C# Random Exploitation Library

This is an alternative, most mostly equivalent, re-implementation of C#'s Random::Next.

This works by keeping everything in equations of the form a * Seed + b mod p.

You can resolve these equations for any Seed to get the output of some (new Random(Seed).Next...).

You can do algebra on the equations to find other more complicated situations.

The equations can be copied to other languages easily. Just ensure you use 64 bit math. Using a 32 bit int will likely overflow and be in congruent mod 2**31 - 1.

Examples

Get the equation that will represent the first output of Random::Next for any Seed.

>>> from csharp_rand import csharp_rand
>>> cs = csharp_rand()
>>> first = cs.sample_equation(0)
>>> print(first)
rand = seed * 1121899819 + 1559595546 mod 2147483647

Then running .resolve(42) will correspond to the output of (new Random(42)).Next().

>>> first.resolve(42)
1434747710

Or you can use .invert() to go backwards, giving you the Seed.

>>> first.invert().resolve(1434747710)
42

More complicated, obtain the 726th output of Random from the 725th.

>>> late = 724 # 725th rand, zero indexed
>>> late_rand = cs.sample_equation(late)
>>> late_rand_plus = cs.sample_equation(late + 1)
>>> late_to_late_plus = late_rand_plus(late_rand.invert())
>>> # check for seed 42
>>> late_to_late_plus.resolve(late_rand.resolve(42)) == late_rand_plus.resolve((42))
True
>>> print(late_to_late_plus)
rand = seed * 1971396503 + 1990619591 mod 2147483647

So late_rand represents the output of calling .Next 725 times. Then late_rand_plus is 726. Since both of these have the same Seed in common, we can invert late_rand and compose with late_rand_plus to get the equation for going from the 725th .Next to 726th .Next.

We can check this by copying the late_to_late_plus and late_rand.invert() equations to a .NET playground.

using System;
					
public class Program
{

	// next two equations take from python csharp library
	private static int check(long seed) {
		long ret = (seed * 1971396503 + 1990619591) % 2147483647;
		return (int)ret;
	}

	private static int invert(long rand) {
		long ret = (rand * 1433598513 + 1157387419) % 2147483647;
		return (int)ret;
	}

	private static bool test(int Seed) {
		Console.WriteLine("Testing Seed {0}: ", Seed);
		var late = 724;
		var prng = new Random(Seed);
		for (int i = 0; i < late; i++) {
			prng.Next();
		}

		var first = prng.Next();
		var second = prng.Next();
		var c = check(first);

		Console.WriteLine("  Random[{0}]: {1}", late, first);
		Console.WriteLine("  Random[{0}]: {1}", late + 1, second);
		Console.WriteLine("  Computed:    {0}", c);
		Console.WriteLine("  Computed seed: {0}", invert(first));

		if (c == second) {
			Console.WriteLine("  Success");
			return true;
		}
		Console.WriteLine("  Failed");
		return false;
	}

	public static void Main() {
		for (int i = 278; i < 291; i++) {
			test(i);
		}
	}
}

Outputs:

Testing Seed 278: 
  Random[724]: 1558502570
  Random[725]: 827201365
  Computed:    827201365
  Computed seed: 278
  Success
Testing Seed 279: 
  Random[724]: 1583339083
  Random[725]: 1435417286
  Computed:    1435417286
  Computed seed: 279
  Success
...