8 releases (breaking)
0.8.0  Nov 1, 2023 

0.7.0  Aug 28, 2023 
0.6.0  Aug 10, 2023 
0.5.0  Jul 23, 2023 
0.1.0  Aug 13, 2022 
#131 in Cryptography
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Used in 4 crates
(2 directly)
3MB
55K
SLoC
crrl
This library implements some primitives for purposes of cryptographic research. Its point is to provide efficient, optimized and constanttime implementations that are supposed to be representative of productionready code, so that realistic performance benchmarks may be performed. Thus, while meant primarily for research, the code here should be fine for production use (though of course I offer no such guarantee; use at your own risks).
So far, only some primitives related to elliptic curve cryptography are implemented:

A generic type
GF255<MQ>
for finite fields of integers modulo a prime 2^255MQ
(for a value ofMQ
between 1 and 32767). TheMQ
value is provided as a type parameter, i.e. the exact field is known at compile time. This type covers the usual modulus 2^25519 (used in Curve25519) as well as 2^25518651 and 2^2553957 (used in doubleodd curves do255e and do255s). 
A generic type
ModInt256<M0, M1, M2, M3>
for arbitrary finite fields of integers modulo a prime between 2^192 and 2^256. Montgomery representation is internally used. The modulus is provided as type parameters, allowing the compiler to apply optimizations when some parts of the modulus allow them (in particular with the modulus used for NIST curve P256). 
Type
GFsecp256k1
implements the specific base field for curve secp256k1 (integers modulo 2^2564294968273). The 64bit backend has a dedicated implementation, while the 32bit version of this type usesModInt256
. 
The macro
define_gfgen
allows defining arbitrary finite fields of integers modulo a prime, with a large range of modulus size. It uses Montgomery representation internally. 
Type
GF448
implements the specific base field for Curve448. The 64bit backend has a dedicated implementation, while the 32bit backend usesdefine_gfgen
. 
Type
ed25519::Point
provides generic group operations in the twisted Edwards curve Curve25519. Ed25519 signatures (as per RFC 8032) are implemented. Typeed25519::Scalar
implements operations on integers modulo the curve subgroup order. 
Type
ristretto255::Point
provides generic group operations in the ristretto255 group, whose prime order is exactly the size of the interesting subgroup of Curve25519. 
Type
ed448::Point
provides generic group operations in the Edwards curve edwards448. Ed448 signatures (as per RFC 8032) are implemented. Typeed448::Scalar
implements operations on integers modulo the curve subgroup order. 
Type
decaf448::Point
provides generic group operations in the decaf448 group, whose prime order is exactly the size of the interesting subgroup of Curve448. 
Type
p256::Point
provides generic group operations in the NIST P256 curve (aka "secp256r1" aka "prime256v1"). ECDSA signatures are supported. Thep256::Scalar
type implements the corresponding scalars (integers modulo the curve order). 
Type
secp256k1::Point
provides generic group operations in the secp256k1 curve (aka "the Bitcoin curve"). ECDSA signatures are supported. Thesecp256k1::Scalar
type implements the corresponding scalars (integers modulo the curve order). The GLV endomorphism is leveraged to speedup point multiplication (key exchange) and signature verification. 
Types
jq255e::Point
andjq255s::Point
implement the doubleodd curves jq255e and jq255s (along with the corresponding scalar typesjq255e::Scalar
andjq255s::Scalar
). Key exchange and Schnorr signatures are implemented. These curves provide a primeorder group abstraction, similar to ristretto255, but with somewhat better performance at the same security level. Moreover, the relevant signatures are both shorter (48 bytes instead of 64) and faster than the usual Ed25519 signatures. 
Function
x25519::x25519()
implements the X25519 function. An optimizedx25519::x2559_base()
function is provided when X25519 is applied to the conventional base point. Similarly,x448::x448()
andx448::x448_base()
provide the same functionality for the X448 function. 
Type
gls254::Point
implements the GLS254 curve (or, more precisely, a primeorder group homomorphic to a subgroup of that curve), which is defined over a binary field.gls254::Scalar
is the type for integers modulo the curve order.gls254::PrivateKey
andgls254:PublicKey
implement highlevel operations such as key exchange and signatures, using that group. 
Module
blake2s
contains some BLAKE2s implementations, with optional SSE2 and AVX2 optimizations.
Types GF255
and ModInt256
have a 32bit and a 64bit implementations
each (actually two 64bit implementations, see later the discussion
about the gf255_m51
feature). The code is portable (it was tested on
32bit and 64bit x86, 64bit aarch64, and 64bit riscv64). Performance
is quite decent; e.g. Ed25519 signatures are computed in about 51500
cycles, and verified in about 114000 cycles, on an Intel "Coffee Lake"
CPU; this is not too far from the best assemblyoptimized
implementations. At the same time, use of operator overloading allows to
express formulas on points and scalar with about the same syntax as
their mathematical description. For instance, the core of the X25519
implementation looks like this:
let A = x2 + z2;
let B = x2  z2;
let AA = A.square();
let BB = B.square();
let C = x3 + z3;
let D = x3  z3;
let E = AA  BB;
let DA = D * A;
let CB = C * B;
x3 = (DA + CB).square();
z3 = x1 * (DA  CB).square();
x2 = AA * BB;
z2 = E * (AA + E.mul_small(121665));
which is quite close to the corresponding description in RFC 7748:
A = x_2 + z_2
AA = A^2
B = x_2  z_2
BB = B^2
E = AA  BB
C = x_3 + z_3
D = x_3  z_3
DA = D * A
CB = C * B
x_3 = (DA + CB)^2
z_3 = x_1 * (DA  CB)^2
x_2 = AA * BB
z_2 = E * (AA + a24 * E)
Optional Features
By default, everything in crrl is compiled, which unfortunately makes for
a relatively long compilation time, especially on notsofast systems.
To only compile support for some primitives, use nodefaultfeatures
then add selectively the features you are interested in with F
; e.g.
use cargo build nodefaultfeatures F ed25519
to only compile the
Ed25519 support (and the primitives that it needs, such as its base
field). The defined primitivecontrolling features are the following:

