# Bulletproofs

Source URL: https://support.dxp.blockstream.com/education/glossary/bulletproofs
Updated: 2026-05-26T17:14:52.000Z
Letter: B

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A type of [zero-knowledge proof](https://support.dxp-staging.blockstream.com/education/glossary/zero-knowledge-proofs-zkps) in Bitcoin-related systems that enable confidentiality without revealing transaction amounts.  
  
For example, Bulletproofs enhance [Confidential Transactions](https://support.dxp-staging.blockstream.com/education/glossary/confidential-transactions) on the [Liquid Network](https://support.dxp-staging.blockstream.com/education/glossary/liquid-network), with Bulletproofs++ serving as a further refined version that is faster and more cost-efficient.  
  
Specifically, Bulletproofs++ are _O_(log(n)) to create and _O_(n) to verify (where _n_ is the number of bits necessary to express the value). With Bulletproofs++, a typical Confidential Transactions would go from being \~10x as expensive as unblinded transactions to being \~2x as expensive as unblinded transactions.  
  
Smaller Bulletproofs++ also mean that transactions add new weight to the blockchain more slowly, which slows the rate at which the initial-block-download burden grows. That is particularly important if Bulletproofs++ are to be used on Bitcoin eventually.  
  
Because Bulletproofs++ generalize to any mathematical computation, in principle, any Simplicity covenant could also be expressed as a Bulletproof. Theoretically, this would make complicated smart contracts and options logic cheaper and more private.  
  
For more information on Bulletproofs, read the latest version of the “_Bulletproofs++: Next Generation Confidential Transactions via Reciprocal Set Membership Arguments_” paper, currently hosted and freely available on the IACR eprint [archive](https://eprint.iacr.org/2022/510?ref=blog.blockstream.com). You can also review the work-in-progress implementation on [GitHub](https://github.com/BlockstreamResearch/secp256k1-zkp/pull/205?ref=blog.blockstream.com).

Additionally, the visual explainer below may also be valuable.

Navigation: Blockstream Help Center > Education > Glossary > Bulletproofs

## Related Terms in This Letter
- [Blind oracle](https://support.dxp.blockstream.com/education/glossary/blind-oracle)
- [Borromean ring signatures](https://support.dxp.blockstream.com/education/glossary/borromean-ring-signatures)
- [Bitcoin Script](https://support.dxp.blockstream.com/education/glossary/bitcoin-script)
- [BitVM](https://support.dxp.blockstream.com/education/glossary/bitvm)
- [BOLT12](https://support.dxp.blockstream.com/education/glossary/bolt12)
- [Bitcoin](https://support.dxp.blockstream.com/education/glossary/bitcoin)
- [Bitcoin Node](https://support.dxp.blockstream.com/education/glossary/bitcoin-node)
- [Bitcoin Core](https://support.dxp.blockstream.com/education/glossary/bitcoin-core)
- [Bulletproofs](https://support.dxp.blockstream.com/education/glossary/bulletproofs) (current)
- [Blind signatures](https://support.dxp.blockstream.com/education/glossary/blind-signatures)
- [Blockchain](https://support.dxp.blockstream.com/education/glossary/blockchain)
- [Block](https://support.dxp.blockstream.com/education/glossary/block)
- [Block Header](https://support.dxp.blockstream.com/education/glossary/block-header)
- [Block Height](https://support.dxp.blockstream.com/education/glossary/block-height)
- [Blockchain Explorer API](https://support.dxp.blockstream.com/education/glossary/blockchain-explorer-api)
- [Broadcast Transaction](https://support.dxp.blockstream.com/education/glossary/broadcast-transaction)