puidjs
Simple, flexible and efficient generation of probably unique identifiers (puid
, aka random strings) of intuitively specified entropy using predefined or custom characters (including Unicode).
const { Chars, puid } = require('puidjs')
const { generator: randId } = puid({ chars: Chars.Alpha, total: 1e5, risk: 1e12 })
randId()
// => 'qZrxxBnmKndIn'
TOC
Overview
puidjs
provides intuitive and efficient generation of random IDs. For the purposes of puidjs
, a random ID is considered a random string used in a context of uniqueness, that is, random IDs are a bunch of random strings that are hopefully unique.
Random string generation can be thought of as a transformation of some random source of entropy into a string representation of randomness. A general purpose random string library used for random IDs should therefore provide user specification for each of the following three key aspects:

Entropy source
What source of randomness is being transformed?
puidjs
allows easy specification of the function used for source randomness 
ID characters
What characters are used in the ID?
puidjs
provides 16 predefined character sets, as well as allows custom characters, including Unicode 
ID randomness
What is the resulting “randomness” of the IDs?
puidjs
allows an intuitive, explicit specification of ID randomness
Usage
Creating a random ID generator using puidjs
is a simple as:
const { puid } = require('puidjs')
const { generator: randId } = puid()
randId()
// => 'fxgA7EO_YklcUnrPenF284'
Entropy Source
puidjs
uses crypto.randomBytes
as the default entropy source. Options can be used to configure a specific entropy source:

entropyBytes
: any function of the form(n: number): Uint8Array
, such ascrypto.randomBytes

entropyValues
: any function of the form(buf: Uint8Array): void
, such ascrypto.getRandomValues
These options make it easy to use puidjs
in either a nodejs
or web environment. It also allows for using any suitable thirdparty entropy source. The project includes an experimental PRNG random bytes generator, prngBytes
, and the test code uses the entropyBytes
option for deterministic testing.
const { puid } = require('puidjs')
const { generator: randId } = puid({ entropyValues: crypto.getRandomValues })
randId()
// => 'j9XyiUzld40fOxSrC7L5sy'
ID Characters
By default, puidjs
use the RFC 4648 file system & URL safe characters. The chars
option can by used to specify any of 16 predefined character sets or custom characters, including Unicode:
const { Chars, puid } = require('puidjs')
const { generator: hexId } = puid({ chars: Chars.Hex })
hexId()
// => '017391a839910b76295e9bf01f89b8e8'
const { generator: dingoskyId } = puid({ chars: 'dingosky' })
dingoskyId()
// => 'ksyssdddgogoigydiskyndkysddddioggooyogdykdy'
const { generator: unicodeId } = puid({ chars: 'dîñgø$kyDÎÑGØßK¥' })
unicodeId()
// => 'Î¥ñdy¥d¥ÎØ¥KkDyîdkø¥kØ¥dø$KßØgøÑ'
ID Randomness
Generated IDs have 128bit entropy by default. puidjs
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:
const { Chars, puid } = require('puidjs')
const { generator: safe32Id } = puid({ total: 10e6, risk: 1e15, chars: Chars.Safe32 })
safe32Id()
// => 'fqGpPbhh3Hn49FMq4g8r'
The bits
option can be used to directly specify an amount of ID randomness:
const { Chars, puid } = require('puidjs')
const { generator: token } = puid({ bits: 256, chars: Chars.HexUpper })
token()
// => 'A9FFAD1F0BC314D34678B0F4D1592665D87B01311C8D37DE61FFF8A6C25F885D'
Installation
Yarn
yarn add puidjs
NPM
npm install puidjs
API
puidjs
exports a higherorder function (HOF), puid
, used to create random ID generators. The puid
HOF takes an optional PuidConfig
object for configuration and returns an object of the form { generator: () => string, error: Error }
that either passes back the puid
generating function or an Error
indicating a problem with the specified configuration.
PuidConfig
The optional PuidConfig
object has the following fields:

total
: Total number of potential (i.e. expected) IDs 
risk
: Risk of repeat intotal
IDs 
bits
: ID entropy bits 
chars
: ID characters 
entropyBytes
: Function of the form(n: number) => Uint8Array
for source entropy 
entropyValues
: Function of the form(buf: Uint8Array) => void
for source entropy
Notes
 All config fields are optional

total/risk
must be set together 
total/risk
andbits
cannot both be set 
chars
must be valid (seeChars.validChars
function) 
entropyBytes
is the form of the functioncrypto.randomBytes

entropyValues
is the form of the functioncrypto.getRandomValues
 Only one of
entropyBytes
orentropyValues
can be set
Defaults

bits
: 128 
chars
:Chars.Safe64

entropyBytes
:crypto.randomBytes
PuidInfo
The puid
generator function includes an info
field that displays generator configuration:

bits
: ID entropy 
bitsPerChar
: Entropy bits per ID character 
chars
: Source characters 
charsName
: Name of predefinedChars
orcustom

ere
: Entropy representation efficiency 
length
: ID string length
Example:
const { Chars, puid } = require('puidjs')
const { generator: genId } = puid({ total: 1e5, risk: 1e14, chars: Chars.Base32 })
genId()
// => 'FJ57265CAUTZITHN'
genId.info
// =>
{
bits: 80,
bitsPerChar: 5,
chars: '234567ABCDEFGHIJKLMNOPQRSTUVWXYZ',
charsName: 'base32',
ere: 0.63,
length: 16
}
Chars
There are 16 predefined character sets:
Name  Characters 

