zkSNARK Algorithm

What Is the ZK-SNARK Algorithm?

A ZK-SNARK (Zero-Knowledge Succinct Non-Interactive Argument of Knowledge) is a powerful cryptographic technique that allows one party to prove the validity of certain information without revealing the information itself. Built on the principles of zero-knowledge, efficiency, and non-interactivity, ZK-SNARKs enable highly private and scalable verification—making them a foundational component of privacy-focused cryptocurrencies like Zcash.

The ZK-SNARK protocol operates through three core algorithms, which work together to generate proofs and verify them efficiently:

Key Generation (G)
The system begins with a trusted setup phase, where a secret parameter λ and the target program C are used to generate two public keys:

Proving Key (pk): Used by the prover to construct a zero-knowledge proof.

Verification Key (vk): Used by the verifier to check the proof’s correctness.
This setup is performed once for each program C and establishes the trust foundation of the system.

Proving Algorithm (P)
With the proving key pk and the private inputs, the prover generates a compact cryptographic proof.
This proof demonstrates that the prover executed program C correctly—without disclosing any underlying data.

Verification Algorithm (V)
Anyone can use the verification key vk to validate the proof in an extremely short time.
The verification process is highly efficient, enabling ZK-SNARKs to be used in real-world blockchain environments where performance and scalability matter.

Thanks to their privacy, security, succinctness, and scalability, ZK-SNARKs have become a core technology in modern blockchain systems. They are widely used in private transactions, off-chain computation verification, zero-knowledge rollups, and many other applications where confidentiality and trustless verification are essential.