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Grill (cryptology)
The grill method (), in cryptology, was a method used chiefly early on, before the advent of the cyclometer, by the mathematician-cryptologists of the Polish Cipher Bureau (''Biuro Szyfrów'') in decrypting German Enigma machine ciphers. The Enigma rotor cipher machine changes plaintext characters into cipher text using a different permutation for each character, and so implements a polyalphabetic substitution cipher. Background The German navy started using Enigma machines in 1926; it was called ''Funkschlüssel C'' ("Radio cipher C"). By 15 July 1928, the German Army (''Reichswehr'') had introduced their own version of the Enigma—the ''Enigma G''; a revised ''Enigma I'' (with plugboard) appeared in June 1930. The Enigma I used by the German military in the 1930s was a 3-rotor machine. Initially, there were only three rotors labeled ''I'', ''II'', and ''III'', but they could be arranged in any order when placed in the machine. Polish cryptologist Marian Rejewski identif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptology
Cryptography, or cryptology (from "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 synonymous with encryption, converting re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bomba (cryptography)
The ''bomba'', or ''bomba kryptologiczna'' (Polish for "bomb" or "cryptologic bomb"), was a special-purpose machine designed around October 1938 by Polish Cipher Bureau cryptologist Marian Rejewski to break German Enigma-machine ciphers. Etymology How the machine came to be called a "bomb" has been an object of fascination and speculation. One theory, most likely apocryphal, originated with Polish engineer and army officer Tadeusz Lisicki (who knew Rejewski and his colleague Henryk Zygalski in wartime Britain but was never associated with the Cipher Bureau). He claimed that Jerzy Różycki (the youngest of the three Enigma cryptologists, and who had died in a Mediterranean passenger-ship sinking in January 1942) named the "bomb" after an ice-cream dessert of that name. This story seems implausible, since Lisicki had not known Różycki. Rejewski himself stated that the device had been dubbed a "bomb" "for lack of a better idea". Perhaps the most credible explanation is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Cryptography
Cryptography, the use of codes and ciphers, began thousands of years ago. Until recent decades, it has been the story of what might be called classical cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids. In the early 20th century, the invention of complex mechanical and electromechanical machines, such as the Enigma rotor machine, provided more sophisticated and efficient means of encryption; and the subsequent introduction of electronics and computing has allowed elaborate schemes of still greater complexity, most of which are entirely unsuited to pen and paper. The development of cryptography has been paralleled by the development of cryptanalysis — the "breaking" of codes and ciphers. The discovery and application, early on, of frequency analysis to the reading of encrypted communications has, on occasion, altered the course of history. Thus the Zimmermann Telegram triggered the United States' entry into World War ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Matrix
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column with all other entries 0. An permutation matrix can represent a permutation of elements. Pre- multiplying an -row matrix by a permutation matrix , forming , results in permuting the rows of , while post-multiplying an -column matrix , forming , permutes the columns of . Every permutation matrix ''P'' is orthogonal, with its inverse equal to its transpose: P^=P^\mathsf. Indeed, permutation matrices can be characterized as the orthogonal matrices whose entries are all non-negative. The two permutation/matrix correspondences There are two natural one-to-one correspondences between permutations and permutation matrices, one of which works along the rows of the matrix, the other along its columns. Here is an example, starting with a permutation in two-line form at the upper left: :\begin \pi\colon\begin1&2&3&4\\3&2&4&1\e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sicherheitsdienst
' (, "Security Service"), full title ' ("Security Service of the ''Reichsführer-SS''"), or SD, was the intelligence agency of the Schutzstaffel, SS and the Nazi Party in Nazi Germany. Established in 1931, the SD was the first Nazi intelligence organization and the Gestapo (formed in 1933) was considered its sister organization through the integration of SS members and operational procedures. The SD was administered as an independent SS office between 1933 and 1939. That year, the SD was transferred over to the Reich Security Main Office (''Reichssicherheitshauptamt''; RSHA), as one of its seven departments. Its first director, Reinhard Heydrich, intended for the SD to bring every single individual within the Third Reich's reach under "continuous supervision". Following Germany's defeat in World War II, the tribunal at the Nuremberg trials officially declared that the SD was a criminal organisation, along with the rest of Heydrich's RSHA (including the Gestapo) both individually ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combination
