Generalization of lattice-based cryptography on hypercomplex algebras

Abstract

We propose a fast, probabilistic, multi-dimensional quantum-resistant public key cryptosystem “STRU cryptosystem” relying on sedenion algebra, which is power associative and flexible, but non-associative and non-alternative. STRU cryptosystem encrypts 16 data vectors at each encryption round. It contains all strengths and strong points of NTRU cryptosystem. A new property that is coined as inverse associative property for the basis elements of the sedenion algebra is verified through the computational method, which is needed for the implementation. The encryption/decryption speed of STRU cryptosystem can be increased to a level even higher than NTRU by slow down of the dimension of the underlying convolution polynomial ring and using parallelism techniques.