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A Boolean function with multiple outputs, : {,} {,} with > is a vectorial or vector-valued Boolean function (an S-box in symmetric cryptography). [ 6 ] There are 2 2 k {\displaystyle 2^{2^{k}}} different Boolean functions with k {\displaystyle k} arguments; equal to the number of different truth tables with 2 k {\displaystyle 2^{k}} entries.
In 2001, Barak et al., showing that black-box obfuscation is impossible, also proposed the idea of an indistinguishability obfuscator, and constructed an inefficient one. [8] [7] [2] Although this notion seemed relatively weak, Goldwasser and Rothblum (2007) showed that an efficient indistinguishability obfuscator would be a best-possible obfuscator, and any best-possible obfuscator would be ...
Balanced Boolean functions are used in cryptography, where being balanced is one of "the most important criteria for cryptographically strong Boolean functions". [3] If a function is not balanced, it will have a statistical bias, making it subject to cryptanalysis such as the correlation attack.
In cryptography, an S-box (substitution-box) is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the key and the ciphertext, thus ensuring Shannon's property of confusion. Mathematically, an S-box is a nonlinear [1] vectorial Boolean function ...
In cryptography a universal one-way hash function (UOWHF, often pronounced "woof") is a type of universal hash function of particular importance to cryptography. UOWHFs are proposed as an alternative to collision-resistant hash functions (CRHFs). CRHFs have a strong collision-resistance property: that it is hard, given randomly chosen hash ...
"For fundamental contributions to the design and analysis of Boolean functions for cryptographic applications, and for sustained educational leadership." Benny Pinkas: 2022 "For impactful research in the theory and practice of secure multi-party computation, sustained educational leadership, and service to the IACR." Yael Tauman Kalai: 2022
In cryptography, a boolean function is said to be complete if the value of each output bit depends on all input bits. This is a desirable property to have in an encryption cipher, so that if one bit of the input is changed, every bit of the output has an average of 50% probability of changing. The easiest way to show why this is good is the ...
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 .