Public-Coin 3-Round Zero-Knowledge from Learning with Errors and Keyless Multi-Collision-Resistant Hash

We construct a public-coin 3-round zero-knowledge argument for NP assuming (i) the sub-exponential hardness of the learning with errors (LWE) problem and (ii) the existence of keyless multicollision-resistant hash functions against slightly super-polynomial-time adversaries. These assumptions are almost identical to those that were used recently to obtain a private-coin 3-round zero-knowledge argument [Bitansky et al., STOC 2018]. (The difference is that we assume subexponential hardness instead of quasi-polynomial hardness for the LWE problem.)

1 Some of these works constructed even 2-round or non-interactive ZK arguments under weak security definitions. 2 More precisely, they obtained it by relying on various cryptographic primitives that can be based on these assumptions.