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In many applications, digital signatures are verified in batches in order to reduce the total verification time. For many digital-signature algorithms, the batch-verification criterion is reasonably obvious. However, the popular ECDSA signature scheme presents some resistance to batch-verification ideas. Randomizers are popularly used to prevent various types of attacks on batch-verification schemes. Recently, several algorithms based upon symbolic computation are proposed for the batch verification of ECDSA signatures. In this paper, the authors demonstrate that the concept of randomizers can be easily embedded in these symbolic-computation algorithms. The performance degradation caused by randomizers is comparable with that associated with ECDSA.
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