# Crate crypto_bigint

source ·## Expand description

## RustCrypto: Cryptographic Big Integers

Pure Rust implementation of a big integer library which has been designed from the ground-up for use in cryptographic applications.

Provides constant-time, `no_std`

-friendly implementations of modern formulas
using const generics.

### Goals

- No heap allocations.
`no_std`

-friendly. - Constant-time by default. Variable-time functions are explicitly marked as such.
- Leverage what is possible today with const generics on
`stable`

rust. - Support
`const fn`

as much as possible, including decoding big integers from bytes/hex and performing arithmetic operations on them, with the goal of being able to compute values at compile-time.

### Minimum Supported Rust Version

**Rust 1.56** at a minimum.

### License

Licensed under either of:

at your option.

#### Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.

### Usage

This crate defines a `UInt`

type which is const generic around an inner
`Limb`

array, where a `Limb`

is a newtype for a word-sized integer.
Thus large integers are represented as a arrays of smaller integers which
are sized appropriately for the CPU, giving us some assurances of how
arithmetic operations over those smaller integers will behave.

To obtain appropriately sized integers regardless of what a given CPU’s
word size happens to be, a number of portable type aliases are provided for
integer sizes commonly used in cryptography, for example:
`U128`

, `U384`

, `U256`

, `U2048`

, `U3072`

, `U4096`

.

`const fn`

usage

The `UInt`

type provides a number of `const fn`

inherent methods which
can be used for initializing and performing arithmetic on big integers in
const contexts:

```
use crypto_bigint::U256;
// Parse a constant from a big endian hexadecimal string.
pub const MODULUS: U256 =
U256::from_be_hex("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551");
// Compute `MODULUS` shifted right by 1 at compile time
pub const MODULUS_SHR1: U256 = MODULUS.shr_vartime(1);
```

#### Trait-based usage

The `UInt`

type itself does not implement the standard arithmetic traits
such as `Add`

, `Sub`

, `Mul`

, and `Div`

.

To use these traits you must first pick a wrapper type which determines
overflow behavior: `Wrapping`

or `Checked`

.

##### Wrapping arithmetic

```
use crypto_bigint::{U256, Wrapping};
let a = Wrapping(U256::MAX);
let b = Wrapping(U256::ONE);
let c = a + b;
// `MAX` + 1 wraps back around to zero
assert_eq!(c.0, U256::ZERO);
```

##### Checked arithmetic

```
use crypto_bigint::{U256, Checked};
let a = Checked::new(U256::ONE);
let b = Checked::new(U256::from(2u8));
let c = a + b;
assert_eq!(c.0.unwrap(), U256::from(3u8))
```

#### Modular arithmetic

This library has initial support for modular arithmetic in the form of the
`AddMod`

, `SubMod`

, `NegMod`

, and `MulMod`

traits, as well as the
support for the `Rem`

trait when used with a `NonZero`

operand.

```
use crypto_bigint::{AddMod, U256};
// mod 3
let modulus = U256::from(3u8);
// 1 + 1 mod 3 = 2
let a = U256::ONE.add_mod(&U256::ONE, &modulus);
assert_eq!(a, U256::from(2u8));
// 2 + 1 mod 3 = 0
let b = a.add_mod(&U256::ONE, &modulus);
assert_eq!(b, U256::ZERO);
```

#### Random number generation

When the `rand_core`

or `rand`

features of this crate are enabled, it’s
possible to generate random numbers using any `CryptoRng`

by using the
`Random`

trait:

```
use crypto_bigint::{Random, U256, rand_core::OsRng};
let n = U256::random(&mut OsRng);
```

##### Modular random number generation

The `RandomMod`

trait supports generating random numbers with a uniform
distribution around a given `NonZero`

modulus.

```
use crypto_bigint::{NonZero, RandomMod, U256, rand_core::OsRng};
let modulus = NonZero::new(U256::from(3u8)).unwrap();
let n = U256::random_mod(&mut OsRng, &modulus);
```

## Re-exports

## Modules

## Macros

## Structs

`T`

.`T`

.## Traits

`self + rhs mod p`

.`GenericArray`

as a big integer.`GenericArray`

.`rhs`

value as the least significant value.`self * rhs mod p`

.`-self mod p`

.`self - rhs mod p`

.## Type Definitions

`ArrayEncoding::ByteSize`

.`LimbUInt`

.