ed25519-dalek-fiat

Fast and efficient Rust implementation of ed25519 key generation, signing, and verification in Rust.

About

This is a thin fork of the ed25519-dalek project, and its main difference is replacing the original curve25519-dalek dependency with curve25519-dalek-fiat. This allows using a formally verified backend supplied by the fiat-crypto project, where primitive curve operations are extracted from Coq proofs of arithmetic correctness.

Documentation

Documentation is available here.

Installation

To install, add the following to your project's Cargo.toml:

ed25519-dalek-fiat = "0.1.0"

Benchmarks

On an Intel Skylake i9-7900X running at 3.30 GHz, without TurboBoost, this code achieves the following performance benchmarks:

∃!isisⒶmistakenot:(master *=)~/code/rust/ed25519-dalek ∴ cargo bench
   Compiling ed25519-dalek v0.7.0 (file:///home/isis/code/rust/ed25519-dalek)
    Finished release [optimized] target(s) in 3.11s
      Running target/release/deps/ed25519_benchmarks-721332beed423bce

Ed25519 signing                     time:   [15.617 us 15.630 us 15.647 us]
Ed25519 signature verification      time:   [45.930 us 45.968 us 46.011 us]
Ed25519 keypair generation          time:   [15.440 us 15.465 us 15.492 us]

By enabling the avx2 backend (on machines with compatible microarchitectures), the performance for signature verification is greatly improved:

∃!isisⒶmistakenot:(master *=)~/code/rust/ed25519-dalek ∴ export RUSTFLAGS=-Ctarget_cpu=native
∃!isisⒶmistakenot:(master *=)~/code/rust/ed25519-dalek ∴ cargo bench --features=avx2_backend
   Compiling ed25519-dalek v0.7.0 (file:///home/isis/code/rust/ed25519-dalek)
    Finished release [optimized] target(s) in 4.28s
      Running target/release/deps/ed25519_benchmarks-e4866664de39c84d
Ed25519 signing                     time:   [15.923 us 15.945 us 15.967 us]
Ed25519 signature verification      time:   [33.382 us 33.411 us 33.445 us]
Ed25519 keypair generation          time:   [15.246 us 15.260 us 15.275 us]

In comparison, the equivalent package in Golang performs as follows:

∃!isisⒶmistakenot:(master *=)~/code/go/src/github.com/agl/ed25519 ∴ go test -bench .
BenchmarkKeyGeneration     30000             47007 ns/op
BenchmarkSigning           30000             48820 ns/op
BenchmarkVerification      10000            119701 ns/op
ok      github.com/agl/ed25519  5.775s

Making key generation and signing a rough average of 2x faster, and verification 2.5-3x faster depending on the availability of avx2. Of course, this is just my machine, and these results—nowhere near rigorous—should be taken with a handful of salt.

Translating to a rough cycle count: we multiply by a factor of 3.3 to convert nanoseconds to cycles per second on a 3300 Mhz CPU, that's 110256 cycles for verification and 52618 for signing, which is competitive with hand-optimised assembly implementations.

Additionally, if you're using a CSPRNG from the rand crate, the nightly feature will enable u128/i128 features there, resulting in potentially faster performance.

If your protocol or application is able to batch signatures for verification, the verify_batch() function has greatly improved performance. On the aforementioned Intel Skylake i9-7900X, verifying a batch of 96 signatures takes 1.7673ms. That's 18.4094us, or roughly 60750 cycles, per signature verification, more than double the speed of batch verification given in the original paper (this is likely not a fair comparison as that was a Nehalem machine). The numbers after the / in the test name refer to the size of the batch:

∃!isisⒶmistakenot:(master *=)~/code/rust/ed25519-dalek ∴ export RUSTFLAGS=-Ctarget_cpu=native
∃!isisⒶmistakenot:(master *=)~/code/rust/ed25519-dalek ∴ cargo bench --features=avx2_backend batch
   Compiling ed25519-dalek v0.8.0 (file:///home/isis/code/rust/ed25519-dalek)
    Finished release [optimized] target(s) in 34.16s
      Running target/release/deps/ed25519_benchmarks-cf0daf7d68fc71b6
Ed25519 batch signature verification/4   time:   [105.20 us 106.04 us 106.99 us]
Ed25519 batch signature verification/8   time:   [178.66 us 179.01 us 179.39 us]
Ed25519 batch signature verification/16  time:   [325.65 us 326.67 us 327.90 us]
Ed25519 batch signature verification/32  time:   [617.96 us 620.74 us 624.12 us]
Ed25519 batch signature verification/64  time:   [1.1862 ms 1.1900 ms 1.1943 ms]
Ed25519 batch signature verification/96  time:   [1.7611 ms 1.7673 ms 1.7742 ms]
Ed25519 batch signature verification/128 time:   [2.3320 ms 2.3376 ms 2.3446 ms]
Ed25519 batch signature verification/256 time:   [5.0124 ms 5.0290 ms 5.0491 ms]

As you can see, there's an optimal batch size for each machine, so you'll likely want to test the benchmarks on your target CPU to discover the best size. For this machine, around 100 signatures per batch is the optimum:

Additionally, thanks to Rust, this implementation has both type and memory safety. It's also easily readable by a much larger set of people than those who can read qhasm, making it more readily and more easily auditable. We're of the opinion that, ultimately, these features—combined with speed—are more valuable than simply cycle counts alone.

