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Higher-order Differential Cryptanalysis
In cryptography, higher-order differential cryptanalysis is a generalization of differential cryptanalysis, an attack used against block ciphers. While in standard differential cryptanalysis the difference between only two texts is used, higher-order differential cryptanalysis studies the propagation of a set of differences between a larger set of texts. Xuejia Lai, in 1994, laid the groundwork by showing that differentials are a special case of the more general case of higher order derivates. Lars Knudsen, in the same year, was able to show how the concept of higher order derivatives can be used to mount attacks on block ciphers. These attacks can be superior to standard differential cryptanalysis. Higher-order differential cryptanalysis has notably been used to break the KN-Cipher, a cipher which had previously been proved to be immune against standard differential cryptanalysis. Higher-order derivatives A block cipher which maps n-bit strings to n-bit strings can, for a fixed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing 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 (data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications. Cryptography prior to the modern age was effectively synony ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Bitwise XOR
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least sign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Daniel J
Daniel is a masculine given name and a surname of Hebrew origin. It means "God is my judge"Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 68. (cf. Gabriel—"God is my strength"), and derives from two early biblical figures, primary among them Daniel from the Book of Daniel. It is a common given name for males, and is also used as a surname. It is also the basis for various derived given names and surnames. Background The name evolved into over 100 different spellings in countries around the world. Nicknames ( Dan, Danny) are common in both English and Hebrew; "Dan" may also be a complete given name rather than a nickname. The name "Daniil" (Даниил) is common in Russia. Feminine versions ( Danielle, Danièle, Daniela, Daniella, Dani, Danitza) are prevalent as well. It has been particularly well-used in Ireland. The Dutch names "Daan" and "Daniël" are also variations of Daniel. A related surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Cube Attack
The cube attack is a method of cryptanalysis applicable to a wide variety of symmetric-key algorithms, published by Itai Dinur and Adi Shamir in a September 2008 preprint. Attack A revised version of this preprint was placed online in January 2009, and the paper has also been accepted for presentation at Eurocrypt 2009. A cipher is vulnerable if an output bit can be represented as a sufficiently low degree polynomial over GF(2) of key and input bits; in particular, this describes many stream ciphers based on LFSRs. DES and AES are believed to be immune to this attack. It works by summing an output bit value for all possible values of a subset of public input bits, chosen such that the resulting sum is a linear combination of secret bits; repeated application of this technique gives a set of linear relations between secret bits that can be solved to discover these bits. The authors show that if the cipher resembles a random polynomial of sufficiently low degree then such set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Cipher
In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with " code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography. Codes generally substitute different length strings of characters in the output, while ciphers generally substitute the same number of characters as are input. There are exceptions and some cipher systems may use slightly more, or fewer, characters when output versus the number that were input. Codes operated by substituting according to a large codebook which linked a random string of characters or numbers to a word or phrase. For example, "UQJHSE" could be the code for "Proceed to the follow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Degree Of A Polynomial
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer. For a univariate polynomial, the degree of the polynomial is simply the highest exponent occurring in the polynomial. The term order has been used as a synonym of ''degree'' but, nowadays, may refer to several other concepts (see order of a polynomial (other)). For example, the polynomial 7x^2y^3 + 4x - 9, which can also be written as 7x^2y^3 + 4x^1y^0 - 9x^0y^0, has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term. To determine the degree of a polynomial that is not in standard form, such as (x+1)^2 - (x-1)^2, one can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Product Rule
In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange's notation as (u \cdot v)' = u ' \cdot v + u \cdot v' or in Leibniz's notation as \frac (u\cdot v) = \frac \cdot v + u \cdot \frac. The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts. Discovery Discovery of this rule is credited to Gottfried Leibniz, who demonstrated it using differentials. (However, J. M. Child, a translator of Leibniz's papers, argues that it is due to Isaac Barrow.) Here is Leibniz's argument: Let ''u''(''x'') and ''v''(''x'') be two differentiable functions of ''x''. Then the differential of ''uv'' is : \begin d(u\cdot v) & = (u + du)\cdot (v + dv) - u\cdot v \\ & = u\cdot dv + v\cdot du + du\cdot dv. \end Since the term ''du''·''dv'' is "negligi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Sum Rule In Differentiation
This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Elementary rules of differentiation Unless otherwise stated, all functions are functions of real numbers (R) that return real values; although more generally, the formulae below apply wherever they are well defined — including the case of complex numbers (C). Constant term rule For any value of c, where c \in \mathbb, if f(x) is the constant function given by f(x) = c, then \frac = 0. Proof Let c \in \mathbb and f(x) = c. By the definition of the derivative, :\begin f'(x) &= \lim_\frac \\ &= \lim_ \frac \\ &= \lim_ \frac \\ &= \lim_ 0 \\ &= 0 \end This shows that the derivative of any constant function is 0. Differentiation is linear For any functions f and g and any real numbers a and b, the derivative of the function h(x) = af(x) + bg(x) with respect to x is: h'(x) = a f'(x) + b g'(x). In Leibniz's notation this is written as: \frac = a\frac + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the deriv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Thomas Jakobsen
Thomas Jakobsen is a mathematician, cryptographer, and computer programmer, formerly an assistant professor at the Technical University of Denmark (DTU) and head of research and development at IO Interactive. His notable work includes designing the physics engine and 3-D pathfinder algorithms for '' Hitman: Codename 47'', and the cryptanalysis of a number of block cipher In cryptography, a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called ''blocks''. Block ciphers are specified cryptographic primitive, elementary components in the design of many cryptographic protocols and ...s. Jakobsen earned an M.Sc. in engineering and Ph.D. in mathematics, both from DTU. External links * Living people Modern cryptographers Danish mathematicians Video game programmers Danish computer scientists Year of birth missing (living people) {{crypto-bio-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 much m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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KN-Cipher
In cryptography, KN-Cipher is a block cipher created by Kaisa Nyberg and Lars Knudsen in 1995. One of the first ciphers designed to be provably secure against ordinary differential cryptanalysis, KN-Cipher was later broken using higher order differential cryptanalysis. Presented as "a prototype...compatible with DES", the algorithm has a 64-bit block size and a 6-round Feistel network structure. The round function is based on the cube operation in the finite field GF(233). The designers did not specify any key schedule In cryptography, the so-called product ciphers are a certain kind of cipher, where the (de-)ciphering of data is typically done as an iteration of ''rounds''. The setup for each round is generally the same, except for round-specific fixed valu ... for the cipher; they state, "All round keys should be independent, therefore we need at least 198 key bits." Cryptanalysis Jakobsen & Knudsen's higher order differential cryptanalysis breaks KN-Cipher with only 5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |