EntropyString for JavaScript

   

Efficiently generate cryptographically strong random strings of specified entropy from various character sets.

TOC

• Installation
• TL;DR
• Overview
• Real Need
• More Examples
• Character Sets
• Custom Characters
• Efficiency
• Custom Bytes
• Entropy Bits
• Upgrading To Version 3
• TL;DR 2

Installation

Yarn

  yarn add entropy-string

NPM

  npm install entropy-string

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TL;DR

Examples

Run any of the examples in the examples directory by:

yarn examples
node examples/dist/tldr_1.js

Usage

Generate a potential of 1 million random strings with 1 in a billion chance of repeat:

const { Entropy } = require('entropy-string')

const bits = Entropy.bits(1e6, 1e9)
const entropy = new Entropy()
const string = entropy.string(bits)

pbbnBD4MQ3rbRN

See Real Need for description of what entropy bits represents.

EntropyString uses predefined charset32 characters by default (see Character Sets). To get a random hexadecimal string with the same entropy bits as above:

const { Entropy, charset16 } = require('entropy-string')

const bits = Entropy.bits(1e6, 1e9)
const entropy = new Entropy(charset16)
const string = entropy.string(bits)

878114ac513a538e22

Custom characters may be specified. Using uppercase hexadecimal characters:

const { Entropy } = require('entropy-string')

const bits = Entropy.bits(1e6, 1e9)
const entropy = new Entropy('0123456789ABCDEF')
const string = entropy.string(bits)

16E26779479356B516

Convenience functions smallID, mediumID, largeID, sessionID and token provide random strings for various predefined bits of entropy. For example, a small id represents a potential of 30 strings with a 1 in a million chance of repeat:

const { Entropy } = require('entropy-string')

const entropy = new Entropy()
const string = entropy.smallID()

DpTQqg

Or, to generate an OWASP session ID:

const { Entropy } = require('entropy-string')

const entropy = new Entropy()
const string = entropy.sessionID()

nqqBt2P669nmjPQRqh4NtmTPn9

Or perhaps you need an 256-bit token using RFC 4648 file system and URL safe characters:

const { Entropy, charset64} = require('entropy-string')

const entropy = new Entropy(charset64)

const string = entropy.token()

t-Z8b9FLvpc-roln2BZnGYLZAX_pn5U7uO_cbfldsIt

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Overview

EntropyString provides easy creation of randomly generated strings of specific entropy using various character sets. Such strings are needed as unique identifiers when generating, for example, random IDs and you don't want the overkill of a UUID.

A key concern when generating such strings is that they be unique. Guaranteed uniqueness, however, requires either deterministic generation (e.g., a counter) that is not random, or that each newly created random string be compared against all existing strings. When randomness is required, the overhead of storing and comparing strings is often too onerous and a different tack is chosen.

A common strategy is to replace the guarantee of uniqueness with a weaker but often sufficient one of probabilistic uniqueness. Specifically, rather than being absolutely sure of uniqueness, we settle for a statement such as "there is less than a 1 in a billion chance that two of my strings are the same". We use an implicit version of this very strategy every time we use a hash set, where the keys are formed from taking the hash of some value. We assume there will be no hash collision using our values, but we do not have any true guarantee of uniqueness per se.

Fortunately, a probabilistic uniqueness strategy requires much less overhead than guaranteed uniqueness. But it does require we have some manner of qualifying what we mean by "there is less than a 1 in a billion chance that 1 million strings of this form will have a repeat".

Understanding probabilistic uniqueness of random strings requires an understanding of entropy and of estimating the probability of a collision (i.e., the probability that two strings in a set of randomly generated strings might be the same). The blog post Hash Collision Probabilities provides an excellent overview of deriving an expression for calculating the probability of a collision in some number of hashes using a perfect hash with an N-bit output. This is sufficient for understanding the probability of collision given a hash with a fixed output of N-bits, but does not provide an answer to qualifying what we mean by "there is less than a 1 in a billion chance that 1 million strings of this form will have a repeat". The Entropy Bits section below describes how EntropyString provides this qualifying measure.

We'll begin investigating EntropyString by considering the Real Need when generating random strings.

