Puid

Simple, fast, flexible and efficient generation of probably unique identifiers (puid, aka random strings) of intuitively specified entropy using pre-defined or custom characters.

iex> defmodule(RandId, do: use(Puid, chars: :alpha, total: 1.0e5, risk: 1.0e12))
iex> RandId.generate()
"YAwrpLRqXGlny"

 

TOC

• Overview
• Usage
• Installation
• Module API
• Characters
• Comparisons
  • Common Solution
  • gen_reference
  • misc_random
  • nanoid
  • Randomizer
  • rand_str
  • SecureRandom
  • ulid
  • UUID

Overview

Puid provides a means to create modules for generating random IDs. Specifically, Puid allows full control over all three key characteristics of generating random strings: entropy source, ID characters and ID randomness.

A general overview provides information relevant to the use of Puid for random IDs.

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Usage

Puid is used to create individual modules for random ID generation. Creating a random ID generator module is a simple as:

iex> defmodule(SessionId, do: use(Puid))
iex> SessionId.generate()
"8nGA2UaIfaawX-Og61go5A"

The code above use default parameters, so Puid creates a module suitable for generating session IDs (ID entropy for the default module is 132 bits). Options allow easy and complete control of all three of the important facets of ID generation.

Entropy Source

Puid uses :crypto.strong_rand_bytes/1 as the default entropy source. The rand_bytes option can be used to specify any function of the form (non_neg_integer) -> binary as the source:

iex > defmodule(PrngId, do: use(Puid, rand_bytes: &:rand.bytes/1))
iex> PrngId.generate()
"bIkrSeU6Yr8_1WHGvO0H3M"

Characters

By default, Puid use the RFC 4648 file system & URL safe characters. The chars option can by used to specify any of 16 pre-defined character sets or custom characters, including Unicode:

iex> defmodule(HexId, do: use(Puid, chars: :hex))
iex> HexId.generate()
"13fb81e35cb89e5daa5649802ad4bbbd"

iex> defmodule(DingoskyId, do: use(Puid, chars: "dingosky"))
iex> DingoskyId.generate()
"yiidgidnygkgydkodggysonydodndsnkgksgonisnko"

iex> defmodule(DingoskyUnicodeId, do: use(Puid, chars: "dîñgø$kyDÎÑGØßK¥", total: 2.5e6, risk: 1.0e15))
iex> DingoskyUnicodeId.generate()
"øßK$ggKñø$dyGîñdyØøØÎîk"

Captured Entropy

Generated IDs have at least 128-bit entropy by default. Puid provides a simple, intuitive way to specify ID randomness by declaring a total number of possible IDs with a specified risk of a repeat in that many IDs:

To generate up to 10 million random IDs with 1 in a trillion chance of repeat:

iex> defmodule(MyPuid, do: use(Puid, total: 10.0e6, risk: 1.0e15))
iex> MyPuid.generate()
"T0bFZadxBYVKs5lA"

The bits option can be used to directly specify an amount of ID randomness:

iex> defmodule(Token, do: use(Puid, bits: 256, chars: :hex_upper))
iex> Token.generate()
"6E908C2A1AA7BF101E7041338D43B87266AFA73734F423B6C3C3A17599F40F2A"

Note this is much more intuitive than guess, or simply not knowing, how much entropy your random IDs actually have.

General Note

The mathematical approximations used by Puid always favor conservative estimatation:

• overestimate the bits needed for a specified total and risk
• overestimate the risk of generating a total number of puids
• underestimate the total number of puids that can be generated at a specified risk

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Installation

Add puid to mix.exs dependencies:

def deps,
  do: [
    {:puid, "~> 2.1"}
  ]

Update dependencies

mix deps.get

Module API

Puid modules have the following functions:

• generate/0: Generate a random puid
• total/1: total puids which can be generated at a specified risk
• risk/1: risk of generating total puids
• encode/1: Encode bytes into a puid
• decode/1: Decode a puid into bytes
• info/0: Module information

The total/1, risk/1 functions provide approximations to the risk of a repeat in some total number of generated puids. The mathematical approximations used purposely overestimate risk and underestimate total.

