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Journal Article
Speeding up Scalar Multiplication in Genus 2 Hyperelliptic Curves with Efficient Endomorphisms
- Authors
- Tae Jun Park, Mun Kyu Lee, Kun Soo Park, Kyo Il Chung
- Issue Date
- 2005-10
- Citation
- ETRI Journal, v.27, no.5, pp.617-627
- ISSN
- 1225-6463
- Publisher
- 한국전자통신연구원 (ETRI)
- Language
- English
- Type
- Journal Article
- Abstract
- This paper proposes an efficient scalar multiplication algorithm for hyperelliptic curves, which is based on the idea that efficient endomorphisms can be used to speed up scalar multiplication. We first present a new Frobenius expansion method for special hyperelliptic curves that have Gallant-Lambert- Vanstone (GLV) endomorphisms. To compute kD for an integer k and a divisor D, we expand the integer k by the Frobenius endomorphism and the GLV endomorphism. We also present improved scalar multiplication algorithms that use the new expansion method. By our new expansion method, the number of divisor doublings in a scalar multiplication is reduced to a quarter, while the number of divisor additions is almost the same. Our experiments show that the overall throughputs of scalar multiplications are increased by 15.6 to 28.3% over the previous algorithms when the algorithms are implemented over finite fields of odd characteristics.
- KSP Keywords
- Finite fields, Frobenius endomorphism, Genus 2 hyperelliptic curves, Scalar Multiplication algorithm, Speed-up