Mersenne primeIn mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p. The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, .
Distributed computingA distributed system is a system whose components are located on different networked computers, which communicate and coordinate their actions by passing messages to one another. Distributed computing is a field of computer science that studies distributed systems. The components of a distributed system interact with one another in order to achieve a common goal. Three significant challenges of distributed systems are: maintaining concurrency of components, overcoming the lack of a global clock, and managing the independent failure of components.
Elliptic curve primalityIn mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods in primality proving. It is an idea put forward by Shafi Goldwasser and Joe Kilian in 1986 and turned into an algorithm by A. O. L. Atkin the same year. The algorithm was altered and improved by several collaborators subsequently, and notably by Atkin and de, in 1993. The concept of using elliptic curves in factorization had been developed by H. W.
Extended Euclidean algorithmIn arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that This is a certifying algorithm, because the gcd is the only number that can simultaneously satisfy this equation and divide the inputs. It allows one to compute also, with almost no extra cost, the quotients of a and b by their greatest common divisor.
OpenSSLOpenSSL is a software library for applications that provide secure communications over computer networks against eavesdropping, and identify the party at the other end. It is widely used by Internet servers, including the majority of HTTPS websites. OpenSSL contains an open-source implementation of the SSL and TLS protocols. The core library, written in the C programming language, implements basic cryptographic functions and provides various utility functions.
Word (computer architecture)In computing, a word is the natural unit of data used by a particular processor design. A word is a fixed-sized datum handled as a unit by the instruction set or the hardware of the processor. The number of bits or digits in a word (the word size, word width, or word length) is an important characteristic of any specific processor design or computer architecture.
4-bit computing4-bit computing is the use of computer architectures in which integers and other data units are 4 bits wide. 4-bit central processing unit (CPU) and arithmetic logic unit (ALU) architectures are those that are based on registers or data buses of that size. Memory addresses (and thus address buses) for 4-bit CPUs are generally much larger than 4-bit (since only 16 memory locations would be very restrictive), such as 12-bit or more, while they could in theory be 8-bit. A group of four bits is also called a nibble and has 24 = 16 possible values.
Indeterminacy in concurrent computationIndeterminacy in concurrent computation is concerned with the effects of indeterminacy in concurrent computation. Computation is an area in which indeterminacy is becoming increasingly important because of the massive increase in concurrency due to networking and the advent of many-core computer architectures. These computer systems make use of arbiters which gives rise to indeterminacy. Patrick Hayes [1973] argued that the "usual sharp distinction that is made between the processes of computation and deduction, is misleading".
Safe and Sophie Germain primesIn number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem. One attempt by Germain to prove Fermat’s Last Theorem was to let p be a prime number of the form 8k + 7 and to let n = p – 1.
Regular primeIn number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli numbers. The first few regular odd primes are: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, ... . In 1850, Kummer proved that Fermat's Last Theorem is true for a prime exponent p if p is regular.
