Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing multiplicative inverses in $ {\rm GF}(p)$


Author: George E. Collins
Journal: Math. Comp. 23 (1969), 197-200
MSC: Primary 65.10
MathSciNet review: 0242345
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Two familiar algorithms, the extended Euclidean algorithm and the Fermat algorithm (based on Fermat's theorem $ {a^p}\equiv a \pmod p$), are analyzed and compared as methods for computing multiplicative inverses in $ {\text{GF}}(p)$. Using Knuth's results on the average number of divisions in the Euclidean algorithm, it is shown that the average number of arithmetic operations required by the Fermat algorithm is nearly twice as large as the average number for the extended Euclidean algorithm. For each of the two algorithms, forward and backward versions are distinguished. It is shown that all numbers computed in the forward extended Euclidean algorithm are bounded by the larger of the two inputs, a property which was previously established by Kelisky for the backward version.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.10

Retrieve articles in all journals with MSC: 65.10


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0242345-5
PII: S 0025-5718(1969)0242345-5
Article copyright: © Copyright 1969 American Mathematical Society