Abstract
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 Shorโs 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 DiffieโHellman (๐ข๐ฒ๐ฒ๐จ๐ฃ๐ฃ๐ง), Group Action Inverse Problem (๐ฆ๐ ๐จ๐ฏ) and Commutative Supersingular Isogeny Knowledge of Exponent (๐ข๐ฒ๐ฒ๐จ๐ช๐ฎ๐ค). It achieves ๐จ๐ญ๐ฃ โ ๐ข๐ข๐ and ๐ค๐ด๐ฅ โ ๐ข๐ฌ๐ security. Ciphertext size in this scheme turns out to be 16622.05 bytes for ๐128 and 12757.45 bytes for ๐256 to achieve NIST-1 level of security.
