Non-repetitive random seek in a range Algorithm

Question

I'm looking for an efficient algorithm that produces random values within a range, without repetitions.

In pseudo-code: (in class Rand)

  Rand(long from, long to) {
    this.from = from;
    this.to = to;
    // ...
  }

  long getNumber() {

    // returns a random number in the [from, to] range
    //  which has never been returned before
  }

Usage:

  Rand r = new Rand(1, 100000000);

  long x = r.getNumber();
  long y = r.getNumber();
  ...

The numbers returned from r.getNumber() should always be different from the ones previously returned.
Of course, if to - from + 1 numbers were returned, the algorithm should start again (or fall in error - not important anyway).

Note that the range may be very large, and thus a randomly arranged array (containing initially [from, to] numbers) is likely to overflow the memory.

Answer 1

A cypher is a one-to-one mapping, otherwise it couldn't be decrypted. Hence, any block cypher will map the numbers 0, 1, 2, 3, 4, 5, ... to different n-bit numbers, where n is the cypher's block size in bits.

It is relatively easy to put together a simple 4-round Feistel cypher with whatever (even) block size you want. With only four rounds it would be fast but insecure. Alternatively use the Hasty Pudding cypher which can have pretty much any block size you want.

Whatever cypher you use, just encrypt the numbers 0, 1, 2, ... and look at the output block. You can throw away any results that are outside your required range and all results are guaranteed unique.