Rot13 for numbers

Question

EDIT: Now a Major Motion Blog Post at http://messymatters.com/sealedbids

The idea of rot13 is to obscure text, for example to prevent spoilers. It's not meant to be cryptographically secure but to simply make sure that only people who are sure they want to read it will read it.

I'd like to do something similar for numbers, for an application involving sealed bids. Roughly I want to send someone my number and trust them to pick their own number, uninfluenced by mine, but then they should be able to reveal mine (purely client-side) when they're ready. They should not require further input from me or any third party.

(Added: Note the assumption that the recipient is being trusted not to cheat.)

It's not as simple as rot13 because certain numbers, like 1 and 2, will recur often enough that you might remember that, say, 34.2 is really 1.

Here's what I'm looking for specifically:

A function seal() that maps a real number to a real number (or a string). It should not be deterministic -- seal(7) should not map to the same thing every time. But the corresponding function unseal() should be deterministic -- unseal(seal(x)) should equal x for all x. I don't want seal or unseal to call any webservices or even get the system time (because I don't want to assume synchronized clocks). (Added: It's fine to assume that all bids will be less than some maximum, known to everyone, say a million.)

Sanity check:

> seal(7)
482.2382   # some random-seeming number or string.
> seal(7)
71.9217    # a completely different random-seeming number or string.
> unseal(seal(7))
7          # we always recover the original number by unsealing.

Answer 1

You can pack your number as a 4 byte float together with another random float into a double and send that. The client then just has to pick up the first four bytes. In python:

import struct, random
def seal(f):
   return struct.unpack("d",struct.pack("ff", f, random.random() ))[0]
def unseal(f):
   return struct.unpack("ff",struct.pack("d", f))[0]

>>> unseal( seal( 3))
3.0
>>> seal(3)
4.4533985422978706e-009
>>> seal(3)
9.0767582382536571e-010