Zero-Knowledge Proofs in Midnight

Zero-knowledge proofs let you prove knowledge of a secret without revealing it. In Midnight, ZK proofs validate that transactions follow contract rules without exposing private data.

Core Concept

A ZK proof proves: "I know values that satisfy these constraints" without revealing the values.

Midnight application: Prove a transaction is valid (correct inputs, authorized user, rules followed) without exposing private state or user secrets.

ZK SNARKs

Midnight uses ZK SNARKs (Zero-Knowledge Succinct Non-interactive Arguments of Knowledge):

How Proofs Work in Midnight

Transaction Structure

Every Midnight transaction contains:

1. •Public transcript - Visible state changes
2. •Zero-knowledge proof - Cryptographic validation

The proof demonstrates: "I know private inputs that, when combined with public data, satisfy the contract's constraints."

Circuit Mental Model

Contract logic compiles to circuits - mathematical constraint systems.

Compact Code → Circuit Constraints → ZK Proof

A circuit defines relationships between variables. The proof shows you know variable assignments satisfying all constraints without revealing the assignments.

Proof Lifecycle

1. Setup      → Generate proving/verification keys (per circuit)
2. Witness    → Prover assembles private inputs
3. Prove      → Generate proof from witness + circuit
4. Verify     → Check proof against public inputs (fast)

Circuits in Practice

What Gets Proven

When a Compact contract executes:

1. •Contract logic compiles to arithmetic circuit
2. •Private values become witness inputs
3. •Public values become public inputs
4. •Proof demonstrates correct execution

Circuit Constraints

Circuits express computations as polynomial constraints:

// Conceptual: proving x * y = z without revealing x, y
constraint: a * b = c
public input: c = 42
witness (private): a = 6, b = 7

Compact to Circuit

// This Compact code...
export circuit guess(guess: Field): Void {
  const product = guess * other_factor;
  assert product == ledger.target;
}

// ...compiles to constraints that prove:
// 1. guess * other_factor equals target
// 2. Without revealing guess or other_factor values

Practical Applications

Proving Without Revealing

In Contracts

// Prove knowledge of factors without revealing them
export circuit proveFactors(
  secret_a: Field,  // Private witness
  secret_b: Field   // Private witness
): Void {
  // Constraint: factors multiply to public target
  assert secret_a * secret_b == ledger.public_target;
}

Key Concepts

Witness

Private inputs the prover knows. Never revealed, used only to generate proof.

Public Inputs

Values visible to everyone. Proof verified against these.

Verification

Checking a proof is fast (milliseconds) regardless of original computation complexity.

Soundness

Computationally infeasible to create valid proof without knowing witness.

Performance Characteristics

References

For detailed technical information:

• •references/snark-internals.md - Elliptic curves, pairings, trusted setup
• •references/circuit-construction.md - How Compact compiles to circuits

Examples

Working patterns:

• •examples/circuit-patterns.compact - Common proof patterns