Alpha  ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz 
AlphaLower  abcdefghijklmnopqrstuvwxyz 
AlphaUpper  ABCDEFGHIJKLMNOPQRSTUVWXYZ 
Alphanum  ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789 
AlphanumLower  abcdefghijklmnopqrstuvwxyz0123456789 
AlphanumUpper  ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789 
Base32  234567ABCDEFGHIJKLMNOPQRSTUVWXYZ 
Base32Hex  0123456789abcdefghijklmnopqrstuv 
base32HexUpper  0123456789ABCDEFGHIJKLMNOPQRSTUV 
Decimal  0123456789 
Hex  0123456789abcdef 
HexUpper  0123456789ABCDEF 
SafeAscii  !#$%&()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[]^_abcdefghijklmnopqrstuvwxyz{}~ 
Safe32  2346789bdfghjmnpqrtBDFGHJLMNPQRT 
Safe64  ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789_ 
Symbol  !#$%&()*+,./:;<=>?@[]^_{}~ 
Any string of up to 256 unique characters, including unicode, can be used for puid
generation.
Motivation
Developers frequently need random strings in applications ranging from longterm (e.g., data store keys) to shortterm (e.g. DOM IDs on a web page). These IDs are, of course, of secondary concern. No one wants to think about them much, they just want to be easy to generate.
But developers should think about the random strings they use. The generation of random IDs is a design choice, and just like any other design choice, that choice should be explicit in nature and based on a familiar with why such choices are made. Yet a cursory review of random string libraries, as well as random string usage in many applications, yields a lack of clarity that belies careful consideration.
What is a random string?
Although this may seem to have an obvious answer, there is actually a key, often overlooked subtlety: a random string is not random in and of itself. To understand this, we need to understand entropy as it relates to computers.
A somewhat simplistic statement for entropy from information theory is: entropy is a measure of uncertainty in the possible outcomes of an event. Given the base 2 system inherent in computers, this uncertainty naturally maps to a unit of bits (known as Shannon entropy). So we see statements like "this random string has 128 bits of entropy". But here is the subtlety:
A random string does not have entropy
Rather, a random string represents captured entropy, entropy that was produced by some other process. For example, you cannot look at the hex string '18f6303a'
and definitively say it has 32 bits of entropy. To see why, suppose you run the following code snippet and get '18f6303a'
:
const randId = () => {
if (Math.random() < 0.5) return '18f6303a'
return '1'
}
randId()
// => '18f6303a'
In this case, the entropy of the string '18f6303a'
is 1 bit. That's it; 1 bit. The same entropy as when the outcome '1'
is observed. In either case, there are only two equally possible outcomes and the resulting entropy is therefore 1 bit. It's important to have this clear understanding:
Entropy is a measure in the uncertainty of an event, independent of the representation of that uncertainty
In information theory you would state the above process has two symbols, 18f6303a
and 1
, and the outcome is equally likely to be either symbol. Hence there is 1 bit of entropy in the process. The symbols don't really matter. It would be much more likely to see the symbols T
and F
, or 0
and 1
, or even ON
and OFF
, but regardless, the process produces 1 bit of entropy and symbols used to represent that entropy do not effect the entropy itself.
Entropy source
Random string generators need an external source of entropy and typically use a system resource for that entropy. In JavaScript, this could be either crypto.randomBytes
or crypto.getRandomValues
, or even Math.random
. Nonetheless, it is important to appreciate that the properties of the generated random strings depend on the characteristics of the entropy source. For example, whether a random string is suitable for use as a secure token depends on the security characteristics of the entropy source, not on the string representation of the token.
ID characters
As noted, the characters (symbols) used for a random string do not determine the entropy. However, the number of unique characters does. Under the assumption that each character is equally probable (which maximizes entropy) it is easy to show the entropy per character is a constant log_{2}(N), where N
is of the number of characters available.
ID randomness
String randomness is determined by the entropy per character times the number of characters in the string. The quality of that randomness is directly tied to the quality of the entropy source. The randomness depends on the number of available characters and the length of the string.
And finally we can state: a random string is a character representation of captured system entropy.
Uniqueness
The goal of puidjs
is to provide simple, intuitive random ID generation using random strings. As noted above, we can consider random string generation as the transformation of system entropy into a character representation, and random IDs as being the use of such random strings to represent unique IDs. There is a catch though; a big catch:
Random strings do not produce unique IDs
Recall that entropy is the measure of uncertainty in the possible outcomes of an event. It is critical that the uncertainty of each event is independent of all prior events. This means two separate events can produce the same result (i.e., the same ID); otherwise the process isn't random. You could, of course, compare each generated random string to all prior IDs and thereby achieve uniqueness. But some such postprocessing must occur to ensure random IDs are truly unique.
