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Abstract. We propose a group signature scheme with constant-size public key and signature length that does not require trapdoor. So system parameters can be shared by multiple groups belonging to different organizations. The scheme is provably secure in the formal model recently proposed by Bellare, Shi and Zhang (BSZ04), using random oracle model, Decisional Bilinear Diffie-Hellman and Strong Diffie-Hellman assumptions. We give a more efficient variant scheme and prove its security in a formal model which is a modification of BSZ04 model and has a weaker anonymity requirement. Both schemes are very efficient and the sizes of signatures are approximately one half and one third, respectively, of the sizes of the well-known ACJT00 scheme. We also use the schemes to construct a traceable signature scheme.

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Abstract. This paper introduces and formalizes homomorphic proofs that allow 'adding' proofs and proof statements to get a new proof of the 'sum' statement. Additionally, we introduce a construction of homomorphic proofs, and show an accumulator scheme with delegatable non-membership proofs (ADNMP) as one of its applications with provable security. Finally, the proposed accumulator method extends the BC-CKLS scheme [1] to create a new provably secure revocable delegatable anonymous credential (RDAC) system. Intuitively, the new accumulator's delegatable non-membership (NM) proofs enable user A, without revealing her identity, to delegate to user B the ability to prove that A's identity is not included in a blacklist that can later be updated. The delegation is redelegatable, unlinkable, and verifiable.