Abstract. Bulletproofs is a ubiquitous zero-knowledge proof protocol that demonstrates a committed value is restricted to a predetermined, short interval such as [0, 2^n); this is called a range proof. This type of protocol is a requirement for cryptocurrencies, as otherwise an adversary could create a transaction for a negative amount, causing modular overflow, thus inflating the supply of coins without bound. In SLVer Bullet, we improve upon the literature by dramatically reducing the verification time of Bulletproofs utilizing divisors, where the verifier randomly selects a line that the aforementioned range claim may be authenticated against, then invokes relationships like Weil's Reciprocity Law. This reduction to verification time is particularly desirable for blockchains, where transactions need only be generated once, but verified repeatedly - hence this protocol applies directly to cryptocurrencies such as Monero.
https://eprint.iacr.org/2025/1345