# Pseudo encrypt constrained to an arbitrary range

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
```