zk-crypto

Rust implementations of cryptographic primitives building toward a full Groth16 zk-SNARK, from ECDSA and elliptic curve operations through R1CS, QAP, trusted setup, and the complete Groth16 protocol.

Resources

RareSkills, J. Scholz, Abstract Algebra (Dummit and Foote), and Wikipedia.

For detailed mathematical theory and proofs, see docs/theory.pdf.

Modules

Module	Description
rational_sums	Verify rational sum equations on elliptic curves via scalar-to-point mapping
ecp_matrix	Matrix-vector multiplication on elliptic curve points; homomorphism verification
ecdsa	ECDSA key generation, signing, and verification over secp256k1
bilinear_pairings	Multi-pairing equation verification on BN254
r1cs	R1CS verification: field-based (Hadamard) and pairing-based
r1cs_to_qap	Lagrange interpolation, QAP construction, polynomial quotient computation
qap_trusted_setup	SRS generation and Pinocchio-style prove/verify (prover sees tau)
groth16::alpha_beta	Groth16 with alpha/beta shifting (no ZK blinding)
groth16::complete	Full Groth16: gamma/delta separation, r/s blinding, public input binding
utils	Shared helpers: field conversion, modular inverse, random scalar generation

Usage

Run all demos:

cargo run --example demo

Run a specific module demo:

cargo run --example ecdsa
cargo run --example rational_sums
cargo run --example ecp_matrix
cargo run --example bilinear_pairings
cargo run --example r1cs
cargo run --example r1cs_to_qap
cargo run --example qap_trusted_setup
cargo run --example groth16_alpha_beta
cargo run --example groth16_complete

List available examples:

cargo run --example

Tests

cargo test

Proptest example:

cargo test demo_proptest -- --ignored --nocapture  

Dependencies

• ark-ec, ark-ff, ark-std, ark-poly -- Arkworks core algebra
• ark-secp256k1 -- secp256k1 curve (ECDSA, rational sums, ECP matrix)
• ark-bn254 -- BN254 curve and bilinear pairings
• sha2 -- SHA-256 message hashing
• getrandom -- OS-entropy random number generation
• num-bigint, num-traits -- Arbitrary precision integers

Dev Dependencies

• proptest -- Property-based testing

Building

cargo build

Documentation

Mathematical theory and proofs are in docs/theory.pdf.