The ISC International Journal of Information Security

Abstract In this paper we will construct a lattice-based public-key cryptosystem using non-commutative quaternion algebra, and since its lattice does not fully fit within Circular and Convolutional Modular Lattice (CCML), we prove it is arguably more secure than the existing lattice-based cryptosystems such as NTRU. As in NTRU, the proposed public-key cryptosystem relies for its inherent security on the intractability of finding the shortest vector in a certain non-convolutional modular lattice, yet it is efficient and cost effective, contrary to cryptosystems such as RSA or ECC. The detailed specification of the proposed cryptosystem, including the underlying algebraic structure, key generation, encryption and decryption process and also the issues regarding key security, message security, and probability of successful decryption are explained. We will further show, based on the existing results for lattice-reduction algorithms, that the proposed cryptosystem with a dimension of 41 will have a security equal to NTRU-167.

Abstract Elliptic Curve Cryptosystems (ECC) have recently received significant attention by researchers due to their high performance such as low computational cost and small key size. In this paper a novel untraceable blind signature scheme is presented. Since the security of proposed method is based on difficulty of solving discrete logarithm over an elliptic curve, performance of the proposed scheme is quite commendable in comparison with the previous work in terms of security and time complexity.