Abstract
In AfricaCrypt 2012, several algorithms are proposed for the batch verification of ECDSA signatures. In this paper, we propose three randomization methods for these batch-verification algorithms. Our first proposal is based on Montgomery ladders, and the second on computing square-roots in the underlying field. Both these techniques use numeric arithmetic only. Our third proposal exploits symbolic computations leading to a seminumeric algorithm. We theoretically and experimentally establish that for standard ECDSA signatures, our seminumeric randomization algorithm in tandem with the batch-verification algorithm S2′ gives the best speedup over individual verification. If each ECDSA signature contains an extra bit to uniquely identify the correct y-coordinate of the elliptic-curve point appearing in the signature, then the second numeric randomization algorithm followed by the naive batch-verification algorithm N′ yields the best performance gains. We detail our study for NIST prime and Koblitz curves.
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Karati, S., Das, A., Roychoudhury, D. (2014). Randomized Batch Verification of Standard ECDSA Signatures. In: Chakraborty, R.S., Matyas, V., Schaumont, P. (eds) Security, Privacy, and Applied Cryptography Engineering. SPACE 2014. Lecture Notes in Computer Science, vol 8804. Springer, Cham. https://doi.org/10.1007/978-3-319-12060-7_16
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DOI: https://doi.org/10.1007/978-3-319-12060-7_16
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