Bulletproofs+: Shorter Proofs for a Privacy-Enhanced Distributed Ledger

This paper presents a new short zero-knowledge argument for the range proof and arithmetic circuits without trusted setup. In particular, it can achieve shortest size of system categories More specifically, when proving that committed value is positive integer less than 64 bits, except negligible error in 128-bit security parameter, 576 bytes long, which 85.7% previous due to Bünz et al. (Bulletproofs, IEEE Security Privacy 2018). Similarly, circuit satisfiability be proven with communication overhead. Nevertheless, computational overheads both generation verification are comparable those Bulletproofs. Bulletproofs established as one important privacy-enhancing technologies distributed ledger its trustless feature size. has been implemented optimized various programming languages practical usage by independent entities since was proposed. The essence based on logarithmic inner product no zero-knowledge. revisits from viewpoint first sublinear linear algebra Groth (CRYPTO 2009) then propose Bulletproofs+, an improved variety main component xmlns:xlink="http://www.w3.org/1999/xlink">zero-knowledge weighted (zk-WIP) enables reduce proof. It already properties, there additional information reducing zk-WIP, incurs minimal transmission cost during reduction process. Note zk-WIP all characteristics argument, such aggregating batch verification; thus, Bulletproofs+ superior aspects.