Abstract
We investigate whether it is possible to obtain any meaningful type of zero-knowledge proofs using a one-message (i.e., non-interactive) proof system. We show that, under reasonable (although not standard) assumptions, there exists a one-message proof system for every language in NP that satisfies the following relaxed form of zero knowledge:
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1
The soundness condition holds only against cheating provers that run in uniform (rather than non-uniform) probabilistic polynomial-time.
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2
The zero-knowledge condition is obtained using a simulator that runs in quasi-polynomial (rather than polynomial) time.
We note that it is necessary to introduce both relaxations to obtain a one-message system for a non-trivial language. We stress that our result is in the plain model, and in particular we do not assume any setup conditions (such as the existence of a shared random string).
We also discuss the validity of our assumption, and show two conditions that imply it. In addition, we show that an assumption of a similar kind is necessary in order to obtain a one-message system that satisfies some sort of meaningful zero-knowledge and soundness conditions.
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Barak, B., Pass, R. (2004). On the Possibility of One-Message Weak Zero-Knowledge. In: Naor, M. (eds) Theory of Cryptography. TCC 2004. Lecture Notes in Computer Science, vol 2951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24638-1_7
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DOI: https://doi.org/10.1007/978-3-540-24638-1_7
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