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sigma

1-out-of-N proofs are public coin Σ-protocols of knowledge of one out of N Pedersen commitments is opening to 0. This repository contains implementations and test suites for 1-out-of-N proofs described in [https://eprint.iacr.org/2015/643.pdf], and also the implementation of the Zerocoin scheme implemented through 1-out-of-N Proofs as is described in the paper [1-out-of-N Proofs Or How to Leak a Secret and Spend a Coin, Groth & Kohlweiss, https://eprint.iacr.org/2014/764.pdf]

Directory layout

   .
   ├── src              # Source code for the protocol & schema
   ├── bitcoin          # Slightly modified source code from bitcoin
   ├── secp256k1        # Slightly modified source code from secp256k1
   ├── tests            # Test executables
   ├── build            # Script to build executables in tests (Linux & MacOS)
   ├── run_all_tests    # Script to run all tests together
   └── README.mdℤ

The code can be compiled using the following command from the root directory of the repository.

./build <directory>

For example, build ~/macos will put the executables protocol_tests, r1_test, serialize_test, sigma_primitive_types_test, coin_tests, coin_tests and coin_spend_tests in the directory ~/macos.

Group

The elliptic curve group secp256k1 used in Bitcoin.

Executables

protocol_tests

The executable protocol_tests runs sigma proof generation and verification tests. It creates random anonymity set, puts there there 0, generates proof and tries to verify. 1. one_out_of_n: It creates valid proof and verifies. 2 prove_and_verify_in_different_set: Proof is valid but anonymity set is modified. 3. prove_coin_out_of_index The index of coin is out of the set. 4. prove_coin_not_in_set Coin at provided index is not 0;

r1_tests

The executable r1_tests runs tests for R1 relation. R1

serialize_test

The executable serialization_test runs tests for EC Group element, Scalar and Sigma proof. It serializes the object, deserializes it to another object and compares them.

coin_spend_tests

The executable coin_spend_tests runs tests for whole schema.