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Real Need

Let's start by reflecting on the common statement: I need random strings 16 characters long.

Okay. There are libraries available that address that exact need. But first, there are some questions that arise from the need as stated, such as:

1. What characters do you want to use?
2. How many of these strings do you need?
3. Why do you need these strings?

The available libraries often let you specify the characters to use. So we can assume for now that question 1 is answered with:

Hexadecimal will do fine.

As for question 2, the developer might respond:

I need 10,000 of these things.

Ah, now we're getting somewhere. The answer to question 3 might lead to a further qualification:

I need to generate 10,000 random, unique IDs.

And the cat's out of the bag. We're getting at the real need, and it's not the same as the original statement. The developer needs uniqueness across a total of some number of strings. The length of the string is a by-product of the uniqueness, not the goal, and should not be the primary specification for the random string.

As noted in the Overview, guaranteeing uniqueness is difficult, so we'll replace that declaration with one of probabilistic uniqueness by asking a fourth question:

4. What risk of a repeat are you willing to accept?

Probabilistic uniqueness contains risk. That's the price we pay for giving up on the stronger declaration of guaranteed uniqueness. But the developer can quantify an appropriate risk for a particular scenario with a statement like:

I guess I can live with a 1 in a million chance of a repeat.

So now we've finally gotten to the developer's real need:

I need 10,000 random hexadecimal IDs with less than 1 in a million chance of any repeats.

Not only is this statement more specific, there is no mention of string length. The developer needs probabilistic uniqueness, and strings are to be used to capture randomness for this purpose. As such, the length of the string is simply a by-product of the encoding used to represent the required uniqueness as a string.

How do you address this need using a library designed to generate strings of specified length? Well, you don't, because that library was designed to answer the originally stated need, not the real need we've uncovered. We need a library that deals with probabilistic uniqueness of a total number of some strings. And that's exactly what EntropyString does.

Let's use EntropyString to help this developer generate 5 hexadecimal IDs from a pool of a potential 10,000 IDs with a 1 in a million chance of a repeat:

const { Entropy, charset16 } = require('entropy-string')

const bits = Entropy.bits(10000, 1000000)
const entropy = new Entropy(charset16)
const strings = Array()
for (let i = 0; i < 5; i++) {
   string = entropy.string(bits)
  strings.push(string)
}

["85e442fa0e83", "a74dc126af1e", "368cd13b1f6e", "81bf94e1278d", "fe7dec099ac9"]

Examining the above code,

const bits = Entropy.bits(10000, 1000000)

is used to determine how much entropy is needed to satisfy the probabilistic uniqueness of a 1 in a million risk of repeat in a total of 10,000 potential strings. We didn't print the result, but if you did you'd see it's about 45.51 bits. Then

const entropy = new Entropy(charset16)

creates a Entropy instance configured to generated strings using the predefined hexadecimal characters provided by charset16. Finally

const string = entropy.string(bits)

is used to actually generate a random string of the specified entropy.

Looking at the IDs, we can see each is 12 characters long. Again, the string length is a by-product of the characters used to represent the entropy we needed. And it seems the developer didn't really need 16 characters after all.

Given that the strings are 12 hexadecimals long, each string actually has an information carrying capacity of 12 * 4 = 48 bits of entropy (a hexadecimal character carries 4 bits). That's fine. Assuming all characters are equally probable, a string can only carry entropy equal to a multiple of the amount of entropy represented per character. EntropyString produces the smallest strings that exceed the specified entropy.

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More Examples

In Real Need our developer used hexadecimal characters for the strings. Let's look at using other characters instead.

We'll start with using 32 characters. What 32 characters, you ask? The Character Sets section discusses the predefined characters available in EntropyString and the Custom Characters section describes how you can use whatever characters you want. By default, EntropyString uses charset32 characters, so we don't need to pass that parameter into new Entropy().

const { Entropy } = require('entropy-string')

const bits = Entropy.bits(10000, 1e6)
const entropy = new Entropy()
const string = entropy.string(bits)

String: MD8r3BpTH3

We're using the same Entropy.bits calculation since we haven't changed the number of IDs or the accepted risk of probabilistic uniqueness. But this time we use 32 characters and our resulting ID only requires 10 characters (and can carry 50 bits of entropy).

