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Title:
Squaring in cyclotomic subgroups
Authors: Koray Karabina
Abstract:We propose new squaring formulae for cyclotomic subgroups 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.
ePrint: https://eprint.iacr.org/2010/542
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