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We put forward a new algebraic framework to generalize and analyze Diffie–Hellman like decisional assumptions which allows us to argue about security and applications by considering only algebraic properties. Our $$\mathcal {D}_{\ell ,k}\text{- }\textsf {MDDH}$$ D ℓ , k - MDDH Assumption states that it is hard to decide whether a vector in $$\mathbb… (More)

Groth-Sahai proofs are efficient non-interactive zero-knowledge proofs that have found widespread use in pairing-based cryptography. We propose efficiency improvements of Groth-Sahai proofs in the SXDH setting, which is the one that yields the most efficient non-interactive zero-knowledge proofs. – We replace some of the commitments with ElGamal… (More)

An attribute-based signature with respect to a signing policy , chosen ad-hoc by the signer, convinces the verifier that the signer holds a subset of attributes satisfying that signing policy. Ideally, the ver-ifier must obtain no other information about the identity of the signer or the attributes he holds. This primitive has many applications in real… (More)

One way to build secure electronic voting systems is to use Mix-Nets, which break any correlation between voters and their votes. One of the characteristics of Mix-Net-based eVoting is that ballots are usually decrypted individually and, as a consequence, invalid votes can be detected during the tallying of the election. In particular, this means that the… (More)

Lossy trapdoor functions, introduced by Peikert and Waters (STOC'08), have received a lot of attention in the last years, because of their wide range of applications in theoretical cryptography. The notion has been recently extended to the identity-based scenario by Bellare et al. (Eurocrypt'12). We provide one more step in this direction, by considering… (More)

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