Deterministic uniqueness checks, however, incur significant processing overhead and are rarely used. Instead, developers (knowingly?) relax the requirement that random IDs are truly, deterministically unique for a much lesser standard, one of probabilistic uniqueness. We "trust" that randomly generated IDs are unique by virtue of the chance of a repeated ID being very low.
And once again, we reach a point of subtlety. (And we thought random strings were easy!) The "trust" that randomly generated IDs are unique actually turns entropy as it's been discussed thus far on it's head. Instead of viewing entropy as a measure of uncertainty in the generation of IDs, we consider entropy as a measure of the probability that no two IDs will be the same. To be sure, we want this probability to be very low, but for random strings it cannot be zero. And to be clear, entropy is not such a measure. Not directly anyway. Yes, the higher the entropy, the lower the probability, but it takes a bit of math to correlate the two in a proper manner. (Don't worry, puidjs
takes care of this math for you).
Furthermore, the probable uniqueness of ID generation is always in some limited context. Consider IDs for a data store. You don't care if a generated ID is the same as an ID used in another data store in another application in another company in a galaxy far, far away. You care that the ID is (probably) unique within the context of your application.
To recap, random string generation does not produce unique IDs, but rather, IDs that are probably unique (within some context). That subtlety is important enough it's baked into the name of puidjs
(and fully at odds with term UUID
).
ID randomness
So what does the statement "these IDs have 122 bits of entropy" actually mean? Entropy is a measure of uncertainty after all, and we're concerned that our IDs be unique, probably unique anyway. So what does "122 bits of entropy" mean for the probable uniqueness of IDs?
First, let's be clear what it doesn't mean. We're concerned with uniqueness of a bunch of IDs in a certain context. The randomness of any one of those ID isn't the real concern. Yes, we can say "given 122 bits of entropy" each ID has a probability of 2^{122} of occurring. And yes, that certainly makes the occurrence of any particular ID rare. But with respect to the uniqueness of IDs, it isn't "enough" to tell the whole story.
And here again we hit another subtlety. It turns out the question, as posed, is underspecified, i.e. it is not specific enough to be answered. To properly determine how entropy relates to the probable uniqueness of IDs, we need to specify how many IDs are to be generated in a certain context. Only then can we determine the probability of generating unique IDs. So our question really needs to be: given N bits of entropy, what is the probability of uniqueness in T random IDs?
Fortunately, there is a mathematical correlation between entropy and the probability of uniqueness. This correlation is often explored via the Birthday Paradox. Why paradox? Because the relationship, when cast as a problem of unique birthdays in some number of people, is initially quite surprising. But nonetheless, the relationship exists, it is wellknown, and puidjs
will take care of the math for us.
At this point we can now note that rather than say "these IDs have N bits of entropy", we actually want to say "generating T of these IDs has a risk R of a repeat". And fortunately, puidjs
allows straightforward specification of that very statement for random ID generation. Using puidjs
, you can easily specify "I want T random IDs with a risk R of repeat". puidjs
will take care of using the correct entropy in efficiently generating the IDs.
Efficiency
The efficiency of generating random IDs has no bearing on the statistical characteristics of the IDs themselves. But who doesn't care about efficiency? Unfortunately, most random string generation, it seems.
Entropy source
As previously stated, random ID generation is basically a transformation of an entropy source into a character representation of captured entropy. But the entropy of the source and the entropy of the captured ID is not the same thing.
To understand the difference, we'll investigate an example that is, surprisingly, quite common. Consider the following strategy for generating random strings: using a fixed list of k characters, use a random uniform integer i, 0 <= i < k
, as an index into the list to select a character. Repeat this n times, where n is the length of the desired string. In JavaScript this might look like:
const commonId = (n) => {
const chars = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789'
let id = ''
for (let i = 0; i < n; i++) {
id += chars.charAt(Math.floor(Math.random() * chars.length))
}
return id
}
commonId(8)
// => 's5hExiXb'
First, consider the amount of source entropy used in the code above. The JavaScript spec doesn't declare the amount of entropy generated by Math.random
, but let's give it the upper bound of 52 bits (since that's the number of bits in the fraction of a JavaScript doubleprecision float). So generating an 8 character ID above consumes 8 * 52 = 416 bits of source entropy.
Second, consider how much entropy was captured by the ID. Given there are 26 characters, each character represents log_{2}(26) = 4.7 bits of entropy. So each generated ID represents 8 * 4.7 = 37.6 bits of entropy.
Hmmm. That means the ratio of ID entropy to source entropy is 37.6 / 424 = 0.09, or a whopping 9%. That's not an efficiency most developers would be comfortable with. Granted, this is a particularly egregious example, but most random ID generation suffers such inefficient use of source entropy.
Without delving into the specifics (see the code?), puidjs
employs various means to maximize the use of source entropy. As comparison, puidjs
