OTRU: A Non-Associative and High Speed Public Key Cryptosystem

In this paper, we propose OTRU, a high speed probabilistic multi-dimensional public key cryptosystem that encrypts eight data vectors in each encryption round. The underlying algebraic structure of the proposed scheme is the power-associative and alternative octonions algebra which can be defined over any Dedekind domain such as convolution polynomial ring. The proposed public key cryptosystem relies for its inherent security on the difficulty of the shortest vector problem (SVP) in a non-circular modular lattice. After a brief introduction to Ntr¯ u, we describe the algebraic structure used in the proposed cryptosystem. Further, we provide the details of the key generation, encryption and decryption algorithms and discuss the issues regarding key security, message security, and probability of successful decryption. OTRU has been designed based on the Ntr¯u core and exhibits high levels of parallelism with full operand length. By reducing the dimension of the underlying convolution polynomial ring (N) and using parallelism techniques we can increase the OTRU encryption/decryption speed to a level even higher than Ntr¯ u.