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Equation System Generator for DES
I’ve uploaded an equation system generator for the “Data Encryption Standard” (DES) hoping to spare others the tedious work of writing one. As far as I know only equation systems but no flexible generators are floating around the net. I implemented three S-Box representations (following Courtois’ and Bard’s paper Algebraic Cryptanalysis of DES): fully cubic equations, quadratic equations with added variables (Matthew Kwan’s bitslice representation) and the former with pre-computed Gröbner bases.
# loading the file
sage: attach des.py
# two rounds only, see DES? for help on the constructor
sage: des = DES(Nr=2)
# default S-Box representation is opns_gb
sage: F,s = des.polynomial_system()
Pre-computing Groebner bases for S-Boxes, this might take a moment.
sage: %time gb = F.groebner_basis()
CPU times: user 15.39 s, sys: 0.03 s, total: 15.42 s
Wall time: 15.78 s
# verify correctness
sage: gb[:14]
[k55, k54, k52, k51 + 1, k50 + 1, k49, k48 + 1, k47 + 1, k46 + 1, k45 + 1, k44 + 1, k43, k42, k41 + 1]
sage: s[des.k[55]]
0
sage: s[des.k[51]]
1
Let me know if you run into any trouble.
Upcoming Workshops
I’m going to attend Sage Days 10 in Nancy, France (October 10-15, 2008). At SD10 I’ll give a contributed talk about matrix multiplication over $\mathbb{F}_2$, i.e. the M4RI library. I’m also going to attend the Second Workshop on Mathematical Cryptology in Santander, Spain (October 23-25, 2008).
