Paper 2011/105

Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation

S. Erickson, M. J. Jacobson Jr., and A. Stein

Abstract

We present a complete set of efficient explicit formulas for arithmetic in the degree 0 divisor class group of a genus two real hyperelliptic curve given in affine coordinates. In addition to formulas suitable for curves defined over an arbitrary finite field, we give simplified versions for both the odd and the even characteristic cases. Formulas for baby steps, inverse baby steps, divisor addition, doubling, and special cases such as adding a degenerate divisor are provided, with variations for divisors given in reduced and adapted basis. We describe the improvements and the correctness together with a comprehensive analysis of the number of field operations for each operation. Finally, we perform a direct comparison of cryptographic protocols using explicit formulas for real hyperelliptic curves with the corresponding protocols presented in the imaginary model.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Submitted to Advances in Mathematics of Communication
Keywords
hyperelliptic curvereduced divisorinfrastructure and distanceCantor’s algorithmexplicit formulasefficient implementationcryptographic key exchange
Contact author(s)
jacobs @ cpsc ucalgary ca
History
2011-03-05: received
Short URL
https://ia.cr/2011/105
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2011/105,
      author = {S.  Erickson and M.  J.  Jacobson Jr. and A.  Stein},
      title = {Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation},
      howpublished = {Cryptology ePrint Archive, Paper 2011/105},
      year = {2011},
      note = {\url{https://eprint.iacr.org/2011/105}},
      url = {https://eprint.iacr.org/2011/105}
}
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