Big Integers
The BigInt module in the standard library exposes some class of integers which do not fit (well) into a Noir native field. It implements modulo arithmetic, modulo a 'big' prime number.
The module can currently be considered as Field
s with fixed modulo sizes used by a set of elliptic curves, in addition to just the native curve. More work is needed to achieve arbitrarily sized big integers.
Currently 6 classes of integers (i.e 'big' prime numbers) are available in the module, namely:
- BN254 Fq: Bn254Fq
- BN254 Fr: Bn254Fr
- Secp256k1 Fq: Secpk1Fq
- Secp256k1 Fr: Secpk1Fr
- Secp256r1 Fr: Secpr1Fr
- Secp256r1 Fq: Secpr1Fq
Where XXX Fq and XXX Fr denote respectively the order of the base and scalar field of the (usual) elliptic curve XXX. For instance the big integer 'Secpk1Fq' in the standard library refers to integers modulo .
Feel free to explore the source code for the other primes:
struct BigInt {
pointer: u32,
modulus: u32,
}
Example usage
A common use-case is when constructing a big integer from its bytes representation, and performing arithmetic operations on it:
fn big_int_example(x: u8, y: u8) {
let a = Secpk1Fq::from_le_bytes(&[x, y, 0, 45, 2]);
let b = Secpk1Fq::from_le_bytes(&[y, x, 9]);
let c = (a + b) * b / a;
let d = c.to_le_bytes();
println(d[0]);
}
Source code: test_programs/execution_success/bigint/src/main.nr#L70-L78
Methods
The available operations for each big integer are:
from_le_bytes
Construct a big integer from its little-endian bytes representation. Example:
// Construct a big integer from a slice of bytes
let a = Secpk1Fq::from_le_bytes(&[x, y, 0, 45, 2]);
// Construct a big integer from an array of 32 bytes
let a = Secpk1Fq::from_le_bytes_32([1;32]);
Sure, here's the formatted version of the remaining methods:
to_le_bytes
Return the little-endian bytes representation of a big integer. Example:
let bytes = a.to_le_bytes();
add
Add two big integers. Example:
let sum = a + b;
sub
Subtract two big integers. Example:
let difference = a - b;
mul
Multiply two big integers. Example:
let product = a * b;
div
Divide two big integers. Note that division is field division and not euclidean division. Example:
let quotient = a / b;
eq
Compare two big integers. Example:
let are_equal = a == b;