I’ve been hacking on an old game I wrote for the school paper I founded: Hangman. (Code: https://github.com/fadend/hangman.) One feature I like: the ability to create your own games with a shareable link. Here’s one for you: https://revfad.com/hangman/?w=JVFUVAT+LBH+N+JBAQRESHY+QNL.
Since I didn’t want the URL parameter to give away the answer, I have the game run the letters through rot13. This has the flaw though that the same letter always gets the same mapping, giving a little bit too much away. Probably just making the offset increment per index or even just alternating per index would have been enough, but I got curious about what pseudorandom number generator I might use instead to choose the offsets.
This led me to George Marsaglia‘s Xorshift and his 2003 paper introducing it: Xorshift RNGs. The paper lists 81 triples of constants a, b, c plus 8 variations on XOR + shift operations to get to the next output.
Here’s a little program to visualize the output: https://revfad.com/xorshiftfun/. (Code: https://github.com/fadend/xorshiftfun.)
One surprising thing: at least as I’ve tried to implement it in JavaScript, the following update steps seem to only yield outputs covering half of the possible space:
y^=y>>a; y^=y<<b; y^=y>>c;
y^=y>>c; y^=y<<b; y^=y>>a;
y^=y<<a; y^=y<<c; y^=y>>b;
y^=y<<c; y^=y<<a; y^=y>>b;
You can see this visually in the output, e.g.:
Not sure if I’ll get to investigating this more deeply since I’ve got some other higher priority things to look at, but I’m a little curious what’s going wrong.
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