uses 87.5% of source entropy in generating random IDs using lower case alpha characters. For character sets with counts equal a power of 2, puidjs
uses 100% of source entropy.
Characters
As previous noted, the entropy of a random string is equal to the entropy per character times the length of the string. Using this value leads to an easy calculation of entropy representation efficiency (ere
). We can define ere
as the ratio of random string entropy to the number of bits required to represent the string. For example, the lower case alphabet has an entropy per character of 4.7, so an ID of length 8 using those characters has 37.6 bits of entropy. Since each lower case character requires 1 byte, this leads to an ere
of 37.6 / 64 = 0.59, or 59%. Nonascii characters, of course, occupy more than 1 byte. puidjs
uses the Buffer.byteLength
function to compute ere
.
The total entropy of a string is the product of the entropy per character times the string length only if each character in the final string is equally probable. This is always the case for puidjs
, and is usually the case for other random string generators. There is, however, a notable exception: the version 4 string representation of a uuid
. As defined in RFC 4122, Section 4.4, a v4 uuid
uses a total of 32 hex and 4 hyphen characters. Although the hex characters can represent 4 bits of entropy each, 6 bits of the hex representation in a uuid
are actually fixed, so there is only 32*4  6 = 122
bits of entropy (not 128). The 4 fixedposition hyphen characters contribute zero entropy. So a 36 character uuid
has an ere
of 122 / (36*8) = 0.40
, or 40%. Compare that to, say, the default puidjs
generator, which has slightly higher entropy (132 bits) and yet yields an ere
of 0.75, or 75%. Who doesn't love efficiency?
Overkill and Under Specify
Overkill
Random string generation is plagued by overkill and under specified usage. Consider the all too frequent use of uuid
s as random strings. The rational is seemingly that the probability of a repeated uuid
is low. Yes, it is admittedly low, but is that sufficient reason to use a uuid
without further thought? For example, suppose a uuid
is used as a key in a data store that will have at most a thousand items. What is the probability of a repeated uuid
in this case? It's 1 in a nonillion. That's 10^30, or 1 followed by 30 zeros, or million times the estimated number of stars in the universe. Really? Doesn't that seem a bit overkill? Do really you need that level of assurance? And if so, why stop there? Why not concatenate two uuid
s and get an even more ridiculous level of "assurance".
Or why not be a bit more reasonable and think about the problem for a moment. Suppose you accept a 1 in 10^15 risk of repeat. That's still a really low risk. Ah, but wait, to do that you can't use a uuid
, because uuid
generation isn't flexible. The characters are fixed, the representation is fixed, and the bits of entropy are fixed. But you could very easily use puidjs
to generate such IDs:
const { puid } = require('puidjs')
const { generator: dbId } = puid({ total: 1000, risk: 1e15 })
dbId()
// => 'c1DVnnbI3RTr'
The resulting ID have 72 bits of entropy. But guess what? You don't care. What you care is having explicitly stated you expect to have 1000 IDs and your level of repeat risk is 1 in a quadrillion. It's right there in the code. And as added bonus, the IDs are only 12 characters long, not 36. Who doesn't like ease, control and efficiency?
Under specify
Another headscratcher in schemes that generate random strings is using an API that explicitly declares string length. Why is this troubling? Because that declaration doesn't specify the actual amount of desired randomness, either needed or achieved. Suppose you are tasked with maintaining code that is using random IDs of 15 characters composed of digits and lower alpha characters. Why are the IDs 15 characters long? Unless there are code comments, you have no idea. And without knowing how many IDs are expected, you can't determine the risk of a repeat, i.e., you can't even make a statement about how random the random IDs actually are! Was 15 chosen for a reason, or just because it made the IDs look good?
Now, suppose you are tasked to maintain this code:
const { puid } = require('puidjs')
const { generator: randId } = puid({ total: 500000, risk: 1e12, chars: Chars.AlphaNumLower })
randId()
// => 'u4a4fbhhwlsikct'
Hmmm. Looks like there are 500,000 IDs expected and the repeat risk is 1 in a trillion. No guessing. The code is explicit. Oh, and by the way, the IDs are 15 characters long. But who cares? It's the ID randomness that matters, not the length.
Efficiencies
Puid
employs a number of efficiencies for random ID generation:
 Only the number of bytes necessary to generate the next
puid
are fetched from the entropy source  Each
puid
character is generated by slicing the minimum number of entropy bits possible  Any leftover bits are carried forward and used in generating the next
puid
 All characters are equally probable to maximize captured entropy
 Only characters that represent entropy are present in the final ID
 Easily specified
total/risk
ensures ID are only as long as actually necessary
tl;dr
Puid
is a simple, flexible and efficient random ID generator:

Ease
Random ID generator specified in one line of code

Flexible
Full control over entropy source, ID characters and amount of ID randomness

Explicit
Clear specification of chosen level of randomness

Efficient
Maximum use of system entropy

Compact
ID strings represent maximum entropy for characters used

Secure
Defaults to a secure source of entropy and at least 128 bits of ID entropy
const { Chars, puid } = require('puidjs')
const { generator: randId } = puid(chars:Chars.SAFE32, total:10e6, risk: 1e15)
randId()
// => 'tp9TJPNM2rmMLN22prFf'