What is a Bitcoin bulletproof?

A Bitcoin Bulletproof is a cryptographic proof technique used to improve the efficiency and privacy of transactions on the Bitcoin blockchain. It is specifically designed to reduce the size of range proofs, which are cryptographic proofs used to prove that certain values fall within a specified range, such as the range of valid amounts in a confidential transaction.

Bulletproofs were first proposed by researchers from Stanford University and University College London in a paper published in May 2018. They are an improvement over existing range proof techniques, such as those used in confidential transactions, which can be computationally expensive and result in large transaction sizes.

Here's how a Bitcoin Bulletproof typically works:

1. **Range Proofs**: In confidential transactions, range proofs are used to prove that the amounts being transferred are within a certain range, such as non-negative integers. These range proofs ensure that no bitcoins are created or destroyed in the transaction and that the amounts are valid and not negative.

2. **Compactness**: Bulletproofs aim to improve the compactness of range proofs by reducing their size while still maintaining their security and efficiency. This is achieved through the use of more efficient cryptographic techniques, such as aggregated range proofs and zero-knowledge proofs.

3. **Efficiency**: By reducing the size of range proofs, Bulletproofs improve the efficiency of confidential transactions on the Bitcoin blockchain. Smaller range proofs result in smaller transaction sizes, lower transaction fees, and improved scalability of the Bitcoin network.

4. **Privacy**: Bulletproofs also enhance the privacy of transactions by reducing the amount of information that needs to be disclosed on the blockchain. With smaller range proofs, less information is revealed about the amounts being transferred, improving the confidentiality of transactions.

Overall, Bitcoin Bulletproofs represent an important advancement in the field of cryptographic proofs and privacy-enhancing technologies for the Bitcoin blockchain. They enable more efficient and private transactions while maintaining the security and integrity of the Bitcoin network. Bulletproofs have been implemented in various Bitcoin software implementations and are used in protocols such as the Confidential Transactions feature of the Elements Project and Liquid sidechain.