Paper 2021/1619

Code-Based Non-Interactive Key Exchange Can Be Made

Zhuoran Zhang and Fangguo Zhang

Abstract

Code-based cryptography plays an important role in post-quantum cryptography. While many crypto-primitives such as public-key encryption, digital signature have been proposed from codes, there is no non-interactive code-based key exchange protocol. We solve the opening problem of constructing a non-interactive key exchange protocol from coding theory in this work. To prove the security of this protocol, we propose a new hard problem called sub-LE problem, which is a sub-problem of code equivalence problem. We prove its hardness by reducing the well-known code linearly equivalence problem to the sub-LE problem. This new hard problem provides many good properties such as partly commutativity. This excites us most because it allows not only the construction of key exchange protocol, but also many other primitives such as a new public-key encryption scheme.