Generate secure, random, uniform integers, compensating for modulo bias
JavaScript
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LICENSE.md
README.md
bigint.js
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statistic-test.js
verify-modulo-reduction.js
verify-readle.js

README.md

secure-random-uniform

Generate secure, random, uniform integers, compensating for modulo bias

Usage

var secureRandom = require('secure-random-uniform')

// Numbers from [0, 2000)
secureRandom(2000)

// Numbers from [100, 110)
secureRandom(10) + 100

// Numbers from [-10, 10]
secureRandom(21) - 10

BigInt support (Experimental!)

var secureRandom = require('secure-random-uniform/bigint')

// Numbers from [0, 2^64)
secureRandom(2n ** 64n)

// Numbers from [0, googol)
secureRandom(10n ** 100n)

API

var num = secureRandomUniform(limit)

Returns a number from the uniform distribution [0, limit) (limit exclusive). Note that limit must not be larger than 2^53 - 1 (Number.MAX_SAFE_INTEGER).

Background

Modulo reduction: Bytes to integers

A naive implementation might look like:

function insecureRandom (limit) {
  return secureRandomSource() % limit
}

However this will only yield a uniform distribution if limit is a divisor of whatever is the maximum value of secureRandomSource(). Consider limit = 3 and the maximum value returned by secureRandomSource() being 5. Then in the long run the frequency of numbers returned will be [0 = 2/5, 1 = 2/5, 2 = 1/5], causing the distribution to be skewed (ie. not uniform). This is called "Modulo Bias".

This module borrows from arc4random_uniform and keeps generating a new random number until it hits a range that's congruent to limit. This is not as bad as it sounds. The worst case is if limit ≈ (2^48 - 1) / 2, in which case it will have a ~ 0.5 chance of doing a redraw. The number of redraws required can be modelled by as 0.5^(redraws) which quickly converges towards zero. In practise only one draw is required on average.

See verify-modulo-reduction.js for a deterministic test of the algorithm

Random bytes to integers

The next issue is transforming random bytes into unsigned numbers. We can efficiently transform bytes into signed 32-bit integers in JS with:

(byte[3] << 24) | (byte[2] << 16) | (byte[1] << 8) | (byte[0])

To make the number unsigned we can do a zero-fill right shift, which will cause the sign bit to become 0:

((byte[3] << 24) | (byte[2] << 16) | (byte[1] << 8) | (byte[0])) >>> 0

To go beyond 32-bit integers, to the maximum of 53-bit integers representable in Javascript Numbers (IEEE 754), we can construct the remaining 21 bits and move them up using a floating point multiplication.

((((buf[6] & 0b00011111) << 16) | (buf[5] << 8) | (buf[4])) >>> 0) * 0x100000000
+ (((byte[3] << 24) | (byte[2] << 16) | (byte[1] << 8) | (byte[0])) >>> 0)

Note that the bitwise operations have been wrapped in parenthesis, otherwise the add and multiplication operation will become 32-bit operations, reducing the number modulo 2^32

See verify-readle.js for verification against a known implementation of converting bytes to unsigned integers.

License

ISC