Pseudo encrypt constrained to an arbitrary range

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pseudo_encrypt_constrained_to_an_arbitrary_range

Works with PostgreSQL

Any version

Written in

PL/pgSQL

Depends on

Nothing

pseudo_encrypt outputs random-looking unique values in the 32-bit range (-2,147,483,648 (-231) through 2,147,483,647 (231 - 1))

To constrain values to a smaller domain [0..N] where N is for instance a power of 10, the Cycle-Walking Cipher technique can be used on top of the Feistel Network.

A variant of pseudo_encrypt() is necessary, with the following changes implemented:

  • Reduce the block size to the nearest even power of 2 greater than the range size. For example for the range [0..10,000,000], the nearest is 224 (16,777,216). Shifts and masks will be adjusted in the code for 2 half-blocks of 12 bits each.
  • Suppress the self-inverse property, so that a value wouldn't cycle back immediately to itself. It's done by inverting the blocks when they're recombined at the end of the loop.
  • Add an outer loop that applies the cipher until the result belongs to the expected range. This is done below in a separate function for clarity.

Sample source code for a 24-bit range:

CREATE FUNCTION pseudo_encrypt_24(VALUE int) returns int AS $$
DECLARE
l1 int;
l2 int;
r1 int;
r2 int;
i int:=0;
BEGIN
 l1:= (VALUE >> 12) & (4096-1);
 r1:= VALUE & (4096-1);
 WHILE i < 3 LOOP
   l2 := r1;
   r2 := l1 # ((((1366 * r1 + 150889) % 714025) / 714025.0) * (4096-1))::int;
   l1 := l2;
   r1 := r2;
   i := i + 1;
 END LOOP;
 RETURN ((l1 << 12) + r1);
END;
$$ LANGUAGE plpgsql strict immutable;
 
CREATE FUNCTION bounded_pseudo_encrypt(VALUE int, MAX int) returns int AS $$
BEGIN
  LOOP
    VALUE := pseudo_encrypt_24(VALUE);
    EXIT WHEN VALUE <= MAX;
  END LOOP;
  RETURN VALUE;
END
$$ LANGUAGE plpgsql strict immutable;

Sample output:

=> select i,bounded_pseudo_encrypt(i, 10000000) as rnd from generate_series(0,10) as x(i);

 i  |   rnd   
----+---------
  0 | 7388415
  1 | 4878904
  2 | 3247539
  3 | 7670618
  4 | 6551624
  5 | 1212319
  6 | 6156301
  7 |  893851
  8 |  337577
  9 |    4289
 10 |  316941

Query proving that the output is unique, and that the set of values covers exactly the intended range (might take a few minutes to run)

=> select count(distinct rnd) from
   (select bounded_pseudo_encrypt(i, 10000000) as rnd
       from generate_series(0,10000000) as x(i)
   ) as list
 where rnd between 0 and 10000000;

  count   
----------
 10000001
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