Some improved algorithms for hyperelliptic curve cryptosystems using degenerate divisors

Masanobu Katagi, Tom Akishita, Izuru Kitamura, Tsuyoshi Takagi

研究成果: ジャーナルへの寄稿Conference article

3 引用 (Scopus)

抄録

Hyperelliptic curve cryptosystems (HECC) can be good alternatives to elliptic curve cryptosystems, and there is a good possibility to improve the efficiency of HECC due to its flexible algebraic structure. Recently, an efficient scalar multiplication technique for application to genus 2 curves using a degenerate divisor has been proposed. This new technique can be used in the cryptographic protocol using a fixed base point, e.g., HEC-DSA. This paper considers two important issues concerning degenerate divisors. First, we extend the technique for genus 2 curves to genus 3 curves. Jacobian variety for genus 3 curves has two different degenerate divisors: degree 1 and 2. We present explicit formulae of the addition algorithm with degenerate divisors, and then present the timing of scalar multiplication using the proposed formulae. Second, we propose several window methods using the degenerate divisors. It is not obvious how to construct a base point D such that deg(D) = deg(aD) < g for integer a, where g is the genus of the underlying curve and deg(D) is the degree of divisor D. We present an explicit algorithm for generating such divisors. We then develop a window-based scheme that is secure against side-channel attacks.

元の言語英語
ページ(範囲)296-312
ページ数17
ジャーナルLecture Notes in Computer Science
3506
出版物ステータス出版済み - 9 27 2005
イベント7th International Conference on Information Security and Cryptology - ICISC 2004 - Seoul, 大韓民国
継続期間: 12 2 200412 3 2004

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Hyperelliptic Curves
Cryptosystem
Divisor
Cryptography
Genus
Curve
Flexible structures
Scalar multiplication
Jacobian Varieties
Elliptic Curve Cryptosystem
Side Channel Attacks
Flexible Structure
Cryptographic Protocols
Algebraic Structure
Explicit Formula
Timing
Integer
Alternatives

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

これを引用

Some improved algorithms for hyperelliptic curve cryptosystems using degenerate divisors. / Katagi, Masanobu; Akishita, Tom; Kitamura, Izuru; Takagi, Tsuyoshi.

:: Lecture Notes in Computer Science, 巻 3506, 27.09.2005, p. 296-312.

研究成果: ジャーナルへの寄稿Conference article

Katagi, M, Akishita, T, Kitamura, I & Takagi, T 2005, 'Some improved algorithms for hyperelliptic curve cryptosystems using degenerate divisors', Lecture Notes in Computer Science, 巻. 3506, pp. 296-312.
Katagi, Masanobu ; Akishita, Tom ; Kitamura, Izuru ; Takagi, Tsuyoshi. / Some improved algorithms for hyperelliptic curve cryptosystems using degenerate divisors. :: Lecture Notes in Computer Science. 2005 ; 巻 3506. pp. 296-312.
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