Instance-Dependent Verifiable Random Functions and Their Application to Simultaneous Resettability

We introduce a notion of instance-dependent verifiable random functions (InstD-VRFs for short). Informally, an InstD-VRF is, in some sense, a verifiable random function [23] with a special public key, which is generated via a (possibly)interactive protocol and contains an instance y ∈ L ∩ {0, 1}∗ for a specific NP language L, but the security requirements on such a function are relaxed: we only require the pseudorandomness property when y ∈ L and only require the uniqueness property when y / ∈ L, instead of requiring both pseudorandomness and uniqueness to hold simultaneously. We show that this notion can be realized under standard assumption. Our motivation is the conjecture posed by Barak et al.[2], which states there exist resettably-sound resettable zero knowledge arguments for NP. The instance-dependent verifiable random functions is a powerful tool to tackle this problem. We first use them to obtain two interesting instancedependent argument systems from the Barak’s public-coin bounded concurrent zero knowledge argument [1], and then, we 1. Construct the first (constant round) zero knowledge arguments for NP enjoying a certain simultaneous resettability under standard hardness assumptions in the plain model, which we call boundedclass resettable ZK arguments with weak resettable-soundness. Though the malicious party (prover or verifier) in such system is limited to a kind of bounded resetting attack, We put NO restrictions on the number of the total resets made by malicious party. 2. show that, under standard assumptions, if there exist public-coin concurrent zero knowledge arguments for NP, there exist the resettablysound resetable zero knowledge arguments for NP.