[Resource Topic] 2021/1377: Fiat-Shamir Transformation of Multi-Round Interactive Proofs

Welcome to the resource topic for 2021/1377

Fiat-Shamir Transformation of Multi-Round Interactive Proofs

Authors: Thomas Attema, Serge Fehr, Michael Klooß


The celebrated Fiat-Shamir transformation turns any public-coin interactive proof into a non-interactive one, which inherits the main security properties (in the random oracle model) of the interactive version. While originally considered in the context of 3-move public-coin interactive proofs, i.e., so-called \Sigma-protocols, it is now applied to multi-round protocols as well. Unfortunately, the security loss for a (2\mu + 1)-move protocol is, in general, Q^\mu, where Q is the number of oracle queries performed by the attacker. In general, this is the best one can hope for, as it is easy to see that this loss applies to the \mu-fold sequential repetition of \Sigma-protocols, but it raises the question whether certain (natural) classes of interactive proofs feature a milder security loss. In this work, we give positive and negative results on this question. On the positive side, we show that for (k_1, \ldots, k_\mu)-special-sound protocols (which cover a broad class of use cases), the knowledge error degrades linearly in Q, instead of Q^\mu. On the negative side, we show that for t-fold \emph{parallel repetitions} of typical (k_1, \ldots, k_\mu)-special-sound protocols with t \geq \mu (and assuming for simplicity that t and Q are integer multiples of \mu), there is an attack that results in a security loss of approximately~\frac12 Q^\mu /\mu^{\mu+t}.

ePrint: https://eprint.iacr.org/2021/1377

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .