Improving Line-Point Zero Knowledge: Two Multiplications for the Price of One

Recent advances in fast protocols for vector oblivious linear evaluation (VOLE) have inspired a family of new VOLE-based lightweight designated-verifier NIZK protocols (Weng et al., S&P 2021, Baum et al., Crypto 2021, Dittmer et al., ITC 2021, Yang et al., CCS 2021). In particular, the Line-Point Zero Knowledge (LPZK) protocol of Dittmer et al. has the advantage of being entirely non-cryptographic given a single instance of a random VOLE correlation.