/Integral-Bel-T-256

Primary LanguagePython

Integral Attack on Bel-T-256

File description

  1. Bel-T.py: The python script used to generate a MILP model for n rounds of the Bel-T block cipher, then search for an integral distinguisher based on the bit-based division property using the Gurobi optimizer.
  2. helpFunction.py: The python module that contains the MILP models describing the division trail through COPY, XOR, AND, modular addition, modular addition with a constant, and modular subtraction.

Dependencies

The only dependency is the Gurobi optimizer which can be found here.

Usage

python Bel-T.py <number of rounds> <Input division property>

Example 1

Create a MILP model for 2-round Bel-T and then search for an integral distinguisher based on the following input division property 00000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000011111111000000000000000000000000. Note: This is "IC1" integral distinguisher in the paper.

  • Command:
python Bel-T.py 2 "00000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000011111111000000000000000000000000"
  • Output:
Integral Distinguisher Found!

# of rounds: 2 , activebits:9 , Input DP: 00000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000011111111000000000000000000000000
balanced bits: 5 [91, 92, 93, 94, 95]
Time used = 43.373281002 Seconds

This output means that the integral distinguisher for 2-round Bel-T and the above-mentioned input division property exists, and the bits 91, 92, 93, 94, and 95 (counted from the most significant bits) are balanced. This distinguisher needs 29 chosen plaintexts.

Example 2

Create a MILP model for 2-round Bel-T and then search for an integral distinguisher based on the following input division property 01111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000000000000000000000000000000000000000

  • Command:
python Bel-T.py 2 "01111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000000000000000000000000000000000000000"
  • Output:
Integral Distinguisher do NOT exist

Time used = 82.1842508316 Seconds

This output means that there is no integral distinguisher for 2-round Bel-T and the above-mentioned input division property.