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MASH-1
For a cryptographic hash function (a mathematical algorithm), a MASH-1 (Modular Arithmetic Secure Hash) is a hash function based on modular arithmetic. History Despite many proposals, few hash functions based on modular arithmetic have withstood attack, and most that have tend to be relatively inefficient. MASH-1 evolved from a long line of related proposals successively broken and repaired. Standard Committee Draft ISO/IEC 10118-4 (Nov 95) Description MASH-1 involves use of an RSA-like modulus N, whose bitlength affects the security. N is a product of two prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...s and should be difficult to factor, and for N of unknown factorization, the security is based in part on the difficulty of extracting modular roots. Let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptographic Hash Function
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output result ( hash value) for a random input string ("message") is 2^ (like for any good hash), so the hash value can be used as a representative of the message; * finding an input string that matches a given hash value (a ''pre-image'') is unfeasible, unless the value is selected from a known pre-calculated dictionary ("rainbow table"). The ''resistance'' to such search is quantified as security strength, a cryptographic hash with n bits of hash value is expected to have a ''preimage resistance'' strength of n bits. A ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of finding a second message that matches the given hash value when one message is already known; * finding any pair of different me ... [...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 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 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 can be expressed within a finite amount of spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a '' hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys. Use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book '' Disquisitiones Arithmeticae'', published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in , but clocks "wrap around" every 12 hours. Because the hour number starts over at zero when it reaches 12, this is arithmetic ''modulo'' 12. In terms of the definition below, 15 is ''congruent'' to 3 modulo 12, so "15:00" on a 24-hour clock is displayed "3:00" on a 12-hour clock. Congruence Given an integer , called a modulus, two integers and are said to be congruent modulo , if is a divisor of their difference (that is, if there is an integer such that ). Congruence modu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA (algorithm)
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ) (the British signals intelligence agency) by the English mathematician Clifford Cocks. That system was declassified in 1997. In a public-key cryptosystem, the encryption key is public and distinct from the decryption key, which is kept secret (private). An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone, via the public key, but can only be decoded by someone who knows the prime numbers. The security of RSA relies on the practical difficulty of factoring the produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which alw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorization
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''factors'', usually smaller or simpler objects of the same kind. For example, is a factorization of the integer , and is a factorization of the polynomial . Factorization is not usually considered meaningful within number systems possessing division, such as the real or complex numbers, since any x can be trivially written as (xy)\times(1/y) whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by ancient Greek mathematicians in the case of integers. They proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bitwise Operation
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Menezes
Alfred Menezes is co-author of several books on cryptography, including the ''Handbook of Applied Cryptography'', and is a professor of mathematics at the University of Waterloo in Canada."Alfred Menezes: Mini-biography" company website Education Alfred Menezes' family is from , a state in western India, but he was born in and grew up in |
Scott Vanstone
Scott A. Vanstone was a mathematician and cryptographer in the University of Waterloo Faculty of Mathematics. He was a member of the school's Centre for Applied Cryptographic Research, and was also a founder of the cybersecurity company Certicom. He received his PhD in 1974 at the University of Waterloo, and for about a decade worked principally in combinatorial design theory, finite geometry, and finite fields. In the 1980s he started working in cryptography. An early result of Vanstone (joint with Ian Blake, R. Fuji-Hara, and Ron Mullin) was an improved algorithm for computing discrete logarithms in binary fields, which inspired Don Coppersmith to develop his famous exp(n^) algorithm (where n is the degree of the field). Vanstone was one of the first to see the commercial potential of Elliptic Curve Cryptography (ECC), and much of his subsequent work was devoted to developing ECC algorithms, protocols, and standards. In 1985 he co-founded Certicom, which later became the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