As another example, let's assume we need to ensure the names of a handful of items are unique. Let's say 30 items. And suppose we decide we can live with a 1 in 100,000 probability of collision (we're just futzing with some coding ideas). Using the predefined provided hex characters:

const { Entropy, charset16, charset4 } = require('entropy-string')

const bits = Entropy.bits(30, 100000)
const entropy = new Entropy(charset16)
const string = entropy.string(bits)

String: dbf40a6

Using the same Entropy instance, we can switch to the predefined charset4 characters and generate a string of the same amount of entropy:

entropy.use(charset4)
string = entropy.string(bits)

String: CAATAGTGGACTG

Okay, we probably wouldn't use 4 characters (and what's up with those characters?), but you get the idea.

Suppose we have a more extreme need. We want less than a 1 in a trillion chance that 10 billion base 32 strings repeat. Let's see, our total of 10 billion is 10¹⁰ and our risk of 1 in a trillion is 10¹², so:

const { Entropy } = require('entropy-string')

const bits = Entropy.bits(1e10, 1e12)
const entropy = new Entropy()
const string = entropy.string(bits)

String: 4J86pbFG9BqdBjTLfD3rt6

Finally, let say we're generating session IDs. Since session IDs are ephemeral, we aren't interested in uniqueness per se, but in ensuring our IDs aren't predictable since we can't have the bad guys guessing a valid session ID. In this case, we're using entropy as a measure of unpredictability of the IDs. Rather than calculate our entropy, we declare it as 128 bits (since we read on the OWASP web site that session IDs should be 128 bits).

const { Entropy } = require('entropy-string')

const entropy = new Entropy()
const string = entropy.string(128)

String: Rm9gDFn6Q9DJ9rbrtrttBjR97r

Since session ID are such an important need, EntropyString provides a convenience function for generating them:

const { Entropy, charset64 } = require('entropy-string')

const entropy = new Entropy(charset64)
const string = entropy.sessionID()

String: DUNB7JHqXCibGVI5HzXVp2

In using 64 characters, note our string length is 22 characters. That's actually 22*6 = 132 bits, so we've got our OWASP session ID requirement covered!

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Character Sets

As we've seen in the previous sections, EntropyString provides predefined character sets. Let's see what's under the hood.

const { charset64 } = require('entropy-string')
const chars = charset64.chars()

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_

The available CharSets are charset64, charset32, charset16, charset8, charset4 and charset2. The predefined characters for each were chosen as follows:

• CharSet 64: ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_
  • The file system and URL safe char set from RFC 4648.  
• CharSet 32: 2346789bdfghjmnpqrtBDFGHJLMNPQRT
  • Remove all upper and lower case vowels (including y)
  • Remove all numbers that look like letters
  • Remove all letters that look like numbers
  • Remove all letters that have poor distinction between upper and lower case values. The resulting strings don't look like English words and are easy to parse visually.  
• CharSet 16: 0123456789abcdef
  • Hexadecimal  
• CharSet 8: 01234567
  • Octal  
• CharSet 4: ATCG
  • DNA alphabet. No good reason; just wanted to get away from the obvious.  
• CharSet 2: 01
  • Binary

You may, of course, want to choose the characters used, which is covered next in Custom Characters.

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Custom Characters

Being able to easily generate random strings is great, but what if you want to specify your own characters. For example, suppose you want to visualize flipping a coin to produce entropy of 10 bits.

const { Entropy, charset2 } = require('entropy-string')

const entropy = new Entropy(charset2)
let flips = entropy.string(10)

flips: 1111001011

The resulting string of 0's and 1's doesn't look quite right. Perhaps you want to use the characters H and T instead.

entropy.useChars('HT')
flips = entropy.string(10)

flips: THHTHTTHHT

As another example, we saw in Character Sets the predefined hex characters for charset16 are lowercase. Suppose you like uppercase hexadecimal letters instead.

const { Entropy } = require('entropy-string')

const entropy = new Entropy('0123456789ABCDEF')
const string = entropy.string(48)

string: 08BB82C0056A

The Entropy constructor allows for three separate cases:

• No argument defaults to the charset32 characters.
• One of six predefined CharSets can be specified.
• A string representing the characters to use can be specified.

