package octez-proto-libs

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include module type of struct include Bls12_381.Fq12 end

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.

exception Not_in_field of Bytes.t

type t = Bls12_381.Fq12.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

val order : Z.t

The order of the field

val size_in_bytes : int

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

val size_in_memory : int

Actual number of bytes allocated for a value of type t

val zero : t

The neutral element of the additive subgroup

val one : t

The neutral element of the multiplicative subgroup

val is_zero : t -> bool

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

val is_one : t -> bool

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

val mul : t -> t -> t

mul a b returns the product of a and b

val 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

val 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

val eq : t -> t -> bool

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

val 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|].

val pow : t -> Z.t -> t

val 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.

val of_bytes_opt : Bytes.t -> t option

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

val to_bytes : t -> Bytes.t

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

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.

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.

val check_bytes : 'a -> 'b

val add : 'a -> 'b -> 'c

val negate : 'a -> 'b