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In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
The functions studied are often, but not always, Boolean-valued, making them Boolean functions. The area has found many applications in combinatorics , social choice theory , random graphs , and theoretical computer science, especially in hardness of approximation , property testing , and PAC learning .
Siegenthaler showed that the correlation immunity m of a Boolean function of algebraic degree d of n variables satisfies m + d ≤ n; for a given set of input variables, this means that a high algebraic degree will restrict the maximum possible correlation immunity. Furthermore, if the function is balanced then m + d ≤ n − 1. [1]
Garbled circuit is a cryptographic protocol that enables two-party secure computation in which two mistrusting parties can jointly evaluate a function over their private inputs without the presence of a trusted third party. In the garbled circuit protocol, the function has to be described as a Boolean circuit.
These properties, when present, work together to thwart the application of statistics, and other methods of cryptanalysis. Confusion in a symmetric cipher is obscuring the local correlation between the input ( plaintext ), and output ( ciphertext ) by varying the application of the key to the data, while diffusion is hiding the plaintext ...
In cryptography, a block cipher is a deterministic algorithm that operates on fixed-length groups of bits, called blocks.Block ciphers are the elementary building blocks of many cryptographic protocols.
In cryptography, the avalanche effect is the desirable property of cryptographic algorithms, typically block ciphers [1] and cryptographic hash functions, wherein if an input is changed slightly (for example, flipping a single bit), the output changes significantly (e.g., half the output bits flip).
The following formula shows that a 4-ary function is bent when its nonlinearity is 6: = = In the mathematical field of combinatorics, a bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables.