Abstract—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(log M)), 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 服务器托管网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 w服务器托管网e call partitionand-sample, with minimal ‘1-norm and invertible challenge differences (with overwhelming probability), while supporting highlysplitting power-of-2 cyclotomic rings. We believe all these results
to be widely applicable and of independent interest.
Index Terms—Post-Quantum, RingCT, Lattice, ZeroKnowledge, Blockchain, Ring Signature
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