Core Concepts
This section covers the fundamental building blocks of zero-knowledge systems.
Overview
Zero-knowledge cryptography combines several key concepts:
- Mathematical Foundations: Number theory, elliptic curves, and polynomial commitments
- Proof Systems: Methods for constructing and verifying proofs
- Cryptographic Primitives: Hash functions, commitments, and encryption
Key Terminology
| Term | Definition |
|---|---|
| Prover | The party demonstrating knowledge of a secret |
| Verifier | The party being convinced of the proof |
| Witness | The secret information the prover knows |
| Statement | The claim being proven |
| Circuit | A computational representation of the statement |
Trust Models
Trusted Setup
Some proof systems require a one-time setup ceremony that generates public parameters. If the setup is compromised, the security guarantees may be weakened.
Transparent Setup
Other systems (like STARKs) require no trusted setup, relying only on publicly verifiable randomness.
Computational Assumptions
Zero-knowledge proofs rely on various hardness assumptions:
- Discrete Logarithm Problem
- Knowledge of Exponent Assumption
- Random Oracle Model
Next: Zero-Knowledge Proofs