Squaring in cyclotomic subgroups
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Abstract:
We propose new squaring formulae for cyclotomic subgroups of the multiplicative group of certain finite fields. Our formulae use a compressed representation of elements having the property that decompression can be performed at a very low cost. The squaring formulae lead to new exponentiation algorithms in cyclotomic subgroups which outperform the fastest previously-known exponentiation algorithms when the exponent has low Hamming weight. Our algorithms can be adapted to accelerate the final exponentiation step of pairing computations.References
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Additional Information
- Koray Karabina
- Affiliation: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- Email: kkarabin@uwaterloo.ca
- Received by editor(s): October 22, 2010
- Received by editor(s) in revised form: August 22, 2011
- Published electronically: June 27, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 82 (2013), 555-579
- MSC (2010): Primary 94A60, 12E20, 14G50
- DOI: https://doi.org/10.1090/S0025-5718-2012-02625-1
- MathSciNet review: 2983036