A Note on Signature Malleability

The signatures produced by this library are malleable, as discussed in the original paper:

While the scalar component of our Signature struct is strictly not malleable, because reduction checks are put in place upon Signature deserialisation from bytes, for all types of signatures in this crate, there is still the question of potential malleability due to the group element components.

We could eliminate the latter malleability property by multiplying by the curve cofactor, however, this would cause our implementation to not match the behaviour of every other implementation in existence. As of this writing, RFC 8032, "Edwards-Curve Digital Signature Algorithm (EdDSA)," advises that the stronger check should be done. While we agree that the stronger check should be done, it is our opinion that one shouldn't get to change the definition of "ed25519 verification" a decade after the fact, breaking compatibility with every other implementation.

However, if you require this, please see the documentation for the verify_strict() function, which does the full checks for the group elements. This functionality is available by default.

If for some reason—although we strongely advise you not to—you need to conform to the original specification of ed25519 signatures as in the excerpt from the paper above, you can disable scalar malleability checking via --features='legacy_compatibility'. WE STRONGLY ADVISE AGAINST THIS.

The legacy_compatibility Feature

By default, this library performs a stricter check for malleability in the scalar component of a signature, upon signature deserialisation. This stricter check, that s < \ell where \ell is the order of the basepoint, is mandated by RFC8032. However, that RFC was standardised a decade after the original paper, which, as described above, (usually, falsely) stated that malleability was inconsequential.

Because of this, most ed25519 implementations only perform a limited, hackier check that the most significant three bits of the scalar are unset. If you need compatibility with legacy implementations, including:

• ed25519-donna
• Golang's /x/crypto ed25519
• libsodium (only when built with -DED25519_COMPAT)
• NaCl's "ref" implementation
• probably a bunch of others

then enable ed25519-dalek's legacy_compatibility feature. Please note and be forewarned that doing so allows for signature malleability, meaning that there may be two different and "valid" signatures with the same key for the same message, which is obviously incredibly dangerous in a number of contexts, including—but not limited to—identification protocols and cryptocurrency transactions.

The verify_strict() Function

The scalar component of a signature is not the only source of signature malleability, however. Both the public key used for signature verification and the group element component of the signature are malleable, as they may contain a small torsion component as a consquence of the curve25519 group not being of prime order, but having a small cofactor of 8.

If you wish to also eliminate this source of signature malleability, please review the documentation for the verify_strict() function.

A Note on Randomness Generation

The original paper's specification and the standarisation of RFC8032 do not specify precisely how randomness is to be generated, other than using a CSPRNG (Cryptographically Secure Random Number Generator). Particularly in the case of signature verification, where the security proof relies on the uniqueness of the blinding factors/nonces, it is paramount that these samples of randomness be unguessable to an adversary. Because of this, a current growing belief among cryptographers is that it is safer to prefer synthetic randomness.

To explain synthetic randomness, we should first explain how ed25519-dalek handles generation of deterministic randomness. This mode is disabled by default due to a tiny-but-not-nonexistent chance that this mode will open users up to fault attacks, wherein an adversary who controls all of the inputs to batch verification (i.e. the public keys, signatures, and messages) can craft them in a specialised manner such as to induce a fault (e.g. causing a mistakenly flipped bit in RAM, overheating a processor, etc.). In the deterministic mode, we seed the PRNG which generates our blinding factors/nonces by creating a PRNG based on the Fiat-Shamir transform of the public inputs. This mode is potentially useful to protocols which require strong auditability guarantees, as well as those which do not have access to secure system-/chip- provided randomness. This feature can be enabled via --features='batch_deterministic'. Note that we do not support deterministic signing, due to the numerous pitfalls therein, including a re-used nonce accidentally revealing the secret key.

In the default mode, we do as above in the fully deterministic mode, but we ratchet the underlying keccak-f1600 function (used for the provided transcript-based PRNG) forward additionally based on some system-/chip- provided randomness. This provides synthetic randomness, that is, randomness based on both deterministic and undeterinistic data. The reason for doing this is to prevent badly seeded system RNGs from ruining the security of the signature verification scheme.

Features

#![no_std]

This library aims to be #![no_std] compliant. If batch verification is required (--features='batch'), please enable either of the std or alloc features.

Nightly Compilers

To cause your application to build ed25519-dalek with the nightly feature enabled by default, instead do:

[dependencies.ed25519-dalek]
version = "1"
features = ["nightly"]

To cause your application to instead build with the nightly feature enabled when someone builds with cargo build --features="nightly" add the following to the Cargo.toml:

[features]
nightly = ["ed25519-dalek/nightly"]

Serde

To enable serde support, build ed25519-dalek with the serde feature.

(Micro)Architecture Specific Backends

By default, ed25519-dalek builds against curve25519-dalek's u64_backend feature, which uses Rust's i128 feature to achieve roughly double the speed as the u32_backend feature. When targetting 32-bit systems, however, you'll likely want to compile with cargo build --no-default-features --features="u32_backend". If you're building for a machine with avx2 instructions, there's also the experimental simd_backends, currently comprising either avx2 or avx512 backends. To use them, compile with RUSTFLAGS="-C target_cpu=native" cargo build --no-default-features --features="simd_backend"

Batch Signature Verification

The standard variants of batch signature verification (i.e. many signatures made with potentially many different public keys over potentially many different message) is available via the batch feature. It uses synthetic randomness, as noted above.

Deterministic Batch Signature Verification

The same notion of batch signature verification as above, but with purely deterministic randomness can be enabled via the batch_deterministic feature.