The last option above will throw an EntropyStringError if the characters string isn't appropriate for creating a CharSet.

const { Entropy } = require('entropy-string')

try {
  const entropy = new Entropy('123456')
}
catch(error) {
  console.log('Error: ' + error.message)
}

Invalid character count: must be one of 2,4,8,16,32,64

try {
  const entropy = new Entropy('01233210')
}
catch(error) {
  console.log(error.message)
}

Characters not unique

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Efficiency

To efficiently create random strings, EntropyString generates the necessary number of bytes needed for each string and uses those bytes in a bit shifting scheme to index into a character set. For example, consider generating strings from the charset32 character set. There are 32 characters in the set, so an index into an array of those characters would be in the range [0,31]. Generating a random string of charset32 characters is thus reduced to generating a random sequence of indices in the range [0,31].

To generate the indices, EntropyString slices just enough bits from the array of bytes to create each index. In the example at hand, 5 bits are needed to create an index in the range [0,31]. EntropyString processes the byte array 5 bits at a time to create the indices. The first index comes from the first 5 bits of the first byte, the second index comes from the last 3 bits of the first byte combined with the first 2 bits of the second byte, and so on as the byte array is systematically sliced to form indices into the character set. And since bit shifting and addition of byte values is really efficient, this scheme is quite fast.

The EntropyString scheme is also efficient with regard to the amount of randomness used. Consider the following common JavaScript solution to generating random strings. To generate a character, an index into the available characters is create using Math.random. The code looks something like:

const chars = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789"
let string = ""
for(let i = 0; i < length; i++) {
  string += chars.charAt(Math.floor(Math.random() * chars.length));
}

bl0mvxXAqXuz5R3N

There are two significant issues with this code. Math.random returns a random float value. At the very best this value has about 53-bits of entropy. Let's assume it's 52-bits for argument sake, i.e. Math.random generates 52 bits of randomness per call. That randomness is in turn used to create an index into the 62 chars, each which represents 5.95 bits of entropy. So if we're creating strings with length=16, the 16 calls generate a total of 16*52 = 816 bits of randomness which are used to inject a total of 95.2 bits of entropy (5.95/char) into string. That means 720 bits (88% of the total) of the generated randomness is simply wasted.

Compare that to the EntropyString scheme. For the example above, slicing off 5 bits at a time requires a total of 80 bits (10 bytes). Creating the same strings as above, EntropyString uses 80 bits of randomness per string with no wasted bits. In general, the EntropyString scheme can waste up to 7 bits per string, but that's the worst case scenario and that's per string, not per character!

const { Entropy } = require('entropy-string')

const entropy = new Entropy()
let string = entropy.string(80)

HFtgHQ9q9fH6B8HM

But there is an even bigger issue with the previous code from a security perspective. Math.random is not a cryptographically strong random number generator. Do not use Math.random to create strings used for security purposes! This highlights an important point. Strings are only capable of carrying information (entropy); it's the random bytes that actually provide the entropy itself. EntropyString automatically generates the necessary bytes needed to create cryptographically strong random strings using the crypto library.

However, if you don't need cryptographically strong random strings, you can request EntropyString use Math.random rather than the crypto library by using entropy.stringRandom:

string = entropy.stringRandom(80)

fdRp9Q3rTMF7TdFN

When using Math.random, the EntropyString scheme uses 48 of the 52(ish) bits of randomness from each call to Math.random. That's much more efficient than the previous code snippet but a bit less so than using bytes from crypto.

Fortunately you don't need to really understand how the bytes are efficiently sliced and diced to get the string. But you may want to provide your own Custom Bytes to create a string, which is the next topic.

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Custom Bytes

As described in Efficiency, EntropyString automatically generates random bytes using the crypto library. But you may have a need to provide your own bytes, say for deterministic testing or to use a specialized byte generator. The entropy.string function allows passing in your own bytes to create a string.

