package bls12-381
Library
Module
Module type
Parameter
Class
Class type
include Ff_sig.PRIME
include Ff_sig.BASE
val order : Z.t
The order of the finite field
val zero : t
The neutral element for the addition
val one : t
The neutral element for the multiplication
val is_zero : t -> bool
is_zero x
returns true
if x
is the neutral element for the addition
val is_one : t -> bool
is_one x
returns true
if x
is the neutral element for the multiplication
val random : ?state:Stdlib.Random.State.t -> unit -> t
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|]
.
val non_null_random : ?state:Stdlib.Random.State.t -> unit -> t
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|]
.
negate x
returns -x mod order
. Equivalently, negate x
returns the unique y
such that x + y mod order = 0
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
val of_bytes_exn : Stdlib.Bytes.t -> t
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.
val of_bytes_opt : Stdlib.Bytes.t -> t option
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.
val to_bytes : t -> Stdlib.Bytes.t
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
val factor_power_of_two : int * Z.t
Returns s, q
such that p - 1 = 2^s * q
val of_string : string -> t
Create a value of type t
from a predefined string representation. It is not required that to_string (of_string t) = t
. By default, decimal representation of the number is used, modulo the order of the field
val to_string : t -> string
String representation of a value of type t
. It is not required that to_string (of_string t) = t
. By default, decimal representation of the number is used.
of_z x
builds an element of type t
from the Zarith element x
. mod
p
is applied if x >= p
to_z x
builds a Zarith element, using the decimal representation. Arithmetic on the result can be done using the modular functions on integers
Returns the Legendre symbol of the parameter. Note it does not work for p
= 2
val is_quadratic_residue : t -> bool
is_quadratic_residue x
returns true
if x
is a quadratic residue i.e. if there exists n
such that n^2 mod p = x
Check if a point, represented as a byte array, is in the field *
add_inplace res a b
is the same than add
but writes the result in res
. No allocation happens.
sub_inplace res a b
is the same than sub
but writes the result in res
. No allocation happens.
mul_inplace res a b
is the same than sub
but writes the result in res
. No allocation happens.
inverse_exn_inplace res a
is the same than inverse_exn
but writes the result in res
. No allocation happens.
double_inplace res a
is the same than double
but writes the result in res
. No allocation happens.
square_inplace res a
is the same than square
but writes the result in res
. No allocation happens.
negate_inplace res a
is the same than negate
but writes the result in res
. No allocation happens.
add_bulk xs
returns the sum of the elements of xs
by performing only one allocation for the output. This method is recommended to save the allocation overhead of using n
times add
.
mul_bulk xs
returns the product of the elements of xs
by performing only one allocation for the output. This method is recommended to save the allocation overhead of using n
times mul
.
compare a b
compares the elements a
and b
based on their bytes representation
inner_product_exn a b
returns the inner product of a
and b
, i.e. sum(a_i * b_i)
. Raise Invalid_argument
if the arguments are not of the same length. Only two allocations are used.
Same than inner_product_exn
but returns an option instead of raising an exception.
val of_int : int -> t
of_int x
is equivalent to of_z (Z.of_int x)
. If x
is is negative, returns the element order - |x|
.