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Branch Number
In cryptography, the branch number is a numerical value that characterizes the amount of diffusion introduced by a vectorial Boolean function that maps an input vector to output vector F(a). For the (usual) case of a linear the value of the ''differential branch number'' is produced by: # applying nonzero values of (i.e., values that have at least one non-zero component of the vector) to the input of ; # calculating for each input value the Hamming weight W (number of nonzero components), and adding weights W(a) and W(F(a)) together; # selecting the smallest combined weight across for all nonzero input values: B_d(F) = \underset (W(a) + W(F(a))). If both and F(a) have components, the result is obviously limited on the high side by the value s+1 (this "perfect" result is achieved when any single nonzero component in makes all components of F(a) to be non-zero). A high branch number suggests higher resistance to the differential cryptanalysis Differential cryptanalysis is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), adversarial behavior. More generally, cryptography is about constructing and analyzing Communication protocol, protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security (confidentiality, data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, Smart card#EMV, chip-based payment cards, digital currencies, password, computer passwords, and military communications. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion (cryptography)
In cryptography, confusion and diffusion are two properties of a secure cipher identified by Claude Shannon in his 1945 classified report ''A Mathematical Theory of Cryptography''. 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 statistics by spreading it over a larger area of ciphertext. Although ciphers can be confusion-only (substitution cipher, one-time pad) or diffusion-only ( transposition cipher), any "reasonable" block cipher uses both confusion and diffusion. These concepts are also important in the design of cryptographic hash functions, and pseudorandom number generators, where decorrelation of the generated values is the main feature. Diffusion (and its avalanche effect) is also ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vectorial Boolean Function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\^k \to \, where \ is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0, the function is a constant element of \. A Boolean function with multiple outputs, f:\^k \to \^m with m>1 is a vectorial or ''vector-valued'' Boolean function (an S-box in symmetric cryptography). There are 2^ different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k-ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k, and two propositional formulas a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Boolean Function
In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a ''polynomial''. An example of a linear function is the function defined by f(x)=(ax,bx) that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables X, Y and Z is aX+bY+cZ+d. Linearity of a mapping is closely related to '' proportionality''. Examples in physics include the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships, such as between velocity and kinetic energy, are ''nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. Linearity of a polynomial means that its degree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Weight
The Hamming weight of a string (computer science), string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a given set of bits, this is the number of bits set to 1, or the digit sum of the Binary numeral system, binary representation of a given number and the Taxicab geometry, ''ℓ''₁ norm of a bit vector. In this binary case, it is also called the population count, popcount, sideways sum, or bit summation. History and usage The Hamming weight is named after the American mathematician Richard Hamming, although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James Whitbread Lee Glaisher, James W. L. Glaisher to give a formula for Gould's sequence, the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Cryptanalysis
Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in information input can affect the resultant difference at the output. In the case of a block cipher, it refers to a set of techniques for tracing differences through the network of transformation, discovering where the cipher exhibits non-random behavior, and exploiting such properties to recover the secret key (cryptography key). History The discovery of differential cryptanalysis is generally attributed to Eli Biham and Adi Shamir in the late 1980s, who published a number of attacks against various block ciphers and hash functions, including a theoretical weakness in the Data Encryption Standard (DES). It was noted by Biham and Shamir that DES was surprisingly resistant to differential cryptanalysis, but small modifications to the algorithm would make it m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joan Daemen
Joan Daemen (; born 1965) is a Belgians, Belgian cryptographer who is currently professor of digital security (symmetric encryption) at Radboud University. He co-designed with Vincent Rijmen the Rijndael cipher, which was selected as the Advanced Encryption Standard (AES) in 2001. More recently, he co-designed the Keccak cryptographic hash, which was NIST hash function competition, selected as the new SHA-3 hash by NIST in October 2012. He has also designed or co-designed the MMB (cipher), MMB, Square (cipher), Square, SHARK (cipher), SHARK, NOEKEON, 3-Way, and BaseKing block ciphers. In 2017 he won the Levchin Prize for Real World Cryptography "for the development of AES and SHA3". He describes his development of encryption algorithms as creating the bricks which are needed to build the secure foundations online. In 1988, Daemen graduated in electro-mechanical engineering at the Katholieke Universiteit Leuven. He subsequently joined the COSIC research group, and has worked on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vincent Rijmen
Vincent Rijmen (; born 16 October 1970) is a Belgium, Belgian cryptographer and one of the two designers of the Rijndael, the Advanced Encryption Standard. Rijmen is also the co-designer of the WHIRLPOOL cryptographic hash function, and the block ciphers Anubis (cipher), Anubis, KHAZAD, Square (cipher), Square, NOEKEON and SHARK. In 1993, Rijmen obtained a degree in electronics engineering at the Katholieke Universiteit Leuven. Afterwards, he was a PhD student at the ESAT/COSIC lab of the K.U.Leuven. In 1997, Rijmen finished his doctoral dissertation titled ''Cryptanalysis and design of iterated block ciphers''. After his PhD he did postdoctoral work at the COSIC lab, on several occasions collaborating with Joan Daemen. One of their joint projects resulted in the algorithm Rijndael, which in October 2000 was selected by the National Institute for Standards and Technology (NIST) to become the Advanced Encryption Standard (AES). Since 1 August 2001, Rijmen has been working as chie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exclusive-or
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR ''excludes'' that case. Some informal ways of describing XOR are "one or the other but not both", "either one or the other", and "A or B, but not A and B". It is symbolized by the prefix operator J Translated as and by the infix operators XOR (, , or ), EOR, EXOR, \dot, \overline, \underline, , \oplus, \nleftrightarrow, and \not\equiv. Definition The truth table of A\nleftrightarrow B shows that it outputs true whenever the inputs differ: Equivalences, elimination, and introduction Exclusive disjunction essentially me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Approximation Table
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\^k \to \, where \ is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0, the function is a constant element of \. A Boolean function with multiple outputs, f:\^k \to \^m with m>1 is a vectorial or ''vector-valued'' Boolean function (an S-box in symmetric cryptography). There are 2^ different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k-ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k, and two propositional formulas are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SageMath
SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, group theory, differentiable manifolds, numerical analysis, number theory, calculus, and statistics. The first version of SageMath was released on 24 February 2005 as free and open-source software under the terms of the GNU General Public License version 2, with the initial goals of creating an "open source alternative to Magma, Maple, Mathematica, and MATLAB". The originator and leader of the SageMath project, William Stein, was a mathematician at the University of Washington. SageMath uses a syntax resembling Python's, supporting procedural, functional, and object-oriented constructs. Development Stein realized when designing Sage that there were many open-source mathematics software packages already written in different languages, namely C, C++, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
