Zero-Knowledge Proofs for Finite Field Arithmetic; or: Can Zero-Knowledge be for Free?

By Ronald Cramer, Ivan Bjerre Damgård. 1998

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Citations in the corpus

A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order (2002, background): “For the associated protocols and additional examples, see [7].”
Non-interactive Distributed-Verifier Proofs and Proving Relations among Commitments (2002, background): “For formal definitions we refer to [7], where this concept was introduced.”
Distributed Paillier Cryptosystem without Trusted Dealer (2010, methodology): “i mod P with a zero-knowledge proof of a multiplicative relation by using the standard techniques such as [ 12 ].”
Advances in Cryptology — ASIACRYPT 2002 (2002, methodology): “As pointed out in [7], the QR-based variant of the generalisation is not too efficient in practice.”
Multiparty Computation from Threshold Homomorphic Encryption (2000, methodology): “For concrete examples that would fit with the examples of threshold encryption we use, see [7].”
Doubly-Efficient zkSNARKs Without Trusted Setup (2018, methodology): “In this section, we describe a straightforward application of “commit-and-prove” techniques [8, 37] (§1) to Gir (§3.”
Libra: Succinct Zero-Knowledge Proofs with Optimal Prover Computation (2019, background): “[47] make the argument system zero-knowledge by putting all the messages in the proof into homomorphic commitments, as proposed by Cramer and Damgard in [24].”
Homomorphic Signature Schemes (2002, background): “Cramer and Damgard use homomorphic bit commitments to drastically simplify zero-knowledge proofs [13].”
Zero-knowledge from secure multiparty computation (2007, unknown): “There has been a vast body of work on improving the efficiency of interactive and non-interactive zero-knowledge proofs; see [5, 10, 32, 33, 11, 6, 23, 28] and references therein.”