Random

A module for obtaining randomness on the Internet Computer (IC).

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

Dealing with randomness on a deterministic computing platform, such as the IC, 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:

motoko no-repl
import Random "mo:base/Random";

`public func blob() : async Blob`

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

Example:

motoko no-repl
let random = Random.Finite(await Random.blob());

class Finite(entropy : Blob)

`public func byte() : ?Nat8`

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

Example:

motoko no-repl
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

`public func coin() : ?Bool`

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

Example:

motoko no-repl
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

`public func range(p : Nat8) : ?Nat`

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

Example:

motoko no-repl
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

`public func binomial(n : Nat8) : ?Nat8`

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

Example:

motoko no-repl
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

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:

motoko no-repl
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);

`public func byteFrom(seed : Blob) : Nat8`

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

Example:

motoko no-repl
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

`public func coinFrom(seed : Blob) : Bool`

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

Example:

motoko no-repl
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

`public 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:

motoko no-repl
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

`public 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:

motoko no-repl
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