A post-quantum signcryption scheme using isogeny based cryptography

Signcryption is an important cryptographic scheme which is used for both confidentiality and unforgeability. It has many interesting practical applications. Enormous growth of quantum computers makes a warning to the existing classical signcryption schemes due to Shor's algorithm. As a result, designing signcryption schemes, which can withstand quantum attack, is an interesting direction of research. Isogeny based cryptography (IBC) is an ideal post-quantum candidate that can be employed to build a quantum computer immune signcryption scheme. Less communication cost and a smaller public key is the main advantage of IBC compared to other post quantum cryptographic branches. In this paper, we design the first signcryption employing IBC. Our scheme is relying on three hard problems: Commutative Supersingular Isogeny Decisional Diffie-Hellman (CSSIDDH), Group Action Inverse Problem (GAIP) and Commutative Supersingular Isogeny Knowledge of Exponent (CSSIKOE). It achieves IND - CCA and EUF - CMA security. Ciphertext size in this scheme turns out to be 16622.05 bytes for p(128) and 12757.45 bytes for p(256) to achieve NIST-1 level of security.