Groth16

Groth16 is a zero-knowledge SNARK construction introduced by Jens Groth in 2016. It enables succinct, non-interactive proofs for statements encoded as arithmetic circuits, using a quadratic arithmetic program (QAP) as the underlying framework. The resulting proofs are small and can be verified very quickly, making Groth16 a popular choice for systems where verification cost is critical, such as privacy-preserving protocols and blockchain applications.

The construction relies on a trusted setup that produces a structured common reference string, consisting of a proving key and a verification key. A circuit is transformed into a QAP, and, given a valid witness, the prover uses the CRS to generate a short proof. The verifier then checks the proof with the verification key by performing a small number of pairing operations on an elliptic-curve group. The proof size and verification time remain essentially constant regardless of the circuit size, which is a key practical advantage.

Limitations and considerations include the requirement of a trusted setup, which, if compromised, can undermine both soundness and privacy. Groth16 is not post-quantum secure, as it relies on discrete logarithm problems in pairing-based curves. After a trusted setup, the CRS must be kept secure and can be reused to produce multiple proofs for the same circuit family.

Impact and usage: Groth16 has been widely adopted in zk-SNARK toolchains and blockchain projects, with multiple libraries and tooling supporting its proofs and verification. It is commonly used for enabling scalable, on-chain verification of complex computations while maintaining strong privacy guarantees.