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In this paper, the authors 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. They describe the power of this framework by proving security under static assumptions for close variants of pre-existing schemes: the LRSW-based Camenisch-Lysyanskaya signature scheme, 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 their result can be viewed as a static replacement for the LRSW assumption.
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