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Paper 2014/333
An optimal representation for the trace zero subgroup
Elisa Gorla and Maike Massierer
Abstract
We give an optimal-size representation for the elements of the trace zero subgroup of the Picard group of an elliptic or hyperelliptic curve of any genus, with respect to a field extension of any prime degree. The representation is via the coefficients of a rational function, and it is compatible with scalar multiplication of points. We provide efficient compression and decompression algorithms, and complement them with implementation results. We discuss in detail the practically relevant cases of small genus and extension degree, and compare with the other known compression methods.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- elliptic curve cryptosystem
- Contact author(s)
- maike @ unsw edu au
- History
- 2016-06-15: last of 3 revisions
- 2014-05-13: received
- See all versions
- Short URL
- https://ia.cr/2014/333
- License
-
CC BY
