Extraction Security of Sequential Aggregate Signatures

Aggregate signature schemes enable anyone to compress many signatures into one. Besides the unforgeability of aggregate signature, another property called aggregate extraction sometimes is useful. In sequential aggregate signature schemes, the aggregate signature is computed incrementally by the signers. We introduce extraction security in the sequential context which can be seen as an analogy of aggregate extraction introduced by Boneh et al. in CRYPTO 2003. In addition to the practical meaning, it also has benefits in the construction of hierarchical identity-based signatures as we will point out. We study several well known aggregate signature schemes and prove some of them satisfy extraction security.