Some improved algorithms for hyperelliptic curve cryptosystems using degenerate divisors

Masanobu Katagi, Tom Akishita, Izuru Kitamura, Tsuyoshi Takagi

Research output: Contribution to journalConference articlepeer-review

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)296-312
Number of pages17
JournalLecture Notes in Computer Science
Publication statusPublished - 2005
Externally publishedYes
Event7th International Conference on Information Security and Cryptology - ICISC 2004 - Seoul, Korea, Republic of
Duration: Dec 2 2004Dec 3 2004

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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