A new non-associative cryptosystem based on NTOW public key cryptosystem and octonions algebra

Extended abstract In this work, we present a public key cryptosystem, called OTWO, based on octonions algebra and NTWO cryptosystem We change the underlying algebraic structure of NTWO and use a different lattice for key generation and decryption that it increases complexity of decryption. Furthermore, the nonassociativity of underlying algebraic structure and existence of different lattice for key generation and decryption improve the security of cryptosystem markedly. Method: The octonion algebra can be consider over a field or any arbitrary commutative ring R [4]. In our work, we use the bivariate convolution polynomial ring R = Z[X]/(X N − 1)

Characterizing NTRU-Variants Using Group Ring and Evaluating their Lattice Security

The encryption scheme NTRU is designed over a quotient ring of a polynomial ring. Basically, if the ring is changed to any other ring, NTRU-like cryptosystem is constructible. In this paper, we propose a variant of NTRU using group ring, which is called GR-NTRU. GR-NTRU includes NTRU as a special case. Moreover, we analyze and compare the security of GR-NTRU for several concrete groups. It is easy to investigate the algebraic structure of group ring by using group representation theory. We apply this fact to the security analysis of GR-NTRU. We show that the original NTRU and multivariate NTRU are most secure among several GR-NTRUs which we investigated