Cryptology ePrint Archive: Report 2010/542

Squaring in cyclotomic subgroups

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.

Category / Keywords: public-key cryptography / Cyclotomic subgroups, squaring, pairing-based cryptography

Date: received 22 Oct 2010, last revised 22 Oct 2010

Contact author: kkarabin at uwaterloo ca

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Version: 20101025:151152 (All versions of this report)

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