pseudo_encrypt() function in plpgsql that takes bigint

4294967295 must be used as the bitmask to select 32 bits (instead of 4294967296).
That’s the reason why currently you get the same value for different inputs.

I’d also suggest using bigint for the types of l2 and r2, they shouldn’t really differ from r1 and l1

And, for better randomness, use a much higher multiplier in the PRNG function to get intermediate block that really occupy 32 bits, like 32767*32767 instead of 32767.

The complete modified version:

CREATE OR REPLACE FUNCTION pseudo_encrypt(VALUE bigint) returns bigint AS $$
DECLARE
l1 bigint;
l2 bigint;
r1 bigint;
r2 bigint;
i int:=0;
BEGIN
    l1:= (VALUE >> 32) & 4294967295::bigint;
    r1:= VALUE & 4294967295;
    WHILE i < 3 LOOP
        l2 := r1;
        r2 := l1 # ((((1366.0 * r1 + 150889) % 714025) / 714025.0) * 32767*32767)::int;
        l1 := l2;
        r1 := r2;
        i := i + 1;
    END LOOP;
RETURN ((l1::bigint << 32) + r1);
END;
$$ LANGUAGE plpgsql strict immutable;

First results:

select x,pseudo_encrypt(x::bigint) from generate_series (1, 10) as x;
 x  |   pseudo_encrypt    
----+---------------------
  1 | 3898573529235304961
  2 | 2034171750778085465
  3 |  169769968641019729
  4 | 2925594765163772086
  5 | 1061193016228543981
  6 | 3808195743949274374
  7 | 1943793931158625313
  8 |   88214277952430814
  9 | 2835217030863818694
 10 |  970815170807835400
(10 rows)

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