[][src]Crate bulletproofs


The fastest Bulletproofs implementation ever, featuring single and aggregated range proofs, strongly-typed multiparty computation, and a programmable constraint system API for proving arbitrary statements (under development).

This library implements Bulletproofs using Ristretto, using the ristretto255 implementation in curve25519-dalek. When using the parallel formulas in the curve25519-dalek AVX2 backend, it can verify 64-bit rangeproofs approximately twice as fast as the original libsecp256k1-based Bulletproofs implementation.

This library provides implementations of:

  • Single-party proofs of single or multiple ranges, using the aggregated rangeproof construction;

  • Online multi-party computation for rangeproof aggregation between multiple parties, using session types to statically enforce correct protocol flow;

  • A programmable constraint system API for expressing rank-1 constraint systems, and proving and verifying proofs of arbitrary statements (under development in the circuit branch);

  • Online multi-party computation for aggregated circuit proofs (planned future work).

These proofs are implemented using Merlin transcripts, allowing them to be arbitrarily composed with other proofs without implementation changes.


The user-facing documentation for this functionality can be found here. In addition, the library also contains extensive notes on how Bulletproofs work. These notes can be found in the library's internal documentation:

Comparative Performance

The following table gives comparative timings for proving and verification of a 64-bit rangeproof on an i7-7800X with Turbo Boost disabled. Times are in microseconds (lower is better), with the relative speed compared to the fastest implementation.

Implementation Group Proving (μs) rel Verification (μs) rel
ours (avx2) ristretto255 7300 1.00x 1040 1.00x
ours (u64) ristretto255 11300 1.54x 1490 1.43x
libsecp+endo secp256k1 14300 1.96x 1900 1.83x
libsecp-endo secp256k1 16800 2.30x 2080 2.00x
Monero ed25519 (unsafe) 53300 7.30x 4810 4.63x

This crate also contains other benchmarks; see the Tests and Benchmarks section below for details.


This code is still research-quality. It is not (yet) suitable for deployment. The development roadmap can be found in the Milestones section of the Github repo.


// Generators for Pedersen commitments.  These can be selected
// independently of the Bulletproofs generators.
let pc_gens = PedersenGens::default();

// Generators for Bulletproofs, valid for proofs up to bitsize 64
// and aggregation size up to 1.
let bp_gens = BulletproofGens::new(64, 1);

// A secret value we want to prove lies in the range [0, 2^32)
let secret_value = 1037578891u64;

// The API takes a blinding factor for the commitment.
let blinding = Scalar::random(&mut thread_rng());

// The proof can be chained to an existing transcript.
// Here we create a transcript with a doctest domain separator.
let mut prover_transcript = Transcript::new(b"doctest example");

// Create a 32-bit rangeproof.
let (proof, committed_value) = RangeProof::prove_single(
    &mut prover_transcript,
).expect("A real program could handle errors");

// Verification requires a transcript with identical initial state:
let mut verifier_transcript = Transcript::new(b"doctest example");
        .verify_single(&bp_gens, &pc_gens, &mut verifier_transcript, &committed_value, 32)

Tests and Benchmarks

Run tests with cargo test. Run benchmarks with cargo bench. This crate uses criterion.rs for benchmarks.


The avx2_backend feature enables curve25519-dalek's AVX2 backend, which implements curve arithmetic using parallel formulas. To use it for Bulletproofs, the target_cpu must support AVX2:

RUSTFLAGS="-C target_cpu=skylake" cargo bench --features "avx2_backend"

Skylake-X CPUs have double the AVX2 registers. To use them, try

RUSTFLAGS="-C target_cpu=skylake-avx512" cargo bench --features "avx2_backend"

This prevents spills in the AVX2 parallel field multiplication code, but causes worse code generation elsewhere ¯\_(ツ)_/¯


This is a research project sponsored by Interstellar, developed by Henry de Valence, Cathie Yun, and Oleg Andreev.



The aggregation module contains the API for performing the aggregated multiparty computation protocol.



The BulletproofGens struct contains all the generators needed for aggregating up to m range proofs of up to n bits each.


Represents a view of the generators used by a specific party in an aggregated proof.


Represents a pair of base points for Pedersen commitments.


The RangeProof struct represents a proof that one or more values are in a range.



Represents an error in proof creation, verification, or parsing.