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| ERIC #: | EJ753913 |
| Title: | Fast Modular Exponentiation and Elliptic Curve Group Operation in Maple |
| Authors: | Yan, S. Y.; James, G. |
| Descriptors: | Mathematics; Item Response Theory; Calculus; Multivariate Analysis; Number Systems; Arithmetic; Mathematical Formulas; Symbols (Mathematics); Computation |
| Source: | International Journal of Mathematical Education in Science & Technology, v37 n6 p745-753 Sep 2006 |
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| Publisher: | Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals/default.html |
| Publication Date: | 2006-09-15 |
| Pages: | 9 |
| Pub Types: | Journal Articles; Reports - Descriptive |
| Abstract: | The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic curve cryptography, in which the elliptic curve group operation, Q[equivalent to]kP(mod q) with P, Q points on elliptic curve E: y[squared]=x[cubed]+ax+b over a finite field [subscript q], is the most fundamental operation and needs to be performed as fast as possible. In this paper, two variants of fast implementations for modular exponentiation and elliptic curve group operation in Maple are presented. |
| Abstractor: | Author |
| Reference Count: | 12 |
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| Note: | N/A |
| Identifiers: | N/A |
| Record Type: | Journal |
| Level: | N/A |
| Institutions: | N/A |
| Sponsors: | N/A |
| ISBN: | N/A |
| ISSN: | ISSN-0020-739X |
| Audiences: | N/A |
| Languages: | English |
| Education Level: | N/A |
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