MatRiCT⁺: more efficient post-quantum private blockchain payments

We introduce MatRiCT+, a practical private blockchain payment protocol based on 'post-quantum' lattice assumptions. MatRiCT+ builds on MatRiCT due to Esgin et al. (ACM CCS'19) and, in general, follows the Ring Confidential Transactions (RingCT) approach used in Monero, the largest privacy-preserving cryptocurrency. In terms of the practical aspects, MatRiCT+ has 2-18× shorter proofs (depending on the number of input accounts, M) and runs 3-11× faster (for a typical transaction) in comparison to MatRiCT. A significant advantage of MatRiCT+ is that the proof length's dependence on M is very minimal (only O(logM)), while MatRiCT has a proof length linear in M. To support its efficiency, we devise several novel techniques in our design of MatRiCT+ to achieve compact lattice-based zeroknowledge proof systems, exploiting the algebraic properties of power-of-2 cyclotomic rings commonly used in practical latticebased cryptography. Along the way, we design a family of 'optimal' challenge spaces, using a technique we call partition-and-sample, with minimal \ell_{1}-norm and invertible challenge differences (with overwhelming probability), while supporting highly-splitting power-of-2 cyclotomic rings. We believe all these results to be widely applicable and of independent interest.