The encode/1, decode/1 functions convert String.t() puids to and from bitstring bits to facilitate binary data storage, e.g. as an Ecto type.

The info/0 function returns a Puid.Info structure consisting of:

• source characters
• name of pre-defined Puid.Chars or :custom
• entropy bits per character
• total entropy bits
  • may be larger than the specified bits since it is a multiple of the entropy bits per character
• entropy representation efficiency
  • ratio of the puid entropy to the bits required for puid string representation
• entropy source function
• puid string length

Example

iex> defmodule(SafeId, do: use(Puid))

iex> SafeId.generate()
"CSWEPL3AiethdYFlCbSaVC"

iex> SafeId.total(1_000_000)
104350568690606000

iex> SafeId.risk(1.0e12)
9007199254740992

iex> SafeId.decode("CSWEPL3AiethdYFlCbSaVC")
<<9, 37, 132, 60, 189, 192, 137, 235, 97, 117, 129, 101, 9, 180, 154, 84, 32>>

iex> SafeId.encode(<<9, 37, 132, 60, 189, 192, 137, 235, 97, 117, 129, 101, 9, 180, 154, 84, 2::size(4)>>)
"CSWEPL3AiethdYFlCbSaVC"

iex> SafeId.info()
%Puid.Info{
  characters: "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_",
  char_set: :safe64,
  entropy_bits: 132.0,
  entropy_bits_per_char: 6.0,
  ere: 0.75,
  length: 22,
  rand_bytes: &:crypto.strong_rand_bytes/1
}

Characters

There are 19 pre-defined character sets:

Name	Characters
:alpha	ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
:alpha_lower	abcdefghijklmnopqrstuvwxyz
:alpha_upper	ABCDEFGHIJKLMNOPQRSTUVWXYZ
:alphanum	ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789
:alphanum_lower	abcdefghijklmnopqrstuvwxyz0123456789
:alphanum_upper	ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789
:base16	0123456789ABCDEF
:base32	ABCDEFGHIJKLMNOPQRSTUVWXYZ234567
:base32_hex	0123456789abcdefghijklmnopqrstuv
:base32_hex_upper	0123456789ABCDEFGHIJKLMNOPQRSTUV
:crockford32	0123456789ABCDEFGHJKMNPQRSTVWXYZ
:decimal	0123456789
:hex	0123456789abcdef
:hex_upper	0123456789ABCDEF
:safe_ascii	!#$%&()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[]^_abcdefghijklmnopqrstuvwxyz{|}~
:safe32	2346789bdfghjmnpqrtBDFGHJLMNPQRT
:safe64	ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_
:symbol	!#$%&()*+,-./:;<=>?@[]^_{|}~
:wordSafe32	23456789CFGHJMPQRVWXcfghjmpqrvwx

Any String of up to 256 unique characters can be used for puid generation, with custom characters optimized in the same manner as the pre-defined character sets. The characters must be unique. This isn't strictly a technical requirement, PUID could handle duplicate characters, but the resulting randomness of the IDs is maximal when the characters are unique, so PUID enforces that restriction.

Description of non-obvious character sets

Name	Description
:base16	https://datatracker.ietf.org/doc/html/rfc4648#section-8
:base32	https://datatracker.ietf.org/doc/html/rfc4648#section-6
:base32_hex	Lowercase of :base32_hex_upper
:base32_hex_upper	https://datatracker.ietf.org/doc/html/rfc4648#section-7
:crockford32	https://www.crockford.com/base32.html
:safe_ascii	Printable ascii that does not require escape in String
:safe32	Alpha and numbers picked to reduce chance of English words
:safe64	https://datatracker.ietf.org/doc/html/rfc4648#section-5
:wordSafe32	Alpha and numbers picked to reduce chance of English words

Note: :safe32 and :wordSafe32 are two different strategies for the same goal.

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Comparisons

As described in the overview, PUID aims to be a general, flexible mechanism for creating random string for use as random IDs. The following comparisons to other Elixir random ID generators is with respect to the issues of random ID generation described in that overview.

