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Used in multi-party-ecdsa
Rust library for building IQC: cryptography based on class groups (Cl) of imaginary quadratic orders.
Cls are easy to generate. Their most interesting and useful property is that finding the group order is considered hard. In recent years we see more and more cryptographic primitives instantiated using Cls. We recommend [6,7,8] to learn more about Cls in practice.
Group Element Representation
Group Element can be represented as (a,b,c) or (a,b,Δ) triple (correspond to BinaryQF and ABDeltaTriple structures respectively). We also support compression from the paper (see BinaryQFCompressed structure).
Contributions for implementing new primitives or improving existing ones are welcome. See open issues first. Existing primitives can be found in the primitives folder :
PoE: Proof of exponantiation: The prover can efficiently convince a verifier that a large exponentiation was done correctly. Statement is
(x,u,w), verifier accept if
w = u^x.
Polynomial commitment: The following algorithms are implemented ( subsection 4.2 and 4.3):
Setup: generate public parameters
Commit: commit to a polynomial
Open: open and verify a commitment
Encode: stand alone code to encode a polynomial as an integer
Decode: converts integer to a unique polynomial
Eval_prover: NI proof that
y = f(z)for a committed polynomial
Eval_verify: NI verifier for eval_proof.
VDF: Verifiable Delay Function. Based on Wesolowski protocol [4,5]. The following interface is implemented. The same setup can be used for multiple proofs.
time(Eval) >> time(Verify):
Setup: generate public key
Eval: using the public key generate a vdf statement
Verify: verify the statement using the public key
Encryption scheme: Linearly homomorphic encryption scheme and a ZK proof. interface includes:
Verify. The encryption scheme is taken from  Theorem 2. The zero knowledge proof is a non interactive version of the proof given in  figure 8. The proof Statement includes a public elliptic curve point
Q = xGand proves that a given ciphertext is encrypts
x. The ZK proof has another, experimental variant. This construcction is in use in 2P-ECDSA. To make to proof more efficient we use the LCM trick. see
The library uses bindings to PARI c library. Running
Cargo build for the first time will take PARI from the depend folder and install it on the machine. It was tested on MacOS and Linux. If you encounter a problem with installation of PARI, please open an issue and try to install it manually. Bindings are generated automatically on the fly which might slow down the build procces by a few seconds.
Tests in rust are multi-thearded if possible. However, PARI configuration supports a single thread. Therefore to make sure all tests run with defined behaviour please use
cargo test -- --test-threads=1.
We use tests to demonstrate correctness of each primitive: At the end of each primitive
.rs file there is a test to show the correct usage of the primitive. There is usually one test or more to show soundness of the implementation, i.e. not knowing a witness will fail a PoK. For all tests we assume 128bit security (conservatively translates into 1600bit Discriminant).
Security assumptions can differ between primitives and are discussed in the relevant papers. They should be understood well before using any primitive. The code is not audited and we did not attempted to make it constant time. Do not use this library in production system.
Hall of Fame
We would like to thank Fabien Laguillaumie, Guilhem Castagnos, Ida Tucker, Claudio Orlandi and Ben Fisch for their support and on-going help. We extend our gratitude to CoBloX research lab and Lloyd Fournier for contributing code, making this library more secure and fast.
 Book: Binary quadratic forms: An algorithmic approach