/EntropyString-Swift

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

Primary LanguageSwiftMIT LicenseMIT

EntropyString for Swift

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

Build Status   Carthage   CocoaPods - EntropyString   License: MIT

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Installation

Carthage

  1. Add the project to your Cartfile.

    github "EntropyString/EntropyString-Swift.git"

  2. Run carthage update and follow the Carthage getting started steps.

  3. Import module EntropyString

    import EntropyString

CocoaPods

  1. Add the project to your Podfile.

    use_frameworks!
pod 'EntropyString', '~> 1.0.0'

  2. Run pod install and open the .xcworkspace file to launch Xcode.

  3. Import module EntropyString

    import EntropyString

Swift Package Manager

  1. Add the project to your Package.swift.

    import PackageDescription

let package = Package(
    name: "YourProject",
    dependencies: [
        .Package(url: "https://github.com/EntropyString/EntropyString-Swift.git",
                 majorVersion: 1)
    ]
)

  2. Import module EntropyString

    import EntropyString

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The remainder of this README is included in the project as a Swift playground.

TL;DR

import EntropyString

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

var random = Random()
var bits = Entropy.bits(for: 1.0e6, risk: 1.0e9)
var string = random.string(bits: bits)

2tF6bMNPqQ82Qj

EntropyString uses predefined charset32 characters by default (reference Character Sets). To get a random hexadecimal string with the same entropy bits as above (see Real Need for description of what entropy bits represents):

random.use(.charset16)
string = random.string(bits: bits)

a946ff97a1c4e64e79

Custom characters may be specified. Using uppercase hexadecimal characters:

try! random.use("0123456789ABCDEF")
string = random.string(bits: bits)

78E3ACABE544EBA7DF

Convenience functions exists for a variety of scenarios. For example, to create OWASP session ID:

string = random.sessionID()

CC287C99158BF152DF98AF36D5E92AE3

Or a 256 bit token using RFC 4648 file system and URL safe characters:

string = random.token(.charSet64)

X2AZRHuNN3mFUhsYzHSE_r2SeZJ_9uqdw-j9zvPqU2O

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Overview

EntropyString provides easy creation of randomly generated strings of specific entropy using various character sets. Such strings are needed when generating, for example, random IDs and you don't want the overkill of a GUID, or for ensuring that some number of items have unique identifiers.

A key concern when generating such strings is that they be unique. To truly guarantee uniqueness 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 all strings is often too onerous and a different tack is needed.

A common strategy is to replace the guaranteed uniqueness with a weaker but often sufficient 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". This strategy requires much less overhead, but 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 requires some 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). Happily, you can use EntropyString without a deep understanding of these topics.

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

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Real Need

Let's start by reflecting on a common statement of need for developers, who might say:

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 the 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 some potential 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:

  • 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 strict 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 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 directly, 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 by generating 5 IDs:

import EntropyString

let random = Random(.charSet16)
let bits = Entropy.bits(for: 10000, risk: 1.0e6)
var strings = [String]()
for i in 0 ..< 5 {
  let string = random.string(bits: bits)
  strings.append(string)
}
print("Strings: \(strings)")

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

To generate the IDs, we first use

let bits = Entropy.bits(for: 10000, risk: 1.0e6)

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

let string = random.string(bits: bits)

to actually generate the random strings of the specified entropy using hexadecimal (charSet16) characters. 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.

Finally, 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 Random().

import EntropyString

let random = Random()
var bits = Entropy.bits(for: 10000, risk: 1.0e6)
var string = random.string(bits: bits, using: .charSet32)

print("String: \(string)\n")

String: PmgMJrdp9h

We're using the same 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. EntropyString.smallID yields strings that have a 1 in a million chance of repeat in 30 strings.

string = random.smallID()

print("String: \(string)\n")

String: ThfLbm

Using the same Random instance, we can switch to the default charSet4 characters:

random.use(charSet: .charSet64)
string = random.smallID()
print("String: \(string)\n")

String: CCCCTCAGGCATAGG

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 strings repeat. Let's see, our risk (trillion) is 10 to the 12th and our total (10 billion) is 10 to the 10th, so:

random.use(.charSet32)
bits = Entropy.bits(for: 1.0e10, risk: 1.0e12)
string = random.string(bits: bits)

String: F78PmfGRNfJrhHGTqpt6Hn

Finally, let say we're generating session IDs. We're not 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 needs to be 128 bits (since we read on the OWASP web site that session IDs should be 128 bits).

string = random.sessionID(.charSet64)

String: b0Gnh6H5cKCjWrCLwKoeuN

Using 64 characters, our string length is 22 characters. That's actually 22*6 = 132 bits, so we've got our OWASP requirement covered! 😌

Also note that we covered our need using strings that are only 22 characters in length. So long to using GUID strings which only carry 122 bits of entropy (commonly used version 4) and use string representations that are 36 characters long (hex with dashes).

