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Identification of Bad Signatures in Batches
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
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Identification of Multiple Invalid Signatures in Pairing-Based Batched Signatures
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Identification of multiple invalid pairing-based signatures in constrained batches
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This paper describes new methods in pairing-based signature schemes for identifying the invalid digital signatures in a batch, after batch verification has failed. These methods efficiently identify non-trivial numbers of invalid signatures in batches of (potentially large) numbers of signatures. Our methods use "divide-and-conquer" search to identify the invalid signatures within a batch, but prune the search tree to substantially reduce the number of pairing computations required. The methods presented in this paper require computing on average O (w ) products of pairings to identify w invalid signatures within a batch of size N , compared with the O (w (log2 (N /w ) + 1)) [for w N /2] that traditional divide-and-conquer methods require. Our methods avoid the problem of exponential growth in expected computational cost that affect earlier proposals which, on average, require computing O (w ) products of pairings. We compare the expected performance of our batch verification methods with previously published divide-and-conquer and exponential cost methods for Cha-Cheon identity-based signatures [6]. However, our methods also apply to a number of short signature schemes and as well as to other identity-based signature schemes.