The paper provides a cryptanalysis the AAβ-cryptosystem recently proposed by Ariffin and Abu. The scheme is in essence a key agreement scheme whose security is based on a discrete logarithm problem in the infinite (additive) group R/Z (the reals modulo 1). The paper breaks the AAβ-cryptosystem (in a passive adversary model) by showing that this discrete logarithm problem can be efficiently solv...

In this paper I propose the fully homomorphic public-key encryption(FHPKE) scheme with zero norm noises that is based on the discrete logarithm assumption(DLA) and computational Diffie–Hellman assumption(CDH) of multivariate polynomials on octonion ring. Since the complexity for enciphering and deciphering become to be small enough to handle, the cryptosystem runs fast. keywords: fully homomorp...

Let be a prime, a positive integer, = , and a divisor of ( 1). We derive lower bounds on the linear complexity over the residue class ring of a ( -periodic) sequence representing the residues modulo of the discrete logarithm in . Moreover, we investigate a sequence over representing the values of a certain polynomial over introduced by Mullen and White which can be identified with the discrete ...

This paper extends the analysis of Pollard’s rho algorithm for solving a single instance of the discrete logarithm problem in a finite cyclic group G to the case of solving more than one instance of the discrete logarithm problem in the same group G. We analyze Pollard’s rho algorithm when used to iteratively solve all the instances. We also analyze the situation when the goal is to solve any o...

In this paper, a new algorithm to solve the discrete logarithm problem is presented which is similar to the usual baby-step giant-step algorithm. Our algorithm exploits the order of the discrete logarithm in the multiplicative group of a finite field. Using randomization with parallelized collision search, our algorithm indicates some weakness in NIST curves over prime fields which are consider...