Efficient reduction of large divisors on hyperelliptic curves | Zendy

Roberto Avanzi | Zendy; Michael J. Jacobson | Zendy; Renate Scheidler | Zendy

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Efficient reduction of large divisors on hyperelliptic curves

Author(s) -

Roberto Avanzi,

Michael J. Jacobson,

Renate Scheidler

Publication year - 2010

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2010.4.261

Subject(s) - mathematics , divisor (algebraic geometry) , hyperelliptic curve , hyperelliptic curve cryptography , reduction (mathematics) , finite field , genus , field (mathematics) , greatest common divisor , good reduction , quadratic equation , arithmetic , pure mathematics , algorithm , discrete mathematics , geometry , botany , computer science , encryption , medicine , public key cryptography , surgery , elliptic curve cryptography , biology , operating system

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 coeffi- cients, 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.

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