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05_6bit_APN_Permutation_Decomposition

README.md

Chapter 5. Decomposition of the 6-bit APN Permutation

This folder contains several scripts for Chapter 5, which is about decomposition, analysis and generalization attempts of the 6-bit APN permutation. The code extensively uses the cryptools, a SageMath-based package of cryptanalytic tools.

Currently, the decomposition process is documented:

  1. 1info.py: information gathering about the S-Box, aligning columns in the LAT.
  2. 2tu.py: performing the TU-decomposition and finding relations between T and U.
  3. 3decomposeT.py: decomposing the T mini-block cipher.
  4. 4decompose_full.py: final decomposition.

Bonus: a very compact code for generating a 6-bit APN involution (in the CCZ-equivalence class of the analyzed APN permutation): (python2 or python3)

mul2 = lambda a: (a<<1) ^ (127 * (a//32))
s = list(range(64))
for a, b in (3, 54), (5, 57), (7, 41), (9, 58):
    for i in range(7):
        s[a], s[b] = b, a
        a, b = mul2(a), mul2(b)
print(s)