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Random

A module for obtaining randomness on the BigFile (BIG).

This module provides the fundamentals for user abstractions to build on.

Dealing with randomness on a deterministic computing platform, such as the BIG, is intricate. Some basic rules need to be followed by the user of this module to obtain (and maintain) the benefits of crypto- graphic randomness:

  • cryptographic entropy (randomness source) is only obtainable asyncronously in discrete chunks of 256 bits (32-byte sized Blobs)
  • all bets must be closed before entropy is being asked for in order to decide them
  • this implies that the same entropy (i.e. Blob) - or surplus entropy not utilised yet - cannot be used for a new round of bets without losing the cryptographic guarantees.

Concretely, the below class Finite, as well as the *From methods risk the carrying-over of state from previous rounds. These are provided for performance (and convenience) reasons, and need special care when used. Similar caveats apply for user-defined (pseudo) random number generators.

Usage:

import Random "mo:base/Random";

Value blob​

let blob : shared () -> async Blob

Obtains a full blob (32 bytes) worth of fresh entropy.

Example:

let random = Random.Finite(await Random.blob());

Class Finite​

class Finite(entropy : Blob)

Drawing from a finite supply of entropy, Finite provides methods to obtain random values. When the entropy is used up, null is returned. Otherwise the outcomes' distributions are stated for each method. The uniformity of outcomes is guaranteed only when the supplied entropy is originally obtained by the blob() call, and is never reused.

Example:

import Random "mo:base/Random";

let random = Random.Finite(await Random.blob());

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
let seedRandom = Random.Finite(seed);

Function byte​

func byte() : ?Nat8

Uniformly distributes outcomes in the numeric range [0 .. 255]. Consumes 1 byte of entropy.

Example:

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
let random = Random.Finite(seed);
random.byte() // => ?20

Function coin​

func coin() : ?Bool

Simulates a coin toss. Both outcomes have equal probability. Consumes 1 bit of entropy (amortised).

Example:

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
let random = Random.Finite(seed);
random.coin() // => ?false

Function range​

func range(p : Nat8) : ?Nat

Uniformly distributes outcomes in the numeric range [0 .. 2^p - 1]. Consumes ⌈p/8⌉ bytes of entropy.

Example:

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
let random = Random.Finite(seed);
random.range(32) // => ?348746249

Function binomial​

func binomial(n : Nat8) : ?Nat8

Counts the number of heads in n fair coin tosses. Consumes ⌈n/8⌉ bytes of entropy.

Example:

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
let random = Random.Finite(seed);
random.binomial(5) // => ?1

Function byteFrom​

func byteFrom(seed : Blob) : Nat8

Distributes outcomes in the numeric range [0 .. 255]. Seed blob must contain at least a byte.

Example:

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
Random.byteFrom(seed) // => 20

Function coinFrom​

func coinFrom(seed : Blob) : Bool

Simulates a coin toss. Seed blob must contain at least a byte.

Example:

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
Random.coinFrom(seed) // => false

Function rangeFrom​

func rangeFrom(p : Nat8, seed : Blob) : Nat

Distributes outcomes in the numeric range [0 .. 2^p - 1]. Seed blob must contain at least ((p+7) / 8) bytes.

Example:

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
Random.rangeFrom(32, seed) // => 348746249

Function binomialFrom​

func binomialFrom(n : Nat8, seed : Blob) : Nat8

Counts the number of heads in n coin tosses. Seed blob must contain at least ((n+7) / 8) bytes.

Example:

let seed : Blob = "\14\C9\72\09\03\D4\D5\72\82\95\E5\43\AF\FA\A9\44\49\2F\25\56\13\F3\6E\C7\B0\87\DC\76\08\69\14\CF";
Random.binomialFrom(5, seed) // => 1