What are the core technical principles of the Taproot upgrade? How does it enhance Bitcoin's privacy, scalability, and smart contract capabilities through Merkelized Abstract Syntax Trees (MAST) and Schnorr Signatures?

Core Technical Principles of the Taproot Upgrade

Taproot is a major Bitcoin upgrade activated in 2021. Its core principle is to optimize Bitcoin script execution and transaction structure by combining Merkelized Abstract Syntax Tree (MAST) and Schnorr Signatures. The specific principles are as follows:

1. Schnorr Signatures:

   • Schnorr signatures are an efficient cryptographic signature scheme that allows multiple signatures to be aggregated into a single signature.
   • In Taproot, signatures from all participants (e.g., members of a multi-signature wallet) can be combined into one compact signature, reducing transaction data size.
   • This is based on key aggregation technology: public keys can be combined into an "aggregated public key," and only one signature is needed to represent all participants during signing.

2. Merkelized Abstract Syntax Tree (MAST):

   • MAST organizes complex Bitcoin scripts (such as smart contract conditions) into a Merkle tree structure.
   • Each leaf node represents a possible execution path (e.g., "timelock unlock" or "multi-signature verification"), and the root node hash is stored on the blockchain.
   • During transaction execution, only the script path that satisfies the conditions and its Merkle proof are revealed; other paths remain hidden.

3. Core Integration of Taproot:

   • A Taproot output (P2TR) combines the above technologies: a Taproot address is essentially an aggregated public key (based on Schnorr), but it may conceal a MAST structure behind it.
   • In the ideal scenario (all participants cooperate), the transaction appears as a simple Schnorr signature payment, revealing no script details.
   • Only in dispute scenarios (e.g., conditions not met) is the specific script path within MAST revealed, and its validity verified using the Merkle proof.
   • This design makes all transactions appear identical on-chain, enhancing privacy and efficiency.

How MAST and Schnorr Signatures Enhance Bitcoin's Features

Enhanced Privacy

• Contribution of Schnorr Signatures:
  • Signature aggregation makes multi-signature transactions appear like single-signature transactions, hiding the number and identity of participants (e.g., a corporate payment cannot be distinguished as a multi-signature operation).
  • Reduces on-chain data leakage, making it harder for attackers to analyze transaction patterns.
• Contribution of MAST:
  • Only the script path satisfying the conditions is revealed; other potential conditions (e.g., alternative unlock methods) remain encrypted and hidden, preventing observers from inferring contract logic.
  • For example, in a timelock contract, only the actually used unlock path is exposed, enhancing the confidentiality of transaction details.
• Combined Effect: Taproot makes the vast majority of transactions appear as "ordinary payments" on the blockchain, significantly reducing privacy leakage risks and approaching cash-like anonymity.

Enhanced Scalability

• Contribution of Schnorr Signatures:
  • Signature aggregation significantly reduces transaction size: e.g., a 10-signer transaction size can be reduced by approximately 50% (from hundreds of bytes down to about 64 bytes).
  • Reduces blockchain storage and bandwidth requirements, increasing network throughput (more transactions processed per second).
• Contribution of MAST:
  • Script data is compressed via the Merkle tree: only the root hash is stored on-chain, and the actual script is revealed only when needed, saving block space.
  • Reduces redundant data, optimizing node storage and verification efficiency.
• Combined Effect: Taproot transactions are smaller and lighter, alleviating Bitcoin's scaling pressure and supporting higher transaction volumes without increasing block size.

Enhanced Smart Contract Capabilities

• Contribution of MAST:
  • Allows defining multiple conditional paths (e.g., "signature from A OR B" or "unlock after timelock") without increasing the on-chain footprint.
  • Supports more complex logic (e.g., multi-step contracts) because unused paths occupy no space, enabling developers to design more flexible scripts.
• Contribution of Schnorr Signatures:
  • Simplifies signature management, making smart contract execution more efficient (e.g., aggregated signatures reduce verification computation).
  • Combined with Taproot, contracts can "revert to" simple payments in cooperative scenarios, avoiding script execution overhead.
• Combined Effect: Taproot unlocks more advanced smart contract applications (such as decentralized finance or conditional payments) while maintaining low cost and privacy, driving Bitcoin's evolution into programmable money.