Fast scalar multiplication for ECC over GF(p) using division chains
WISA'10 Proceedings of the 11th international conference on Information security applications
A duality in space usage between left-to-right and right-to-left exponentiation
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
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Exponentiation may be performed faster than the traditional square and multiply method by iteratively reducing the exponent modulo numbers which themselves require few multiplications, such as those with few non-zero bits. For a suitable choice of such divisors, this reduces the expected number of non-squaring multiplications by over half at the cost of a single extra register. The method is applicable to exponentiation in any multiplicative group where squaring is as expensive as multiplication and not cheaper than integer division. In particular, both hardware and software implementations of the RSA crypto-system can benefit.