On Provably Secure Code-Based Signature and Signcryption Scheme

Signcryption is a cryptographic protocol that provides authentication and confidentiality as a single primitive at a cost lower than the combined cost of sign and encryption. Due to the improved efficiency, signcryption schemes have found significant applications in areas related to E-commerce. Shor’s algorithm [22] poses a threat to number-theoretic algorithms, as it can solve the number-theoretic hard problems in polynomial time using quantum computers. Therefore, code-based cryptography offers an exciting alternative to number-theoretic cryptography, as it is not only resistant to quantum algorithms, but also, the base operation (matrix-vector multiplication) is far less computationally intensive compared to the modular exponentiation required in number-theoretic schemes. Courtois, Finiasz and Sendrier proposed the only practical code-based signature(CFS signature) [7]. It can be used to realise many cryptographic primitives. But the signature is currently not provably secure due to the existence of the high rate distinguisher [11]. In this paper, we make use of an alternate key-construct for the CFS signature, and thus prove its existential unforgeability under chosen message attacks (EUF-CMA). Also, we propose a code-based signcryption scheme and proved its security. To the best of our knowledge, this is the first code-based, provably secure signature and signcryption scheme in literature.