Paper 2007/365
Pairings on Jacobians of Hyperelliptic Curves
Christian Robenhagen Ravnshoj
Abstract
Consider the jacobian of a hyperelliptic genus two curve defined over a finite field. Under certain restrictions on the endomorphism ring of the jacobian we give an explicit description all non-degenerate, bilinear, anti-symmetric and Galois-invariant pairings on the jacobian. From this description it follows that no such pairing can be computed more efficiently than the Weil pairing. To establish this result, we need an explicit description of the representation of the Frobenius endomorphism on the l-torsion subgroup of the jacobian. This description is given. In particular, we show that if the characteristic polynomial of the Frobenius endomorphism splits into linear factors modulo l, then the Frobenius is diagonalizable. Finally, under the restriction that the Frobenius element is an element of a certain subring of the endomorphism ring, we prove that if the characteristic polynomial of the Frobenius endomorphism splits into linear factors modulo l, then the embedding degree and the total embedding degree of the jacobian with respect to l are the same number.
Metadata
- Available format(s)
-
PDF PS
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Hyperelliptic curve cryptography
- Contact author(s)
- cr @ imf au dk
- History
- 2007-09-13: received
- Short URL
- https://ia.cr/2007/365
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2007/365, author = {Christian Robenhagen Ravnshoj}, title = {Pairings on Jacobians of Hyperelliptic Curves}, howpublished = {Cryptology {ePrint} Archive, Paper 2007/365}, year = {2007}, url = {https://eprint.iacr.org/2007/365} }