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signature s hemes based on the Gap-DiÆe-Hellman-group signature s heme Alexandra Boldyreva August 12, 2002 Abstra t We propose a robust proa tive threshold signature s heme, a multisignature s heme and a blind signature s heme whi h work in any Gap DiÆe-Hellman (GDH) group (where the Computational DiÆe-Hellman problem is hard but the De isional DiÆe-Hellman problem is easy). Our onstru tions are based on the re ently proposed GDH signature s heme of Boneh et al. [BLS℄. Due to the instrumental stru ture of GDH groups and of the base s heme, it turns out that most of our onstru tions are simpler, more eÆ ient and have more useful properties than similar existing onstru tions. We support all the proposed s hemes with proofs under the appropriate omputational assumptions, using the orresponding notions of se urity.