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In last years, there has been an increasing effort to leverage DistributedLedger Technology (DLT), including blockchain. One of the main topics ofinterest, given its importance, is the research and development of privacymechanisms, as for example is the case of Zero Knowledge Proofs (ZKP). ZKP is acryptographic technique that can be used to hide information that is put intothe ledger, while still allowing to perform validation of this data. In thiswork we describe different strategies to construct Zero Knowledge Range Proofs(ZKRP), as for example the scheme proposed by Boudot in 2001; the one proposedin 2008 by Camenisch et al, and Bulletproofs, proposed in 2017. We also comparethese strategies and discuss possible use cases. Since Bulletproofs is the mostefficient construction, we will give a detailed description of its algorithmsand optimizations. Bulletproofs is not only more efficient than previousschemes, but also avoids the trusted setup, which is a requirement that is notdesirable in the context of Distributed Ledger Technology (DLT) and blockchain.In case of cryptocurrencies, if the setup phase is compromised, it would bepossible to generate money out of thin air. Interestingly, Bulletproofs canalso be used to construct generic Zero Knowledge Proofs (ZKP), in the sensethat it can be used to prove generic statements, and thus it is not onlyrestricted to ZKRP, but it can be used for any kind of Proof of Knowledge(PoK). Hence Bulletproofs leads to a more powerful tool to provide privacy forDLT. Here we describe in detail the algorithms involved in Bulletproofsprotocol for ZKRP. Also, we present our implementation, which was open sourced.

A Survey on Zero Knowledge Range Proofs and Applications