Shorter Proofs for Privacy-Enhanced Distributed Ledger

We present a new short zero-knowledge argument for the range proof and the arithmetic circuits without a trusted setup. In particular, the proof size of our protocol is the shortest of the category of proof systems with a trustless setup. More concretely, when proving a committed value is a positive integer less than 64 bits, except for negligible error in the 128-bit security parameter, the proof size is 576 byte long, which is of 85.7% size of the previous shortest one due to Bunzetal.