Improved batch verification of signatures using generalized sparse exponents

We propose an efficient method for batch verification of exponentiation using width-w Non-Adjacent Forms (w-NAFs), which can be applied to modified DSA and ECDSA signatures. We further generalize this method to use tau-adic w-NAF scalars on elliptic curves with complex multiplication such as Koblitz curves. The theoretical analyses and experimental results show that our method accelerates the individual verification by a factor of up to 7.49 in the single-signer case and by up to 1.47 in the multiple-signer case for 1000 instances over a Koblitz curve K233. Our method can also be exploited to accelerate batch verification of pairing-based signatures.