Index calculus for hyperelliptic curves

Roberto M. Avanzi, Nicolas Thériault

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


As stated in Section 20.2.1, the index calculus algorithm can be applied to compute discrete logarithms in the Jacobian of hyperelliptic curves. For groups of this type, the set of primes are prime divisors or, in terms of the ideal class group, prime ideals. These divisors can be single 𝔽q-rational points or the sums of all Galois conjugates over 𝔽q of a non-𝔽q-rational point: In other words, if a divisor D has Mumford representation [u(x), v(x)], D is prime if and only if the polynomial u(x) is irreducible over 𝔽q.

Original languageEnglish
Title of host publicationHandbook of Elliptic and Hyperelliptic Curve Cryptography
PublisherCRC Press
Number of pages17
ISBN (Electronic)9781420034981
ISBN (Print)1584885181, 9781584885184
StatePublished - 1 Jan 2005
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2006 Taylor & Francis Group, LLC.

ASJC Scopus subject areas

  • General Mathematics
  • General Computer Science


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