Abstract
This article points out a gap between two natural formulations of the concept of a proof of knowledge, and shows that in all natural cases (e.g., NP-statements) this gap can be bridged. The aforementioned formulations differ by whether they refer to (all possible) probabilistic or deterministic prover strategies. Unlike in the rest of cryptography, in the current context, the obvious transformation of probabilistic strategies to deterministic strategies does not seem to suffice per se. The source of trouble is “bad interaction” between the expectation operator and other operators, which appear in the definition of a proof of knowledge (reviewed here).
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References
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Bellare, M., Goldreich, O. (2011). On Probabilistic versus Deterministic Provers in the Definition of Proofs of Knowledge. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_14
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DOI: https://doi.org/10.1007/978-3-642-22670-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22669-4
Online ISBN: 978-3-642-22670-0
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