Pearson-Like Hash S-Box Finder (Useful for making minimal hash maps for keyword identification in lexers)

pearson_finder.py

#!/usr/bin/env python3
"""
The MIT License (MIT)

Copyright (c) 2025 martandrMC

Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:

The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
"""

"""
This is a revision of my previous finder written in Java:
https://gist.github.com/martandrMC/ab888dbeb265b340b5ab1285ed1dd972
This one's written in Python and uses Z3 to solve the S-Box.
This time it can handle about 60 keywords before it becomes
unreasonably slow, which is just enough to handle the C keyword set.

This version does not actually qualify as a Pearson Hash due to
the non-injective nature of the generated S-Box. However it still
fulfills its hereby given purpose.
"""

import z3

from typing import List

def pearson_hash(sbox: List[int], source: str) -> int:
	result: int = 0
	for char in source:
		result = sbox[result ^ ord(char)]
	return result

def find_sbox(keys: List[str]) -> List[int]:
	if(len(keys) > 256): return None

	solver = z3.Solver()
	sbox = z3.Array('sbox', z3.BitVecSort(8), z3.BitVecSort(8))
	hashes = z3.Array('hashes', z3.BitVecSort(8), z3.BitVecSort(8))

	for i in range(len(keys)):
		for j in range(i + 1, len(keys)):
			solver.add(hashes[i] != hashes[j])

	# Injective S-Box Constraint (Makes it go MUCH slower)
	# for i in range(256):
	# 	for j in range(i + 1, 256):
	# 		solver.add(sbox[i] != sbox[j])

	for i,k in enumerate(keys):
		solver.add(pearson_hash(sbox, k) == hashes[i])

	if solver.check() != z3.sat: return None
	model = solver.model()

	sbox_result = [0] * 256
	for i in range(256):
		sbox_result[i] = model.eval(sbox[i]).as_long()
	return sbox_result

def main():
	keys = []
	while True:
		try: keys.append(input())
		except EOFError: break

	sbox = find_sbox(keys)
	if sbox == None: return

	kmap = [-1] * 256
	for i,k in enumerate(keys):
		kmap[pearson_hash(sbox, k)] = i

	for i in range(16):
		for j in range(16):
			item = sbox[16*i + j]
			print(f'0x{item:02x}', end=',')
			if j < 15: print(' ', end='')
		print('')
	
	print('')

	for i in range(16):
		for j in range(16):
			item = kmap[16*i + j]
			print(f'{item:3d}', end=',')
			if j < 15: print(' ', end='')
		print('')

if __name__ == "__main__": main()