UTXO Indexer

The UTXO Indexer actively monitors Bitcoin’s blockchain to trace and verify UTXOs linked to Nexio transactions.

Within this system, each UTXO is mathematically represented as a tuple u = (pk, v, σ, d), where:

• pk represents the recipient’s public key,
• v denotes value in satoshis,
• σ represents the signature, and
• d encompasses additional data like script structures.

The complete UTXO set U at any block height h can be expressed as U(h) = {u₁, u₂, ..., uₙ}. The Indexer meticulously catalogs all zk-proofs and state changes validated by Nexio’s decentralized signers, ensuring they are securely indexed and fully traceable within Bitcoin’s immutable ledger.

​

Real-Time Blockchain Monitoring and Validation

The UTXO Indexer connects to a Bitcoin node to process each new block 𝐵 , scanning for transactions with Nexio-specific markers. For each transaction 𝑡𝑥 , the Indexer extracts the zk-proof 𝜋 , verifies it, and updates the blockchain state if valid. This process ensures that only verified zk-proofs contribute to state transitions, maintaining the ledger’s integrity.

The core logic for this operation is as follows:

1. Indexing Transactions: The Indexer scans each transaction in a new block:
   • If a Nexio marker is found, the zk-proof is extracted and verified.
   • Verified transactions are added to the Indexer’s dataset.
2. Proof Verification: zk-proofs are validated using:
   
   $Verify(pk,msg,σ)=true if g H(msg) =pk σ modp, false otherwise$
   
   where g is the generator point and p is the field prime.
3. State Validation: State transitions are validated using:
   
   $S′=T(S,tx)$
   
   where TTT maps the current state SSS and transaction tx to a new state S′. The Indexer ensures that:

• The zk-proof π\piπ is valid.
• The resulting state S′S’S′ satisfies all defined conditions for a valid transition.

This streamlined process establishes a secure audit trail, enhancing indexing efficiency (EEE) defined as:

$E = \left( \frac{n_{\text{relevant}}}{n_{\text{total}}} \right) \times 100\%$

where n relevant is the number of relevant transactions processed, and n total​ is the total transactions scanned.

By combining real-time monitoring, proof validation, and state transitions, the UTXO Indexer ensures secure and efficient indexing of Nexio-related transactions within Bitcoin’s immutable ledger.

​

Efficient Proofs & Secure Finality

The UTXO Listener employs sophisticated pattern matching to identify zk-proof data, with a security guarantee expressed as P(attack) = 1 - (1 - (h/H))^k, where H represents Bitcoin’s hash rate, h represents attacker hash rate, and k represents the number of confirmation blocks. This mathematical foundation ensures robust security while maintaining efficient operation.

The system also establishes a finality threshold F = ⌈-log(ε)/log(1-p)⌉, where ε represents acceptable error probability and p represents the probability of successful block reversion. This threshold, combined with the dual-layer security model, creates a robust environment for all zk-proof-linked operations.

By anchoring zk-proofs directly to Bitcoin, the UTXO Listener leverages Bitcoin’s security to create a trusted environment where each proof maintains its integrity with a mathematically verifiable guarantee. The layered anchoring approach supports Nexio’s objective to offer reliable cross-chain finality, ensuring that each transaction and state transition is secure and correct.