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Character Sets

As we've seen in the previous sections, EntropyString provides predefined characters for each of the supported character sets. Let's see what's under the hood. The available CharSets are .charSet64, .charSet32, .charSet16, .charSet8, .charSet4 and .charSet2.

import EntropyString

print("CharSet 64: \(RandomString.characters(for: .charSet64))\n")
print("CharSet 32: \(RandomString.characters(for: .charSet32))\n")
print("CharSet 16: \(RandomString.characters(for: .charSet16))\n")
print("CharSet  8: \(RandomString.characters(for: .charSet8))\n")
print("CharSet  4: \(RandomString.characters(for: .charSet4))\n")
print("CharSet  2: \(RandomString.characters(for: .charSet2))\n")

The 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 10 bits of entropy.

import EntropyString

let random = Random(.charSet2)
var flips = random.string(bits: 10)

print("flips: \(flips)\n")

flips: 0101001110

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.

try! random.use("HT")
flips = random.string(bits: 10)

print("flips: \(flips)\n")

flips: HTTTHHTTHH

As another example, we saw in Character Sets the predefined hex characters for charSet16 are lowercase. Suppose you like uppercase hexadecimal letters instead.

try! random.use("0123456789ABCDEF")
let hex = random.string(bits: 48)

print("hex: \(hex)\n")

hex: 4D20D9AA862C

The Random 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.

do {
  try random.use("abcdefg")
}
catch {
  print(error)
}

invalidCharCount

do {
  try random.use("01233210")
}
catch {
  print(error)
}

charsNotUnique

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Efficiency

To efficiently create random strings, EntropyString generates the necessary number of random bytes needed for each string and uses those bytes in a bit shifting scheme to index into a character set. For example, to generate strings from the 32 characters in the charSet32 character set, each index needs to 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 random 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 bytes 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 bytes are 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 Swift solution to generating random strings. To generated a character, an index into the available characters is create using arc4random_uniform. The code looks something like:

for _ in 0 ..< len {
  let offset = Int(arc4random_uniform(charCount))
  let index = chars.index(chars.startIndex, offsetBy: offset)
  let char = chars[index]
  string += String(char)
}

In the code above, arc4random_uniform generates 32 bits of randomness per call, returned as an UInt32. The returned value is used to create index. Suppose we're creating strings with len = 16 and charCount = 32. Generating each string character consumes 32 bits of randomness while only injecting 5 bits (log2(32)) of entropy into the resulting random string. The resulting string has an information carrying capacity of 16 * 5 = 80 bits, so creating each string requires a total of 512 bits of randomness while only actually carrying 80 bits of that entropy forward in the string itself. That means 432 bits (84% 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!

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 know that Secure Bytes are used, and that's the next topic.

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Secure Bytes

As described in Efficiency, EntropyString uses an underlying array of bytes to generate strings. The entropy of the resulting strings is, of course, directly related to the randomness of the bytes used. That's an important point. Strings are only capable of carrying information (entropy); the random bytes actually provide the entropy itself.

EntropyString automatically generates the necessary number of bytes needed to create a random string. On Apple OSes, EntropyString uses either SecRandomCopyBytes or arc4random_buf, both of which are cryptographically secure random number generators. SecRandomCopyBytes is the stronger of the two, but can fail if the system entropy pool lacks sufficient randomness. Rather than propagate that failure, if SecRandomCopyBytes fails EntropyString falls back and uses arc4random_buf to generate the bytes. Though not as strong, arc4random_buf does not fail.

You may, of course, want feedback as to when or if SecRandomCopyBytes fails. Random.string(bits:using:secRand) provides the inout parameter secRand that acts as a flag should a SecRandomCopyBytes call fail.

On Linux OSes, EntropyString always uses arc4random_buf. The secRand parameter is ignored.

import EntropyString

let random = Random()
var secRand = true
random.string(bits: 20, secRand: &secRand)

secRand: true

If SecRandomCopyBytes is used, the secRand parameter will remain true; otherwise it will be set to false.

You can also pass in secRand as false, in which case the entropy call will not attempt to use SecRandomCopyBytes and will use arc4random_buf instead.

secRand = false
random.string(bits: 20, secRand: &secRand)

Rather than have EntropyString generate bytes automatically, you can provide your own Custom Bytes to create a string, which is the next topic.

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Custom Bytes

As described in Secure Bytes, EntropyString automatically generates random bytes using either SecRandomCopyBuf or arc4random_buf. These functions are fine, but you may have a need to provide your own bytes for deterministic testing or to use a specialized byte generator. The function random.string(bits:using) allows specifying 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):

import EntropyString

let random = Random()
let bytes: [UInt8] = [250, 200, 150, 100]
let string = try! random.string(bits: 30, using: bytes)

print("String: \(string)\n")

string: Th7fjL

The bytes provided can come from any source. However, if the number of bytes is insufficient to generate the string as described in the Efficiency section, an EntropyStringError.tooFewBytes is thrown.

do {
  try random.string(bits: 32, using: bytes)
}
catch {
  print(error)
}

error: tooFewBytes

Note the number of bytes needed is dependent on the number of characters in the character set. For a string representation of entropy, we can only have multiples of the entropy bits per character. In the example above, each character represents 5 bits of entropy. So we can't get exactly 32 bits and we round up by the bits per character to a total 35 bits. We need 5 bytes (40 bits), not 4 (32 bits).

CharSet.bytes_needed(bits) can be used to determine the number of bytes needed to cover a specified amount of entropy for a given character set.

let bytes_needed = random.charSet.bytesNeeded(bits: 32)

print("\nBytes needed: \(bytes_needed)\n")

Bytes needed: 5

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TL;DR 2

Take Away

  • You don't need random strings of length L.
    • String length is a by-product, not a goal.
  • You don't need truly unique strings.
    • Uniqueness is too onerous. You'll do fine with probabilistically unique strings.
  • Probabilistic uniqueness involves measured risk.
    • Risk is measured as "1 in n chance of generating a repeat"
    • Bits of entropy gives you that measure.
  • You need to a total of N strings with a risk 1/n of repeat.
    • The characters are arbitrary.
  • You need EntropyString.
A million potential strings with a 1 billion chance of a repeat:
  import EntropyString

  let random = Random()
  let bits = Entropy.bits(for: 1.0e6, risk: 1.0e9)
  let string = random.string(bits: bits)

DdHrT2NdrHf8tM

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