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Efficient Exponentiation in GF(p m ) Using the Frobenius Map
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- Authors
- Mun Kyu Lee, Ho Won Kim, Do Won Hong, Kyo Il Chung
- Issue Date
- 2006-10
- Citation
- International Conference on Computational Science and Its Applications (ICCSA) 2006 (LNCS 3983), v.3983, pp.584-593
- Publisher
- Springer
- Language
- English
- Type
- Conference Paper
- Abstract
- The problem of exponentiation over a finite field is to compute A e for a field element A and a positive integer e. This problem has many useful applications in cryptography and information security. In this paper, we present an efficient exponentiation algorithm in optimal extension field (OEF) GF(pm], which uses the fact that the Frobenius map, i.e., the p-th powering operation is very efficient in OEFs. Our analysis shows that the new algorithm is twice as fast as the conventional square-and-multiply exponentiation. One of the important applications of our new algorithm is random generation of a base point for elliptic curve cryptography, which is an attractive public-key mechanism for resource-constrained devices. We present a further optimized exponentiation algorithm for this application. Our experimental results show that the new technique accelerates the generation process by factors of 1.62-6.55 over various practical elliptic curves. © Springer-Verlag Berlin Heidelberg 2006.
- KSP Keywords
- Base point, Elliptic Curve Cryptography(ECC), Elliptic curves, Extension field, Finite fields, Public Key, Random generation, Resource Constrained Devices(RCD), generation process, information Security, new algorithm