A cryptographic system based on finite field transforms

In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work.

Cubic Sieve Congruence of the Discrete Logarithm Problem, and fractional part sequences

The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontrivial solution to the Cubic Sieve Congruence (CSC) x(3) equivalent to y(2)z (mod p), where p is a given prime number. A nontrivial solution must also satisfy x(3) not equal y(2)z and 1 <= x, y, z < p(alpha), where alpha is a given real number such that 1/3 < alpha <= 1/2. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. CSC can be parametrized as x equivalent to v(2)z (mod p) and y equivalent to v(3)z (mod p). In this paper, we give a deterministic polynomial-time (O(ln(3) p) bit-operations) algorithm to determine, for a given v, a nontrivial solution to CSC, if one exists. Previously it took (O) over tilde (p(alpha)) time in the worst case to determine this. We relate the CSC problem to the gap problem of fractional part sequences, where we need to determine the non-negative integers N satisfying the fractional part inequality {theta N} < phi (theta and phi are given real numbers). The correspondence between the CSC problem and the gap problem is that determining the parameter z in the former problem corresponds to determining N in the latter problem. We also show in the alpha = 1/2 case of CSC that for a certain class of primes the CSC problem can be solved deterministically in <(O)over tilde>(p(1/3)) time compared to the previous best of (O) over tilde (p(1/2)). It is empirically observed that about one out of three primes is covered by the above class. (C) 2013 Elsevier B.V. All rights reserved.

Connecting Active-Site Loop Conformations and Catalysis in Triosephosphate Isomerase: Insights from a Rare Variation at Residue96 in the Plasmodial Enzyme

Despite extensive research into triosephosphate isomerases (TIMs), there exists a gap in understanding of the remarkable conjunction between catalytic loop-6 (residues 166-176) movement and the conformational flip of Glu165 (catalytic base) upon substrate binding that primes the active site for efficient catalysis. The overwhelming occurrence of serine at position96 (98% of the 6277 unique TIM sequences), spatially proximal to E165 and the loop-6 residues, raises questions about its role in catalysis. Notably, Plasmodium falciparum TIM has an extremely rare residuephenylalanineat this position whereas, curiously, the mutant F96S was catalytically defective. We have obtained insights into the influence of residue96 on the loop-6 conformational flip and E165 positioning by combining kinetic and structural studies on the PfTIM F96 mutants F96Y, F96A, F96S/S73A, and F96S/L167V with sequence conservation analysis and comparative analysis of the available apo and holo structures of the enzyme from diverse organisms.