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The Calcualtion of Multiplicative Inverses Over GF(P) Efficiently Where P is a Mersenne Prime
May 1986 (vol. 35 no. 5)
pp. 478482
ASCII Text  x  
J.J. Thomas, J.M. Keller, G.N. Larsen, "The Calcualtion of Multiplicative Inverses Over GF(P) Efficiently Where P is a Mersenne Prime," IEEE Transactions on Computers, vol. 35, no. 5, pp. 478482, May, 1986.  
BibTex  x  
@article{ 10.1109/TC.1986.1676791, author = {J.J. Thomas and J.M. Keller and G.N. Larsen}, title = {The Calcualtion of Multiplicative Inverses Over GF(P) Efficiently Where P is a Mersenne Prime}, journal ={IEEE Transactions on Computers}, volume = {35}, number = {5}, issn = {00189340}, year = {1986}, pages = {478482}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1986.1676791}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  The Calcualtion of Multiplicative Inverses Over GF(P) Efficiently Where P is a Mersenne Prime IS  5 SN  00189340 SP478 EP482 EPD  478482 A1  J.J. Thomas, A1  J.M. Keller, A1  G.N. Larsen, PY  1986 KW  rings of integers KW  Euclid's algorithm KW  Fermat prime KW  finite fields KW  Mersenne prime KW  modulo P KW  multiplicative inverse KW  prime number VL  35 JA  IEEE Transactions on Computers ER   
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.
Index Terms:
rings of integers, Euclid's algorithm, Fermat prime, finite fields, Mersenne prime, modulo P, multiplicative inverse, prime number
Citation:
J.J. Thomas, J.M. Keller, G.N. Larsen, "The Calcualtion of Multiplicative Inverses Over GF(P) Efficiently Where P is a Mersenne Prime," IEEE Transactions on Computers, vol. 35, no. 5, pp. 478482, May 1986, doi:10.1109/TC.1986.1676791
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