Michele Ciampi, Giuseppe Persiano, Luisa Siniscalchi, Ivan Visconti
The Fiat-Shamir (FS) transform is a popular technique for obtaining practical zero-knowledge argument systems. The FS transform uses a hash function to generate, without any further over-head, non-interactive zero-knowledge (NIZK) argument systems from public-coin honest-verifier zero-knowledge (public-coin HVZK) proof systems. In the proof of zero knowledge, the hash function is modeled as a programmable random oracle (PRO). In TCC 2015, Lindell embarked on the challenging task of obtaining a similar transform with improved heuristic security. Lindell showed that, for several interesting and practical languages, there exists an efficient transform in the non-programmable random oracle (NPRO) model that also uses a common reference string (CRS). A major contribution of Lindell’s transform is that zero knowledge is proved without random oracles and this is an important step towards achieving efficient NIZK arguments in the CRS model without random oracles. In this work, we analyze the efficiency and generality of Lindell’s transform and notice a significant gap when compared with the FS transform. We then propose a new transform that aims at filling this gap. Indeed our transform is almost as efficient as the FS transform and can be applied to a broad class of public-coin HVZK proof systems. Our transform requires a CRS and an NPRO in the proof of soundness, similarly to Lindell’s transform. 1
Abstract. Most prior designated confirmer signature schemes either prove security in the random oracle model (ROM) or use general zeroknowledge proofs for NP statements (making them impractical). By slightly modifying the definition of designated confirmer signatures, Goldwasser and Waisbard presented an approach in which the Confirm and ConfirmedSign protocols could be implemented without appealing to general zero-knowledge proofs for NP statements (their Disavow protocol still requires them). The Goldwasser-Waisbard approach could be instantiated using Cramer-Shoup, GMR, or Gennaro-Halevi-Rabin signatures. In this paper, we provide an alternate generic transformation to convert any signature scheme into a designated confirmer signature scheme, without adding random oracles. Our key technique involves the use of a signature on a commitment and a separate encryption of the random string used for commitment. By adding this “layer of indirection, ” the underlying protocols in our schemes admit efficient instantiations (i.e., we can avoid appealing to general zero-knowledge proofs for NP statements) and furthermore the performance of these protocols is not tied to the choice of underlying signature scheme. We illustrate this using the Camenisch-Shoup variation on Paillier’s cryptosystem and Pedersen commitments. The confirm protocol in our resulting scheme requires 10 modular exponentiations (compared to 320 for Goldwasser-Waisbard) and our disavow protocol requires 41 modular exponentiations (compared to using a general zero-knowledge proof for Goldwasser-Waisbard). Previous schemes use the encryption of a signature paradigm, and thus run into problems when trying to implement the confirm and disavow protocols efficiently. 1