Scalable Zero Knowledge with No Trusted Setup

Abstract

One of the approaches to constructing zero knowledge (ZK) arguments relies on “PCP techniques” that date back to influential works from the early 1990’s [Babai et al., Arora et al. 1991-2]. These techniques require only minimal cryptographic assumptions, namely, the existence of a family of collision-resistant hash functions [Kilian, STOC 1992], and achieve two remarkable properties: (i) all messages generated by the verifier are public random coins, and (ii) total verification time is merely poly-logarithmic in the time needed to naïvely execute the computation being verified [Babai et al., STOC 1991]. Those early constructions were never realized in code, mostly because proving time was too large. To address this, the model of interactive oracle proofs (IOPs), which generalizes the PCP model, was recently suggested. Proving time for ZK-IOPs was reduced to quasi-linear, even for problems that require nondeterministic exponential time to decide [Ben-Sasson et al., TCC 2016, ICALP 2017]. Despite these recent advances it was still not clear whether ZK-IOP systems can lead to concretely efficient succinct argument systems. Our main claim is that this is indeed the case. We present a new construction of an IOP of knowledge (which we call a zk-STIK) that improves, asymptotically, on the state of art: for log-space computations of length T it is the first to (Formula Presented) arithmetic prover complexity and (Formula Presented) verifier arithmetic complexity. Prior IOPs had additional (Formula Presented) factors in both prover and verifier. Additionally, we report a C++ realization of this system (which we call libSTARK). Compared to prevailing ZK realizations, it has the fastest proving and (total) verification time for sufficiently large sequential computations.