In this paper, we introduce the abstraction of Dual Form Signatures as a useful framework for proving security (existential unforgeability) from static assumptions for schemes with special structure that are used as a basis of other cryptographic protocols and applications. We demonstrate the power of this framework by proving security under static assumptions for close variants of pre-existing schemes: the LRSWbased Camenisch-Lysyanskaya signature scheme, and the identity-based sequential aggregate signatures of Boldyreva, Gentry, O’Neill, and Yum. The Camenisch-Lysyanskaya signature scheme was previously proven only under the interactive LRSW assumption, and our result can be viewed as a static replacement for the LRSW assumption. The scheme of Boldyreva, Gentry, O’Neill, and Yum was also previously proven only under an interactive assumption that was shown to hold in the generic group model. The structure of the public key signature scheme underlying the BGOY aggregate signatures is quite distinctive, and our work presents the first security analysis of this kind of structure under static assumptions.
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