Module `Bls12_381.Fq12`Source

Represents the field extension constructed as described here. The interface does not provide the full requirements to be a field (like the addition).

In many applications, the field extension won't be used and GT will be used instead. However, this library exposes the field extension to allow the user to use Pairing.miller_loop and post-pone the call to Pairing.final_exponentiation_exn follwing its taste.

Sourceexception Not_in_field of Bytes.t

Sourcetype t

An element of the field extension. It is not ensured the element are in the prime multiplicative subgroup. If you need inhabitants of the prime subgroup, use the module GT

Sourceval order : Z.t

The order of the field

Sourceval size_in_bytes : int

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

Sourceval size_in_memory : int

Actual number of bytes allocated for a value of type t

Sourceval zero : t

The neutral element of the additive subgroup

Sourceval one : t

The neutral element of the multiplicative subgroup

Sourceval is_zero : t -> bool

is_zero x returns true if x is the neutral element of the additive subgroup

Sourceval is_one : t -> bool

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

Sourceval mul : t -> t -> t

mul a b returns the product of a and b

Sourceval inverse_exn : t -> t

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

Sourceval inverse_opt : t -> t option

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

Sourceval eq : t -> t -> bool

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

Sourceval random : ?state:Random.State.t -> unit -> t

Generates a random element.

The routines in the module Random.State are used to generate the elements. A state can be given to the function to be used. If no state is given, Random.get_state is used.

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

Sourceval pow : t -> Z.t -> t

Sourceval of_bytes_exn : Bytes.t -> t

of_bytes_exn bs builds a value of type t. Each coordinate is expected to be in little endian and the constant monomial is always encoded first. The size of bs is expected to be size_in_bytes. If the element is not in the field or if bs is not of size size_in_bytes, raises Not_in_field with bs in parameter.

Sourceval of_bytes_opt : Bytes.t -> t option

Same than of_bytes_exn but returns an option instead of raising an exception

Sourceval to_bytes : t -> Bytes.t

to_bytes p encodes the point p following the encoding described by of_bytes_exn

Source

val of_string : 
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  String.t ->
  t

Construct an element of Fq12 based on the following pattern:

Fq12 = (Fq6 (Fq2(x: x0, y: x1)) Fq2(x: x2, y: x3)) Fq2(x: x4, y: x5)), Fq6 ( Fq2(x: x6, y: x7)) Fq2(x: x8, y: x9)) Fq2(x: x10, y: x11))

x0, ..., x11 are the parameters of the function. No check is applied.

Example of usage (pairing result of the multiplicative neutre elements): ```OCaml Fq12.of_string "2819105605953691245277803056322684086884703000473961065716485506033588504203831029066448642358042597501014294104502" "1323968232986996742571315206151405965104242542339680722164220900812303524334628370163366153839984196298685227734799" "2987335049721312504428602988447616328830341722376962214011674875969052835043875658579425548512925634040144704192135" "3879723582452552452538684314479081967502111497413076598816163759028842927668327542875108457755966417881797966271311" "261508182517997003171385743374653339186059518494239543139839025878870012614975302676296704930880982238308326681253" "231488992246460459663813598342448669854473942105054381511346786719005883340876032043606739070883099647773793170614" "3993582095516422658773669068931361134188738159766715576187490305611759126554796569868053818105850661142222948198557" "1074773511698422344502264006159859710502164045911412750831641680783012525555872467108249271286757399121183508900634" "2727588299083545686739024317998512740561167011046940249988557419323068809019137624943703910267790601287073339193943" "493643299814437640914745677854369670041080344349607504656543355799077485536288866009245028091988146107059514546594" "734401332196641441839439105942623141234148957972407782257355060229193854324927417865401895596108124443575283868655" "2348330098288556420918672502923664952620152483128593484301759394583320358354186482723629999370241674973832318248497" ``` Source.

Undefined behaviours if the given elements are not in the field or any other representation than decimal is used. Use this function carefully.

See https://docs.rs/crate/pairing/0.16.0/source/src/bls12_381/README.md for more information on the instances used by the library.

FIXME: the function is not memory efficient because the elements are copied multiple times.

Source

val of_z : 
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  Z.t ->
  t

Same than of_string, using Z.t elements

FIXME: the function is not memory efficient because the elements are copied multiple times.

Install

Dune Dependency

Authors

Maintainers

Sources

doc/bls12-381/Bls12_381/Fq12/index.html

Module `Bls12_381.Fq12`Source

package bls12-381

Install

Dune Dependency

Authors

Maintainers

Sources

doc/bls12-381/Bls12_381/Fq12/index.html

Module Bls12_381.Fq12Source

Module `Bls12_381.Fq12`Source