Abstract
We present a simple zero-knowledge proof of knowledge protocol of which many protocols in the literature are instantiations. These include Schnorr’s protocol for proving knowledge of a discrete logarithm, the Fiat-Shamir and Guillou-Quisquater protocols for proving knowledge of a modular root, protocols for proving knowledge of representations (like Okamoto’s protocol), protocols for proving equality of secret values, a protocol for proving the correctness of a Diffie-Hellman key, protocols for proving the multiplicative relation of three commitments (as required in secure multi-party computation), and protocols used in credential systems.
This shows that a single simple treatment (and proof), at a high level of abstraction, can replace the individual previous treatments. Moreover, one can devise new instantiations of the protocol.
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Maurer, U. (2009). Unifying Zero-Knowledge Proofs of Knowledge. In: Preneel, B. (eds) Progress in Cryptology – AFRICACRYPT 2009. AFRICACRYPT 2009. Lecture Notes in Computer Science, vol 5580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02384-2_17
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DOI: https://doi.org/10.1007/978-3-642-02384-2_17
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