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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.
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).