Suppose we want a string capable of 30 bits of entropy using 32 characters. We pass in 4 bytes to cover the 30 bits needed to generate six base 32 characters:

const { Entropy } = require('entropy-string')

const entropy = new Entropy()
const bytes = Buffer.from([250, 200, 150, 100])
let string = entropy.stringWithBytes(30, bytes)

Th7fjL

The bytes provided can come from any source. However, the number of bytes must be sufficient to generate the string as described in the Efficiency section. entropy.stringWithBytes throws an Error if the string cannot be formed from the passed bytes.

try {
  string = entropy.stringWithBytes(32, bytes)
}
catch(error) {
  console.log('  Error: ' + error.message)
}

error: Insufficient bytes: need 5 and got 4

Note the number of bytes needed is dependent on the number of characters in our set. In using a string to represent entropy, we can only have multiples of the bits of entropy per character used. So in the example above, to get at least 32 bits of entropy using a character set of 32 characters (5 bits per char), we'll need enough bytes to cover 35 bits, not 32, so an Error is thrown.

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Entropy Bits

Thus far we've avoided the mathematics behind the calculation of the entropy bits required to specify a risk that some number random strings will not have a repeat. As noted in the Overview, the posting Hash Collision Probabilities derives an expression, based on the well-known Birthday Problem, for calculating the probability of a collision in some number of hashes (denoted by k) using a perfect hash with an output of M bits:

There are two slight tweaks to this equation as compared to the one in the referenced posting. M is used for the total number of possible hashes and an equation is formed by explicitly specifying that the expression in the posting is approximately equal to 1/n.

More importantly, the above equation isn't in a form conducive to our entropy string needs. The equation was derived for a set number of possible hashes and yields a probability, which is fine for hash collisions but isn't quite right for calculating the bits of entropy needed for our random strings.

The first thing we'll change is to use M = 2^N, where N is the number of entropy bits. This simply states that the number of possible strings is equal to the number of possible values using N bits:

Now we massage the equation to represent N as a function of k and n:

The final line represents the number of entropy bits N as a function of the number of potential strings k and the risk of repeat of 1 in n, exactly what we want. Furthermore, the equation is in a form that avoids really large numbers in calculating N since we immediately take a logarithm of each large value k and n.

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Upgrading To Version 3

EntropyString version 3 does not introduce any new functionality. The sole purpose of the version 3 release is to simplify and tighten the API. Backward incompatible changes made in this effort necessitated a semantic major release.

The two major changes are:

• Replace class EntropyString.Random with class EntropyString.Entropy
  
• Replace all camelCase charSetNN with charsetNN
  

Change: EntropyString.Random -> EntropyString.Entropy

Change all instances of new Random() to new Entropy()

For example,

  const { Random } = require('entropy-string')
  const random = new Random()
  const string = random.sessionID()

becomes

  const { Entropy } = require('entropy-string')
  const random = new Entropy()
  const string = random.sessionID()

or

  const { Entropy } = require('entropy-string')
  const entropy = new Entropy()
  const string = entropy.sessionID()

Change: charSetNN -> charsetNN

Change all occurrences of charSetNN to charsetNN. charset is common enough in programming circles to negate the need for camelCase.

For example,

  const { Random, charSet64 } = require('entropy-string')
  const random = new Random(charSet64)
  const string = random.sessionID()

becomes

  const { Entropy, charset64 } = require('entropy-string')
  const entropy = new Entropy(charset64)
  const string = entropy.sessionID()

Other minor changes:

• Remove bitsWithRiskPower and bitsWithPowers from Entropy
• Move predefined CharSet declarations from CharSet to Entropy
• Entropy.bits is a class method of the new Entropy class

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TL;DR 2

Take Away

• Don't specify randomness using strings of length.
  • String length is a by-product, not a goal.
• Don't require truly uniqueness.
  • You'll do fine with probabilistically uniqueness.
• Probabilistic uniqueness involves specified risk.
  • Risk is specified as "1 in n chance of generating a repeat"
• Do specify bits of entropy.
  • Specified as the risk of repeat in a total number of strings
• Characters used are arbitrary.
• You need EntropyString.

Base 32 character string with a 1 in a million chance of a repeat a billion strings:

  const { Entropy } = require('entropy-string')
  
  const bits = Entropy.bits(1e6,1e9)
  const entropy = new Entropy()
  const string = entropy.string(bits)

LtH4p6rnRHT2bb2rf3

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