Batch verification of ECDSA signatures

Abstract

In this paper, we study several algorithms for batch verification of ECDSA signatures. The first of these algorithms is based upon the naive idea of taking square roots in the underlying field. We also propose two new and efficient algorithms which replace square-root computations by symbolic manipulations. Experiments carried out on NIST prime curves demonstrate a maximum speedup of above six over individual verification if all the signatures in the batch belong to the same signer, and a maximum speedup of about two if the signatures in the batch belong to different signers, both achieved by a fast variant of our second symbolic-manipulation algorithm. In terms of security, all the studied algorithms are equivalent to standard ECDSA*batch verification. These algorithms are practical only for small (≤ 8) batch sizes. To the best of our knowledge, this is the first reported study on the batch verification of original ECDSA signatures. © 2012 Springer-Verlag.