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a ''k''-combination of a set ''S'' is a subset of ''k'' distinct elements of ''S''. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not matter.) If the set has ''n'' elements, the number of ''k''-combinations, denoted by C(n,k) or C^n_k, is equal to the binomial coefficient \binom nk = \frac, which can be written using factorials as \textstyle\frac whenever k\leq n, and which is zero when k>n. This formula can be derived from the fact that each ''k''-combination of a set ''S'' of ''n'' members has k! permu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clock (cryptography)
In cryptography, the clock was a method devised by Polish mathematician-cryptologist Jerzy Różycki, at the Polish General Staff's Cipher Bureau, to facilitate decrypting German Enigma ciphers. The method determined the rightmost rotor in the German Enigma by exploiting the different turnover positions. For the Poles, learning the rightmost rotor reduced the rotor-order search space by a factor of 3 (the number of rotors). The British improved the method, and it allowed them to use their limited number of bombes more effectively (the British confronted 5 to 8 rotors). Method This method sometimes made it possible to determine which of the Enigma machine's rotors was at the far right, that is, in the position where the rotor always revolved at every depression of a key. The clock method was developed by Jerzy Różycki during 1933–1935. Marian Rejewski's grill method could determine the right-hand rotor, but that involved trying each possible rotor permutation (there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered to be the father of theoretical computer science. Born in London, Turing was raised in southern England. He graduated from University of Cambridge, King's College, Cambridge, and in 1938, earned a doctorate degree from Princeton University. During World War II, Turing worked for the Government Code and Cypher School at Bletchley Park, Britain's codebreaking centre that produced Ultra (cryptography), Ultra intelligence. He led Hut 8, the section responsible for German naval cryptanalysis. Turing devised techniques for speeding the breaking of Germ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first meaning is the six permutations (orderings) of the set : written as tuples, they are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Anagrams of a word whose letters are all different are also permutations: the letters are already ordered in the original word, and the anagram reorders them. The study of permutations of finite sets is an important topic in combinatorics and group theory. Permutations are used in almost every branch of mathematics and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of distinct objects is factorial, us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field complex analysis, and the study of permutation groups in abstract algebra. Cauchy also contributed to a number of topics in mathematical physics, notably continuum mechanics. A profound mathematician, Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated: : "More concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy)." Cauchy was a prolific worker; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and mathematical physics. Biography Youth and education Cauchy was the son of Lou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transposition (mathematics)
In mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has ''k'' elements, it may be called a ''k''-cycle. Some authors widen this definition to include permutations with fixed points in addition to at most one non-trivial cycle. In Permutation#Cycle notation, cycle notation, cyclic permutations are denoted by the list of their elements enclosed with parentheses, in the order to which they are permuted. For example, the permutation (1 3 2 4) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 is a 4-cycle, and the permutation (1 3 2)(4) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 is considered a 3-cycle by some authors. On the other hand, the permutation (1 3)(2 4) that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs and . For the wider definition of a cyclic permutation, allowi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germanic Umlaut
The Germanic umlaut (sometimes called i-umlaut or i-mutation) is a type of linguistic umlaut (linguistics), umlaut in which a back vowel changes to the associated front vowel (fronting (phonology), fronting) or a front vowel becomes closer to (raising (phonetics), raising) when the following syllable contains , , or . It took place separately in various Germanic languages starting around 450 or 500 Common Era, CE and affected all of the early languages except Gothic language, Gothic. An example of the resulting vowel alternation is the English plural ''foot ~ feet'' (from Proto-Germanic , pl. ). Germanic umlaut, as covered in this article, does not include other historical vowel phenomena that operated in the history of the Germanic languages such as Germanic a-mutation and the various language-specific processes of u-mutation (other), u-mutation, nor the earlier Indo-European ablaut (''vowel gradation''), which is observable in the conjugation of Germanic strong ver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
