Abstract
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 language | English |
|---|---|
| Title of host publication | Handbook of Elliptic and Hyperelliptic Curve Cryptography |
| Publisher | CRC Press |
| Pages | 511-527 |
| Number of pages | 17 |
| ISBN (Electronic) | 9781420034981 |
| ISBN (Print) | 1584885181, 9781584885184 |
| State | Published - 1 Jan 2005 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2006 Taylor & Francis Group, LLC.
ASJC Scopus subject areas
- Mathematics (all)
- Computer Science (all)