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Common Solution

Comments

• Entropy source: Generating indexes via a PRNG is straightforward, though wasteful when compared to bit slicing. Generating indexes via a CSPRNG is not straightforward except for hex characters.
• Characters: Full control
• Captured entropy: Indirectly specified via ID length

Timing

PUID is much faster.

Generate 100000 random IDs with 128 bits of entropy using alphanumeric characters

  Common Solution   (PRNG) : 4.977226
  Puid              (PRNG) : 0.831748

  Common Solution (CSPRNG) : 8.435073
  Puid            (CSPRNG) : 0.958437

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misc_random

Comments

• Entropy source: No control. Fixed to PRNG :random.uniform/1
• Characters: No control. Fixed to :alphanum
• Captured entropy: Indirectly specified via ID length

Timing

Quite slow compared to PUID

Generate 50000 random IDs with 128 bits of entropy using alphanum characters

  Misc.Random (PRNG) : 12.196646
  Puid        (PRNG) : 0.295741

  Misc.Random (CSPRNG) : 11.9858
  Puid        (CSPRNG) : 0.310417

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nanoid

Comments:

• Entropy source: Limited control; choice of CSPRNG or PRNG
• Characters: Full control
• Captured entropy: Indirectly specified via ID length

Timing:

nanoid is much slower than PUID

  Generate 75000 random IDs with 126 bits of entropy using safe64 characters

    Nanoid (CSPRNG) : 6.354221
    Puid   (CSPRNG) : 0.226448

    Nanoid (PRNG) : 1.229842
    Puid   (PRNG) : 0.31025

  Generate 75000 random IDs with 195 bits of entropy using alphanum characters

    Nanoid (CSPRNG) : 10.295134
    Puid   (CSPRNG) : 0.809756

    Nanoid (PRNG) : 1.678025
    Puid   (PRNG) : 0.808203

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Randomizer

Comments

• Entropy source: No control
• Characters: Limited to five pre-defined character sets
• Captured entropy: Indirectly specified via ID length

Timing

Slower than PUID

Generate 100000 random IDs with 128 bits of entropy using alphanum characters

  Randomizer   (PRNG) : 1.201281
  Puid         (PRNG) : 0.829199

  Randomizer (CSPRNG) : 4.329881
  Puid       (CSPRNG) : 0.807226

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SecureRandom

Comments

• Entropy source: No control. Fixed to :crypto.strong_rand_bytes/1
• Characters: Limited control for 3 specified use cases
• Captured entropy: Indirectly specified via ID length

Timing

About the same as PUID when using CSPRNG

Generate 500000 random IDs with 128 bits of entropy using hex characters

  SecureRandom (CSPRNG) : 1.19713
  Puid         (CSPRNG) : 1.187726

Generate 500000 random IDs with 128 bits of entropy using safe64 characters

  SecureRandom (CSPRNG) : 2.103798
  Puid         (CSPRNG) : 1.806514

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ulid

Comments

• Entropy source: No control. Fixed to CSPRNG (per spec)
• Characters: No control. Fixed to :base32
• Captured entropy: 80-bits per timestamp context

A significant characteristic of ulid is the generation of lexicographically sortable IDs. This is not a goal for PUID; however, one could use PUID to generate such IDs by prefixing a timestamp to a generated puid. Such a solution would be similar to ulid while still providing full control to entropy source, characters, and captured entropy per timestamp context.

Timing

ulid and PUID are not directly comparable with regard to speed.

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UUID

Comments

• Entropy source: No control. Fixed to crypto.strong_rand_bytes/1
• Character: No control. Furthermore, string representation is inefficient
• Capture entropy: No control. Fixed to 122 bits

Timing

Similar to PUID when using CSPRNG

Generate 500000 random IDs with 122 bits of entropy using hex
  UUID     : 1.925131
  Puid hex : 1.823116

Generate 500000 random IDs with 122 bits of entropy using safe64
  UUID        : 1.751625
  Puid safe64 : 1.367201

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