In this paper we present a new finite field-based public key cryptosystem (NETRU) which is a non-commutative variant of CTRU. The original CTRU is defined by the ring of polynomials in one variable over a finite fieldF2. This system works in the ring R=F2 [x]/áxN-1ñ and is already broken by some attacks such as linear algebra attack. We extend this system over finite fields Zp, wherep is a prime (or prime power) and it operates over the non-commutative ring M=Mk (Zp) [T, x]/áXn-Ik*kñ, where M is a matrix ring of k by k matrices of polynomials in R=Zp [T, x]/áxn -1ñ. In the proposed NETRU, the encryption and decryption computations are non-commutative and hence the system is secure against linear algebra attack as lattice-based attacks. NETRU is designed based on the CTRU core and exhibits high levels of security with two-sided matrix multiplication.

This paper presents a novel image cryptosystem using a specific feature of boundary elementary cellular automata with permutation-diffusion architecture. The characteristics of some periodic boundary elementary cellular automata (CAs) with the length of 8 have been studied over the past years. The State-transition diagram shows that some elementary cellular automata (ECA) rule lead to some state attractors that are suitable to use to implement an encrypting function in order to transform the pixels’ values while meeting the basic requirements of the encryption scheme. Minimizing computational overhead, the production of these attractors could be done by using an initial global state of the CA solely, and the implementation of which needs no extra hardware cost. Correspondingly, the proposed new image cryptosystem includes an encryption method based on both permutations of the image pixels and the replacement of the pixel values. The permutation method is optional and can be done by every permutation algorithm. Simulation results revealed this fact that the proposed CA-based image cryptosystem shows strong performance in terms of encryption and decryption. The outstanding characteristics of the proposed image encryption method are as follows: lossless and symmetric private key encryption, low data expansion, the possibility of encryption when there is more than one image with the use of just one key image, large keyspace, and checking data integrity.

This paper presents a new and efficient implementation approach for the elliptic curve cryptosystem (ECC) based on a novel finite field multiplication in GF (2m) and an efficient scalar multiplication algorithm. This new finite field multiplication algorithm performs zero chain multiplication and required additions in only one clock cycle instead of several clock cycles. Using modified (limited number of shifts) Barrel shifter, the partial result is also shifted in one clock cycle instead of several clock cycles. Both the canonical recoding technique and the sliding window method are applied to the multiplier to reduce the average number of required clock cycles. In the scalar multiplication algorithm of the proposed implementation approach, the point addition and point doubling operations are computed in parallel. The sliding window method and the signed-digit representation are also used to reduce the average number of point operations. Based on our analysis, the computation cost (the average number of required clock cycles) is effectively reduced in both the proposed finite field multiplication algorithm and the proposed implementation approach of ECC in comparison with other ECC finite field multiplication algorithms and implementation approaches.