Description

This repo contains circuits to build ElGamal scheme over the Baby Jubjub curve.

The code to conduct the general elliptic curve operations is a custiom twisted edwards curve from the noble-curves package to prove compliant results to the field elements dependant circom-circuits.

The protocol in general aims to realize zero knowledge encryption/decryption that offers linear homomorphic properties.

• An encoding/decoding algorithm is crucial to preserve linear homomorphism. Many existing mapping, imbedding or encoding techniques are mostly utilized to map a plaintext to a curve point and the encoded point is in most cases undistinguishable when added to another point.

• The decoding algorithm in this repo is inspired from solana-zk-token that uses baby-step/giant-step algorithm to break the discrete log of a 32-bit scalar multiplication to the base point.

  • Caching a lookuptable offers O(1) time comlexity that makes decoding faster.
  • Additionally, other optimizations were tried to make it even faster by implementing Worker Threads to parallelize computation.
  • Unfortunately, it is not efficient enough to use native js concurrency and that is why the protocol will take advantage of Rust's Fearless Concurrency to break the 32-bit ECDL as fast as possible.

Install

yarn install to install the dependencies.

Build

1. yarn ptau to download a powerssOfTau file directly for a direct and swift compilation to build circuits later.

2. yarn build-circuits to build deterministic development circuits.

3. yarn precompute-lookupTable <size> to precompute a lookupTable used to help break the discrete log of the base multiplied by a 32-bit scalar.

• Note: Building a lookupTable of size=19 is crucial to run the tests!

Test

yarn test to run different circuit tests for EC operations as well as ElGamal encryption and decryption.

yarn test-circuits to run circuit tests only.

yarn test-elgamal to run ElGamal Encrypt/Decrypt & Encode/Decode tests only.

Note: What is meant by "Testing compliance of Encrypt/Decrypt circuits" is that getting the output of the "encrypt" circuit and using it as the input of the "decrypt" circuit result in a decrypted message that is identical to the original message used as an input in the "encrypt" circuit.

Bechmarking

Note: You can run the following commands individually or just read a summary of the benchmarks in the benchmarks README

yarn r1cs-info-elgamal to log all important Encrypt/Decrypt circuit infos;

yarn benchmark-babyjub to benchmark Baby Jubjub EC addition and multiplication between noble & circomlibjs packages.

yarn benchmark-decode to benchmark decoding speed using different lookup table sizes. yarn benchmark-circom_tester to benchmark the speed between snarkjs and circom_tester for circuit testing purposes.

Clean

yarn delete-lookupTables to delete all the lookupTables.

Scripts

The ptau and build-all-circuits scripts make it much easier to compile all circuit and manage the derived files in an organized way by combining Circom and SnarkJS workflow into a single command.

By providing configuration containing your Phase 1 Powers of Tau and circuits, this plugin will:

1. Compile the circuits

2. Apply the final beacon

3. Output your wasm and zkey files

Security Considerations

• ERC-2494 points to a set of solid security considerations that prove that the Baby Jubjub elliptic curve is indeed resistant against ```weak curve attacks``.
• The literature also states that the discrete logarithm problem remains difficult in the Baby Jubjub curve verifiying resistance againt the following known attacks:
  • Rho method
  • Additive and multiplicative transfers
  • High discriminant
• The package @noble/curves offers securtiy against time attacks for EC multiplication that is explicitly included in its API.
• The public key in the encrypt circuit is checked to be a point on curve and not an infinity point as a counter for invalid curve attacks(same logic applied for the ts code).
• The ephemeralKey and encryptedMessage inputs are also checked to be points on curve inside the Decrypt circuit.
• The nonces and big numbers are randomly generators by RNG functions imported from the maci package that depends on secure audited code.

References

If you want to learn about the details of ElGamal Scheme over Elliptic Curves, feel free to visit this Notion Page.