Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 296-312 |
| Number of pages | 17 |
| Journal | Lecture Notes in Computer Science |
| Volume | 3506 |
| Publication status | Published - Sep 27 2005 |
| Event | 7th International Conference on Information Security and Cryptology - ICISC 2004 - Seoul, Korea, Republic of Duration: Dec 2 2004 → Dec 3 2004 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
Some improved algorithms for hyperelliptic curve cryptosystems using degenerate divisors. / Katagi, Masanobu; Akishita, Tom; Kitamura, Izuru; Takagi, Tsuyoshi.
In: Lecture Notes in Computer Science, Vol. 3506, 27.09.2005, p. 296-312.Research output: Contribution to journal › Conference article
}
TY - JOUR
T1 - Some improved algorithms for hyperelliptic curve cryptosystems using degenerate divisors
AU - Katagi, Masanobu
AU - Akishita, Tom
AU - Kitamura, Izuru
AU - Takagi, Tsuyoshi
PY - 2005/9/27
Y1 - 2005/9/27
N2 - 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.
AB - 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.
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M3 - Conference article
AN - SCOPUS:24944586307
VL - 3506
SP - 296
EP - 312
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
SN - 0302-9743
ER -