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Published in:

2017 | OriginalPaper | Chapter

# Efficient Rational Proofs for Space Bounded Computations

Authors : Matteo Campanelli, Rosario Gennaro

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## Abstract

We present new protocols for the verification of space bounded polytime computations against a rational adversary. For such computations requiring sublinear space our protocol requires only a verifier running in sublinear-time. We extend our main result in several directions: (i) we present protocols for randomized complexity classes, using a new composition theorem for rational proofs which is of independent interest; (ii) we present lower bounds (i.e. conditional impossibility results) for Rational Proofs for various complexity classes.
Our new protocol is the first rational proof not based on the circuit model of computation, and the first sequentially composable protocols for a well-defined language class.
Footnotes
1
We also point out that in [16] a rational protocol for P, polytime computations, is presented, but for the case of a computationally bounded prover, i.e. a rational argument.

2
This is basically the covert adversary model for multiparty computation introduced in [2].

3
We point out that the new machine $$M_2$$ introduces a small error. For our specific case this error keeps the overall error probability negligible and we can ignore it.

4
A common reference string is a string generated by a trusted party to which both the prover and the verifier have access; it is a common assumption in cryptographic literature, e.g. Non-Interactive Zero Knowledge [7].

5
Since we only sketch our proof the reader is invited to see details of the proof [15].

6
We stress that in this comparison we are interested in protocols with similar efficiency parameters. For example, the work in [3] presents several large complexity classes for which we have rational proofs. However, these protocols require a polynomial verifier and do not obtain a noticeable reward gap.

7
The construction in Theorem 5.1 in [4] is shown to be sequentially composable in [8].

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