Complexity Bounds and Practical Deployment Considerations
Linear-time proof systems such as Libra reduce prover cost to O(C) and verifier cost to O(log² C). Practical benchmarks show sub-second verification for commitments under 128-bit security.
| Operation | Time T(n) | Space S(n) | Communication |
|---|---|---|---|
| Entropy generation | O(k) | O(k) | setup |
| Commitment creation | O(1) | O(1) | O(1) |
| Homomorphic add / mul | O(1) | O(1) | local |
| ZK proof generation | O(|C|) | O(|π|) | O(|π|) |
| ZK verification | O(1) | O(1) | local |
| Epoch transition | O(n) | O(n) | O(n) |
Modern zero-knowledge proof systems achieve linear-time generation and logarithmic verification, enabling practical deployment at scale.
Optimized implementations achieve sub-second verification times for commitments under 128-bit security parameters.
Multi-core processors with sufficient RAM for proof generation, with GPU acceleration for cryptographic operations where applicable.
Efficient proof transmission protocols with compression and batched verification for high-throughput deployments.
Optimized commitment storage with efficient indexing for fast retrieval and verification of historical transactions.
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