International Association
for Cryptologic Research

We investigate proof systems where security holds against rational parties instead of malicious ones. Our starting point is the notion of rational arguments}, a variant of rational proofs (Azar and Micali, STOC 2012) where security holds against rational adversaries that are also computationally bounded.

Rational arguments are an interesting primitive because they allow for sublinear verification and a more efficient protocol in general. In this paper we aim at narrowing the gap between literature on rational schemes and real world applications. Our contribution is two-fold.

We provide the first construction of rational arguments for the class of polynomial computations that is practical (i.e., it can be applied to real-world computations on reasonably common hardware) and with logarithmic communication. Techniques-wise, we obtain this result through a compiler from information-theoretic protocols and rational proofs for polynomial evaluation. The latter could be of independent interest.

As a second contribution, we propose a new notion of extractability for rational arguments. Through this notion we can obtain arguments where knowledge of a witness is incentivized (rather than incentivizing mere soundness). We show how our aforementioned compiler can also be applied to obtain efficient extractable rational arguments for $\mathsf{NP}$.