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The Magic Words Are Squeamish Ossifrage
"The Magic Words are Squeamish Ossifrage" was the solution to a challenge ciphertext posed by the inventors of the RSA cipher in 1977. The problem appeared in Martin Gardner's ''Mathematical Games column'' in the August 1977 issue of ''Scientific American''. It was solved in 1993–94 by a large, joint computer project co-ordinated by Derek Atkins, Michael Graff, Arjen Lenstra and Paul Leyland. More than 600 volunteers contributed CPU time from about 1,600 machines (two of which were fax machines) over six months. The coordination was done via the Internet and was one of the first such projects. ''Ossifrage'' ('bone-breaker', from Latin) is an older name for the bearded vulture, a scavenger famous for dropping animal bones and live tortoises on top of rocks to crack them open. The 1993–94 effort began the tradition of using the words "squeamish ossifrage" in cryptanalytic challenges. The difficulty of breaking the RSA cipher—recovering a plaintext message given a ciphertext a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ciphertext
In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher to decrypt it. This process prevents the loss of sensitive information via hacking. Decryption, the inverse of encryption, is the process of turning ciphertext into readable plaintext. Ciphertext is not to be confused with codetext because the latter is a result of a code, not a cipher. Conceptual underpinnings Let m\! be the plaintext message that Alice wants to secretly transmit to Bob and let E_k\! be the encryption cipher, where _k\! is a cryptographic key. Alice must first transform the plaintext into ciphertext, c\!, in order to securely send the message to Bob, as follows: : c = E_k(m). \! In a symmetric-key system, Bob knows Alice's encryption key. Once the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decryption
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decipher a ciphertext back to plaintext and access the original information. Encryption does not itself prevent interference but denies the intelligible content to a would-be interceptor. For technical reasons, an encryption scheme usually uses a pseudo-random encryption key generated by an algorithm. It is possible to decrypt the message without possessing the key but, for a well-designed encryption scheme, considerable computational resources and skills are required. An authorized recipient can easily decrypt the message with the key provided by the originator to recipients but not to unauthorized users. Historically, various forms of encryption have been used to aid in cryptography. Early encryption techniques were often used in military ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Cryptography
Cryptography, the use of codes and ciphers to protect secrets, 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' en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA Numbers
In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. The challenge was ended in 2007. RSA Laboratories (which is an acronym of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size, up to US$200,000 (and prizes up to $20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come. , the smallest 23 of the 54 listed numbers have been factored. While the RSA challenge officially ended in 2007, people ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributed
Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a variable **Cumulative distribution function, in which the probability of being no greater than a particular value is a function of that value *Frequency distribution, a list of the values recorded in a sample *Inner distribution, and outer distribution, in coding theory *Distribution (differential geometry), a subset of the tangent bundle of a manifold *Distributed parameter system, systems that have an infinite-dimensional state-space *Distribution of terms, a situation in which all members of a category are accounted for *Distributivity, a property of binary operations that generalises the distributive law from elementary algebra * Distribution (number theory) *Distribution problems, a common type of problems in combinatorics where the goal i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brute Force Attack
In cryptography, a brute-force attack consists of an attacker submitting many passwords or passphrases with the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct one is found. Alternatively, the attacker can attempt to guess the key which is typically created from the password using a key derivation function. This is known as an exhaustive key search. A brute-force attack is a cryptanalytic attack that can, in theory, be used to attempt to decrypt any encrypted data (except for data encrypted in an information-theoretically secure manner). Such an attack might be used when it is not possible to take advantage of other weaknesses in an encryption system (if any exist) that would make the task easier. When password-guessing, this method is very fast when used to check all short passwords, but for longer passwords other methods such as the dictionary attack are used because a brute-force search ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Software Foundation