omnes
: enables all of the following. 
decaf448
: decaf448 primeorder group (based on edwards448) 
ed25519
: edwards25519 curve and signatures (RFC 8032: Ed25519) 
ed448
: edwards448 curve and signatures (RFC 8032: Ed448) 
frost
: FROST threshold signatures (support macros + standard ciphersuites, but only for the curves which are also enabled in this build) 
jq255e
: jq255e primeorder group and signatures 
jq255s
: jq255s primeorder group and signatures 
lms
: LMS support (hashbased signatures) 
p256
: NIST P256 curve and signatures (ECDSA) 
ristretto255
: ristretto255 primeorder group (based on edwards25519) 
secp256k1
: secp256k1 curve and signatures (ECDSA) 
x25519
: X25519 key exchange primitive (RFC 7748) 
x448
: X448 key exchange primitive (RFC 7748) 
modint256
: generic finite field implementation (prime order of up to 256 bits) 
gf255
: generic finite field implementation (for prime orderq = 2^255  MQ
withMQ < 2^15
) 
gfgen
: generic finite field implementation (generating macro; prime modulus of arbitrary length) 
gls254
: GLS254 primeorder group and signatures 
gls254bench
: additional benchmarking code for GLS254 
blake2s
: BLAKE2s hash function
Some operations have multiple backends. An appropriate backend is selected at compiletime, but this can be overridden by enabling some features:

