Efficient exponentiation in GF(pm) using the Frobenius map

Authors:
Mun-Kyu Lee;Howon Kim;Dowon Hong;Kyoil Chung
Affiliations:
School of Computer Science and Engineering, Inha University, Incheon, Korea;Electronics and Telecommunications Research Institute, Daejeon, Korea;Electronics and Telecommunications Research Institute, Daejeon, Korea;Electronics and Telecommunications Research Institute, Daejeon, Korea
Venue:
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part IV
Year:
2006

Citing 6
Cited 0

Fast exponentiation in GF(2n)

Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Processor-efficient exponentiation in finite fields

Information Processing Letters
A survey of fast exponentiation methods

Journal of Algorithms
Efficient Algorithms for Pairing-Based Cryptosystems

CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms

CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Efficient parallel exponentiation in GF(qn) using normal basis representations

Journal of Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

The problem of exponentiation over a finite field is to compute Ae 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.