Efficient reduction of large divisors on hyperelliptic curves

Roberto Avanzi, Michael J. Jacobson, Renate Scheidler

Research output: Contribution to journalArticlepeer-review


We present an algorithm for reducing a divisor on a hyperelliptic curve of arbitrary genus over any finite field. Our method is an adaptation of a procedure for reducing ideals in quadratic number fields due to Jacobson, Sawilla and Williams, and shares common elements with both the Cantor and the NUCOMP algorithms for divisor arithmetic. Our technique is especially suitable for the rapid reduction of a divisor with very large Mumford coefficients, obtained for example through an efficient tupling technique. Results of numerical experiments are presented, showing that our algorithm is superior to the standard reduction algorithm in many cases.

Original languageEnglish
Pages (from-to)261-279
Number of pages19
JournalAdvances in Mathematics of Communications
Issue number2
StatePublished - May 2010
Externally publishedYes


  • Continued fraction expansion
  • Divisor
  • Hyperelliptic curve
  • Reduction
  • Scalar multiplication

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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