w32_backend
: enforce use of the 32bit code, even on 64bit systems. 
w64_backend
: enforce use of the 64bit code, even on 32bit systems. 
gf255_m64
: enforce use of 64bit limbs forGF255<MQ>
; this is the default on 64bit machines, except RISCV (riscv64) where 51bit limbs are used by default. This feature has no effect if the 32bit code is used. 
gf255_m51
: encode use of 51bit limbs forGF255<MQ>
; this is the default on 64bit RISCV targets (riscv64), but not on other 64bit architectures where 64bit limbs are normally preferred. This feature has no effect if the 32bit code is used. 
gfb254_m64
: enforce use of the generic implementation of the binary field GF(2^254). This feature has no effect if the 32bit code is used. 
gfb254_x86clmul
: enforce use of the AVX2+pclmulqdq implementation of the binary field GF(2^254). This code is used automatically if the compilation target is an x86 with the relevant hardware support; this feature bypasses the automatic detection. This feature has no effect if the 32bit code is used. 
gfb254_arm64pmull
: enforce use of the NEON+pmull implementation of the binary field GF(2^254). This code is used automatically if the compilation target is an aarch64 system; this feature bypasses the automatic detection. This feature has no effect if the 32bit code is used.
Security and Compliance
All the code is strict, both in terms of timingbased sidechannels
(everything is constanttime, except if explicitly stated otherwise,
e.g. in a function whose name includes vartime
) and in compliance to
relevant standards. For instance, the Ed25519 signature support applies
and enforces canonical encodings of both points and scalars.
There is no attempt at "zeroizing memory" anywhere in the code. In
general, such memory cleansing is a fool's quest. Note that since most
of the library use no_std
rules, dynamic allocation happens only on
the stack, thereby limiting the risk of leaving secret information
lingering all over the RAM. The only functions that use heap allocation
only store public data there.
WARNING: I reiterate what was written above: although all of the code aims at being representative of optimized productionready code, it is still fairly recent and some bugs might still lurk, however careful I am when writing code. Any assertion of suitability to any purpose is explcitly denied. The primary purpose is to help with "trying out stuff" in cryptographic research, by offering an easytouse API backed by performance close enough to what can be done in actual applications.
Truncated Signatures
Support for truncated signatures is implemented for Ed25519 and
ECDSA/P256. Standard signatures can be shortened by 8 to 32 bits (i.e.
the size may shrink from 64 down to 60 bytes), and the verifier rebuilds
the original signature during verification (at some computational cost).
This is not a groundbreaking feature, but it can be very convenient in
some situations with tight constraints on bandwidth and a requirement to
work with standard signature formats. See
ed25519::PublicKey::verify_trunc_raw()
and
p256::PublicKey::verify_trunc_hash()
for details.
FROST Threshold Schnorr Signatures
The FROST protocol for a distributed Schnorr signature generation scheme
has been implemented, as per the v14 draft specification:
draftirtfcfrgfrost14.
Four ciphersuites are provided, with similar APIs, in the
frost::ed25519
, frost::ristretto255
, frost::ed448
, frost::p256
and
frost::secp256k1
modules. A sample code showing how to use the API is
provided in the frostsample.rs file.
While FROST is inherently a distributed scheme, the implementation can also be used in a single signer mode by using the "group" private key directly.
Benchmarks
cargo bench
runs some benchmarks, but there are a few caveats:

The cycle counter is used on x86. If frequency scaling ("TurboBoost") is not disabled, then you'll get wrong and meaningless results.

On aarch64, the cycle counter is also accessed directly, which will in general fail with some CPU exception. Access to the counter must first be enabled, which requires (on Linux) a specific kernel module. This one works for me.

On riscv64gc, the cycle counter is accessed directly. In general, that counter is not enabled and all benches return zero; to enable the cycle counter, run the benchmark binary inside the
perf
tool (which comes with thelinuxtools
). 
On architectures other than i386, x8664, aarch64 and riscv64gc, benchmark code will simply not compile.
TODO
In general, about anything related to cryptography may show up here, if there is a use case for it.
Dependencies
~1.5MB
~12K SLoC