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comment Why does DES implement so much Cross Wiring?
No. The DES standard is an interoperability standard as describe in the paper The DES Encryption Standard Past and Future, providing interoperability with a particular hardware implementation (seen in the two IBM DES patents). You could also note that prior to FIPS Pub 46-3 DES was only compliant when implemented in hardware. It's so cumbersome because it is defined 'independent of physical implementation'. See 1.1 Development of Security Standards in the paper.
comment DES hardware implementation of substitution lookup table [ ReWorked ]
What does this have to do with the Digital Encryption Standard?
comment P10 to P8 in S-DES
See SIMPLIFIED DES, William Stallings.
comment what is the current actual budget - as of 2015 - needed to build a DES breaker machine?
With a less than fully populated RIVYERA to hit 56 hours for half the key space, plus Non-Recurring Engineering costs you'd likely still be under $10K. Some of us might literally spend more time dealing with the RIVYERA API than the DES algorithm. It looks like under a man month for the properly skilled implementer with the Xilinx tools. (John Gilmore asked if I was interested in doing a DES Cracker ASIC in 1991, the barrier at the time the NRE costs for a silicon vendor).
comment Security of DES P_BOX
In ON THE DESIGN OF PERMUTATION P IN DES TYPE CRYPTOSYSTEMS You'll find reference to D. W. Davies, "Some Regular Properties of the Data Encryption Standard", also hinted in D.W. Davies book "Security for Computer Networks", 2nd, Hamiltonian cycles in the DES, P. 66. Also note other than E Perm bleed over the only way C key bits affect S Boxes 5-8 or D key bits affect S Boxes 1-4 outputs is through the P Permutation and successive rounds.
comment DES S-Box properties
Have you read coppersmith94.pdf? The criteria for (S-7) (your 1) is given in the section entitled Discussion of Criteria and puts an upper bound (on the probability of a linear approximation. (S-8) (your 2) is the three active S box case described there. You haven't cited references or specified the book.
comment How is the initial permutation of DES created?
You haven't describe the interface type for your DES function (e.g. array of bits, arrays of bytes, array of .., 64 bit value).