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The expansion function is interpreted as for the initial and final permutations. Note that some bits from the input are duplicated at the output; e.g. the fifth bit of the input is duplicated in both the sixth and eighth bit of the output. Thus, the 32-bit half-block is expanded to 48 bits.
The Data Encryption Standard (DES / ˌ d iː ˌ iː ˈ ɛ s, d ɛ z /) is a symmetric-key algorithm for the encryption of digital data. Although its short key length of 56 bits makes it too insecure for modern applications, it has been highly influential in the advancement of cryptography.
The identity is its minimum, and the permutation formed by reversing the identity is its maximum. If a permutation were assigned to each inversion set using the element-based definition, the resulting order of permutations would be that of a Cayley graph, where an edge corresponds to the swapping of two elements on consecutive places. This ...
In other words, a derangement is a permutation that has no fixed points. The number of derangements of a set of size n is known as the subfactorial of n or the n th derangement number or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include !n, D n, d n, or n¡ . [a] [1] [2]
Linear approximations for S-boxes then must be combined with the cipher's other actions, such as permutation and key mixing, to arrive at linear approximations for the entire cipher. The piling-up lemma is a useful tool for this combination step. There are also techniques for iteratively improving linear approximations (Matsui 1994).
The block cipher E is a pseudo-random permutation (PRP) if no adversary has an advantage significantly greater than 0, given specified restrictions on q and the adversary's running time. If in Step 2 above adversaries have the option of learning f −1 ( X ) instead of f ( X ) (but still have only small advantages) then E is a strong PRP (SPRP).
The variant described by Sorkin (1984) has 16 Feistel rounds, like DES, but no initial or final permutations.The key and block sizes are both 128 bits. The Feistel function operates on a 64-bit half-block of data, together with a 64-bit subkey and 8 "interchange control bits" (ICBs).
In mathematics, the Robinson–Schensted correspondence is a bijective correspondence between permutations and pairs of standard Young tableaux of the same shape. It has various descriptions, all of which are of algorithmic nature, it has many remarkable properties, and it has applications in combinatorics and other areas such as representation theory.