The Free Software Foundation (FSF) is a 501(c)#501(c)(3), 501(c)(3) non-profit organization founded by Richard Stallman on October 4, 1985, to support the free software movement, with the organization's preference for software being distributed under copyleft ("share alike") terms, such as with its own GNU General Public License. The FSF was incorporated in Boston, Massachusetts, United States, US, where it is also based. From its founding until the mid-1990s, FSF's funds were mostly used to employ software developers to write free software for the GNU Project. Since the mid-1990s, the FSF's employees and volunteers have mostly worked on legal and structural issues for the free software movement and the free software community. Consistent with its goals, the FSF aims to use only free software on its own computers. History The Free Software Foundation was founded in 1985 as a Nonprofit corporation, non-profit corporation supporting free software development. It continued existi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Field Sieve
In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than . Heuristically, its complexity for factoring an integer (consisting of bits) is of the form :\exp\left( \left(\sqrt + o(1)\right)(\ln n)^(\ln \ln n)^\right) =L_n\left .html"_;"title="frac,\sqrt[3">frac,\sqrt[3right/math> (in_L-notation.html" ;"title="">frac,\sqrt[3right.html" ;"title=".html" ;"title="frac,\sqrt[3">frac,\sqrt[3right">.html" ;"title="frac,\sqrt[3">frac,\sqrt[3right/math> (in L-notation">">frac,\sqrt[3right.html" ;"title=".html" ;"title="frac,\sqrt[3">frac,\sqrt[3right">.html" ;"title="frac,\sqrt[3">frac,\sqrt[3right/math> (in L-notation), where is the natural logarithm. It is a generalization of the special number field sieve: while the latter can only factor numbers of a certain special form, the general number field sieve can factor any number apart from prime powers (which are trivial to factor by taking roots). The pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Pomerance
Carl Bernard Pomerance (born 1944 in Joplin, Missouri) is an American number theorist. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number has at least seven distinct prime factors. He joined the faculty at the University of Georgia, becoming full professor in 1982. He subsequently worked at Lucent Technologies for a number of years, and then became a distinguished Professor at Dartmouth College. Contributions He has over 120 publications, including co-authorship with Richard Crandall of ''Prime numbers: a computational perspective'' (Springer-Verlag, first edition 2001, second edition 2005), and with Paul Erdős. He is the inventor of one of the integer factorization methods, the quadratic sieve algorithm, which was used in 1994 for the factorization of RSA-129. He is also one of the discoverers of the Adleman–Pomerance–Rumely primality test. Awards and honors He has won ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Sieve
The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is considerably simpler than the number field sieve. It is a general-purpose factorization algorithm, meaning that its running time depends solely on the size of the integer to be factored, and not on special structure or properties. It was invented by Carl Pomerance in 1981 as an improvement to Schroeppel's linear sieve. Basic aim The algorithm attempts to set up a congruence of squares modulo ''n'' (the integer to be factorized), which often leads to a factorization of ''n''. The algorithm works in two phases: the ''data collection'' phase, where it collects information that may lead to a congruence of squares; and the ''data processing'' phase, where it puts all the data it has collected into a matrix and solves it to obtain a congruence of square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thorsten Kleinjung
Thorsten (Thorstein, Torstein, Torsten) is a Scandinavian given name. The Old Norse name was ''Þórsteinn''. It is a compound of the theonym ''Þór'' (''Thor'') and ''steinn'' "stone", which became ''Thor'' and ''sten'' in Old Danish and Old Swedish. The name is one of a group of Old Norse names containing the theonym ''Thor'', besides other such as ''Þórarin, Þórhall, Þórkell, Þórfinnr, Þórvald, Þórvarðr, Þórolf'', most of which, however, do not survive as modern names given with any frequency. The name is attested in medieval Iceland, e.g. Þorsteinn rauður Ólafsson (c. 850 – 880), Þōrsteinn Eirīkssonr (late 10th century), and in literature such as '' Draumr Þorsteins Síðu-Hallssonar''. The Old English equivalent of the Scandinavian and Norman name is ''Thurstan'', attested after the Norman conquest of England in the 11th century as the name of a medieval archbishop of York (died 1140), of an abbot of Pershore (1080s) and of an abbot of Glast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
