package bls12-381
Page
Library
Module
Module type
Parameter
Class
Class type
Source
Module Bls12_381.Fr
Source
include Ff_sig.PRIME
include Ff_sig.BASE
minimal number of bytes required to encode a value of the field.
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
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
negate x
returns -x mod order
. Equivalently, negate x
returns the unique y
such that x + y mod order = 0
inverse_opt x
returns x^-1
if x
is not 0
as an option, else None
div_opt a b
returns a * b^-1
as an option. Return None
if b = zero
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.
Create a value 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
String representation of a value 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 t from the Zarith element x
. mod order
is applied if x >= order
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
is_quadratic_residue x
returns true
if x
is a quadratic residue i.e. if there exists n
such that n^2 mod p = 1
Actual number of bytes allocated for a value of type t
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.