noir_rsa

Optimized Noir library that evaluates RSA signatures.

This library uses https://github.com/noir-lang/noir-bignum as a dependency.

Benchmarks

The benchmarking source code and its details can be found in this repository.

For the results, "UP" stands for UltraPlonk and "UH" stands for UltraHonk.

The benchmark results for the verification of one signature are the following:

Bit length	Circuit size	Avg. proving time (UP) [ms]	Avg. proving time (UH) [ms]
1024	2204	234.8	181
2048	7131	345.6	261.9

Also, the results for the verification of 10 signatures are the following:

Bit length	Circuit size	Avg. proving time (UP) [ms]	Avg. proving time (UH) [ms]
1024	21516	970.9	514.4
2048	63821	1801.7	964.2

The benchmarks were executed using a laptop with Intel(R) Core(TM) i7-13700H CPU and 32 GB of RAM.

Dependencies

noir_rsa requires Noir ≥v0.36.0. Refer to Noir's docs for installation steps.

Installation

In your Nargo.toml file, add the version of this library you would like to install under dependency:

[dependencies]
noir_rsa = { tag = "v0.3.3", git = "https://github.com/noir-lang/noir_rsa" }

Usage

See tests in lib.nr for examples.

End-to-end example

Generate RSA signature

To verify an RSA signature, you first need a signature.

Depending on the application you are building, you might be expecting user signatures from existing signing services (e.g. emails, passports, git commits), or you might be building the ability for users to sign directly in your application.

Either way, you are free to choose how you collect / generate the signatures as long as they comply with the PKCS#1 v1.5 RSA cryptography specifications (ex. by following https://docs.rs/rsa/latest/rsa/#pkcs1-v15-signatures).

You need to install Rustup and run it in order to install Rust:

curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
rustup

Then clone this repo, move into the signature_gen folder, and run cargo run, optionally with the message to sign:

cd signature_gen
cargo run # or cargo run -- --msg "hello world!"

The program prints the hash of the message, the RSA signature, and the BigNumber instance you should use. These are parsed to a compatible format, ready to be used in the Noir RSA library.

Use it in your Noir test

Move into the example folder. Replace the hardcoded values with result of the previous step. Since you know the size of your key, you can import those types from the rsa lib:

-    let hash: [u8; 32] = etc...
-    let signature: BN2048 = etc...
-    let bn = etc...
+    let hash: [u8; 32] = paste from terminal...
+    let signature: BN2048 = paste from terminal...
+    let bn = paste from terminal...

Run the test:

nargo test

Prove it

Run nargo check to initialize Prover.toml:

nargo check

Run the same cargo command, but with the --toml flag:

cargo run -- --msg "hello world!" --toml

Copy and paste it to Prover.toml. Example:

bn = [
    [
        "0xcba7415fa9d2192d5cdac144f95f75",
        "0x2b46305b91eeed9e9a992076172b46",
        "0x76c9e6e0a407e67bc0a3ee276927d7",
        "0x0d0eaa3b10ab266755ea20c44619f6",
        "0x4b040e9ab1acb761b1ab9a60309ee4",
        "...etc"
    ]
]

Then execute it, and prove it i.e. with barretenberg:

nargo execute rsa
bb prove -b ./target/example.json -w ./target/rsa.gz -o ./target/proof

Verify it

To verify, we need to export the verification key:

bb write_vk -b ./target/example.json -o ./target/vk

And verify:

bb verify -k ./target/vk -p ./target/proof