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A P-box is a permutation of all the bits: it takes the outputs of all the S-boxes of one round, permutes the bits, and feeds them into the S-boxes of the next round. A good P-box has the property that the output bits of any S-box are distributed to as many S-box inputs as possible.
In cryptography, a permutation box (or P-box) is a method of bit-shuffling used to permute or transpose bits across S-boxes inputs, creating diffusion while transposing. [1]An example of a 64-bit "expansion" P-box which spreads the input S-boxes to as many output S-boxes as possible.
Mathematically, an S-box is a nonlinear [1] vectorial Boolean function. [2] In general, an S-box takes some number of input bits, m, and transforms them into some number of output bits, n, where n is not necessarily equal to m. [3] An m×n S-box can be implemented as a lookup table with 2 m words of n bits each.
The Rijndael S-box can be replaced in the Rijndael cipher, [1] which defeats the suspicion of a backdoor built into the cipher that exploits a static S-box. The authors claim that the Rijndael cipher structure is likely to provide enough resistance against differential and linear cryptanalysis even if an S-box with "average" correlation ...
• The compression P-box changes the 56 bits key to 48 bits key, which is used as a key for the corresponding round. The table is row major way, means, Actual Bit position = Substitute with the bit of row * 8 + column.
Confusion inevitably involves some diffusion, [6] so a design with a very wide-input S-box can provide the necessary diffusion properties, [citation needed] but will be very costly in implementation. Therefore, the practical ciphers utilize relatively small S-boxes, operating on small groups of bits ("bundles" [7]).
For transformation involving reasonable number of n message symbols, both of the foregoing cipher systems (the S-box and P-box) are by themselves wanting. Shannon suggested using a combination of S-box and P-box transformation—a product cipher. The combination could yield a cipher system more powerful than either one alone.
A p-box can also be understood as bounds on the x-value at any particular probability level. In the example, the 95th percentile is sure to be between 9 and 16. If the left and right bounds of a p-box are sure to enclose the unknown distribution, the bounds are said to be rigorous, or absolute.