The order of the finite field

Minimal number of bytes required to encode a value of the field

check_bytes bs returns true if bs is a correct byte representation of a field element

copy x creates a fresh copy of x

The neutral element for the addition

The neutral element for the multiplication

is_zero x returns true if x is the neutral element for the addition

is_one x returns true if x is the neutral element for the multiplication

Use carefully!

random () returns a random element of the field. A state for the PRNG can be given to initialize the PRNG in the requested state. If no state is given, no initialisation is performed.

To create a value of type Random.State.t, you can use Random.State.make [|42|].

Use carefully!

non_null_random () returns a non null random element of the field. A state for the PRNG can be given to initialize the PRNG in the requested state. If no state is given, no initialisation is performed.

To create a value of type Random.State.t, you can use Random.State.make [|42|].

add a b returns a + b mod order

Infix operator for add

sub a b returns a - b mod order

mul a b returns a * b mod order

Infix operator for mul

eq a b returns true if a = b mod order, else false

Infix operator for eq

negate x returns -x mod order. Equivalently, negate x returns the unique y such that x + y mod order = 0

Infix operator for negate

inverse_exn x returns x^-1 mod order if x is not 0, else raise Division_by_zero. Equivalently, inverse_exn x returns the unique y such that x * y mod order = 1

inverse_opt x returns x^-1 mod order as an option if x is not 0, else returns None. Equivalently, inverse_opt x returns the unique y such that x * y mod order = 1

div_exn a b returns a * b^-1. Raise Division_by_zero if b = zero. Equivalently, div_exn returns the unique y such that b * y mod order = a

div_opt a b returns a * b^-1 as an option. Return None if b = zero. Equivalently, div_opt returns the unique y such that b * y mod order = a

Infix operator for div_exn

square x returns x^2 mod order

double x returns 2x mod order

pow x n returns x^n mod order

Infix operator for pow

Construct a value of type t from the bytes representation in little endian of the field element. For non prime fields, the encoding starts with the coefficient of the constant monomial. Raise Not_in_field if the bytes do not represent an element in the field.

From a predefined little endian bytes representation, construct a value of type t. The same representation than of_bytes_exn is used. Return None if the bytes do not represent an element in the field.

Convert the value t to a bytes representation. The number of bytes is size_in_bytes and the encoding must be in little endian. For instance, the encoding of 1 in prime fields is always a bytes sequence of size size_in_bytes starting with the byte 0b00000001.

For non prime fields, the encoding starts with the coefficient of the constant monomial. For instance, an element a + b * X in GF(p^2) will be encoded as to_bytes a || to_bytes b where || is the concatenation of bytes