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comment Purpose of DES parity bits
Some of us lived through that history. That we can find documentation provides perspective.
comment Purpose of DES parity bits
Checking history this morning, the original DES patent in 1976 (US3,958,081) describes parity for external use. A 1981 Motorola patent (US4,262,358) describes an particular application of key parity testing per round, followed by an IBM patent (US5,432,848) in 1994. The latter reflect a time when the HW wasn't so dear in cost. Motorola fielded handheld secure radios where multiple key generators would have been cost and power prohibitive.
comment Purpose of DES parity bits
DES takes around 4700 NAND gates, it's a HW design from a time when a 1 MIPS machine was big iron. Using MSI TTL it could be implemented in an 8 x 10 inch printed circuit board. Adding 48 16 to 1 multiplexers to use static key storage would have tripled the size and power, easier to duplicate the entire thing and compare outputs or just test parity once a block. In today's SW crypto world the underlying HW reliability is better due to higher levels of integration and you can precalculate round keys and periodically test without interfering with traffic, having MIPS and memory to spare.
comment Purpose of DES parity bits
You'd also find in a hardware implementation the parity could be checked once every 16 rounds during operation. Because the C and D registers would shift a distance of 1 or 2 every round and the key wouldn't get loaded except when changed it'd be nice to know it's still intact over some long use interval.
comment Number of shifts in DES key schedule
The 16 values of the key schedule add up to 28, matching the length of C or D allowing cyclic operation. The program keytab referenced in the linked answer has a -c option that shows the number of key bits in common between rounds. Any two adjacent rounds have 40 key bits in common. Non-adjacent rounds have either 41, 42 or 43 key bits in common. You can modify the key schedule in keytab.c as long as the number of shifts add up to 28 and use the -c option to see what happens. (It alters the distribution slightly).
comment How is a per round key generated in DES algorithm?
keytab.c, keytab -s outputs key tables shown as CD reg bits shows the round keys, which have 24 of 28 bits derived independently from each of C and D via PC2 (Permuted Choice 2). Was written to replicate tables found in Metyas and Meyers Cryptography. See DES Key Schedule Algorithm
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).