On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Number Theory in Digital Signal Processing
Number Theory in Digital Signal Processing
Implementing Exact Calculations in Hardware
IEEE Transactions on Computers
State of the Art in Ultra-Low Power Public Key Cryptography for Wireless Sensor Networks
PERCOMW '05 Proceedings of the Third IEEE International Conference on Pervasive Computing and Communications Workshops
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The extended Euclidean algorithm is typically used to calculate multiplicative inverses over finite fields and rings of integers. The algorithm presented here has approximately the same number of average iterations and maximum number of iterations. It is shown, when P is a Mersenne prime, implementation of this algorithm on a processor, designed especially for mod P arithmetic operations, produces a more efficient algorithm with respect to the amount of program statements and number of operations. It is then shown heuristically, when the division and multiplications are performed simultaneously, the Euclidean algorithm has fewer subiterations.