Post-Quantum Signature Scheme on Commutative Algebras

Using two 3-dimensional finite algebras with commutative and associative multiplication operation as a single algebraic support, a post-quantum digital signature scheme is developed, which is characterized in exploiting the 3-dimensional cyclicity of the multiplicative groups of the algebras. The security of the introduced signature algorithm is based on the computational comlexity of the hidden logarithm problem given simultaneously in two finite algebras. Doubling the signature verification equation and scalar multiplications are used as particular design techniques. The advantage of the developed algorithm is the comparatively small sizes of the public key and signature.