protocol gives more flexibility especially when used in association with any primitives constructed based on Permuted Goppa Syndrome Decoding Problem. A comprehensive security of such protocol is provided and the protocol is secured under the CK model.