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Very Smooth Hash
In cryptography, Very Smooth Hash (VSH) is a secure cryptographic hash function invented in 2005 by Scott Contini, Arjen Lenstra and Ron Steinfeld. Provably secure means that finding collisions is as difficult as some known hard mathematical problem. Unlike other secure collision-resistant hashes, VSH is efficient and usable in practice. Asymptotically, it only requires a single multiplication per log(''n'') message-bits and uses RSA-type arithmetic. Therefore, VSH can be useful in embedded environments where code space is limited. Two major variants of VSH were proposed. For one, finding a collision is as difficult as finding a nontrivial modular square root of a very smooth number modulo ''n''. The other one uses a prime modulus ''p'' (with no trapdoor), and its security proof relies on the hardness of finding discrete logarithms of very smooth numbers modulo ''p''. Both versions have similar efficiency. VSH is not suitable as a substitute for a random oracle, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scott Contini
Scott may refer to: Places Canada * Scott, Quebec, municipality in the Nouvelle-Beauce regional municipality in Quebec * Scott, Saskatchewan, a town in the Rural Municipality of Tramping Lake No. 380 * Rural Municipality of Scott No. 98, Saskatchewan United States * Scott, Arkansas * Scott, Georgia * Scott, Indiana * Scott, Louisiana * Scott, Missouri * Scott, New York * Scott, Ohio * Scott, Wisconsin (other) (several places) * Fort Scott, Kansas * Great Scott Township, St. Louis County, Minnesota * Scott Air Force Base, Illinois * Scott City, Kansas * Scott City, Missouri * Scott County (other) (various states) * Scott Mountain, a mountain in Oregon * Scott River, in California * Scott Township (other) (several places) Elsewhere * 876 Scott, minor planet orbiting the Sun * Scott (crater), a lunar impact crater near the south pole of the Moon *Scott Conservation Park, a protected area in South Australia People * Scott (surname), including a list ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristic (algebra)
In mathematics, the characteristic of a ring (mathematics), ring , often denoted , is defined to be the smallest number of times one must use the ring's identity element, multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive identity the ring is said to have characteristic zero. That is, is the smallest positive number such that: :\underbrace_ = 0 if such a number exists, and otherwise. Motivation The special definition of the characteristic zero is motivated by the equivalent definitions characterized in the next section, where the characteristic zero is not required to be considered separately. The characteristic may also be taken to be the exponent (group theory), exponent of the ring's additive group, that is, the smallest positive integer such that: :\underbrace_ = 0 for every element of the ring (again, if exists; otherwise zero). Some authors do not include the multiplicative identity element in their r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Security Engineering
Security engineering is the process of incorporating security controls into an information system so that the controls become an integral part of the system’s operational capabilities. It is similar to other systems engineering activities in that its primary motivation is to support the delivery of engineering solutions that satisfy pre-defined functional and user requirements, but it has the added dimension of preventing misuse and malicious behavior. Those constraints and restrictions are often asserted as a security policy. In one form or another, security engineering has existed as an informal field of study for several centuries. For example, the fields of locksmithing and security printing have been around for many years. The concerns for modern security engineering and computer systems were first solidified in a RAND paper from 1967, "Security and Privacy in Computer Systems" by Willis H. Ware. This paper, later expanded in 1979, provided many of the fundamental informati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Message Authentication Code
In cryptography, a message authentication code (MAC), sometimes known as a ''tag'', is a short piece of information used for authenticating a message. In other words, to confirm that the message came from the stated sender (its authenticity) and has not been changed. The MAC value protects a message's data integrity, as well as its authenticity, by allowing verifiers (who also possess the secret key) to detect any changes to the message content. Terminology The term message integrity code (MIC) is frequently substituted for the term ''MAC'', especially in communications to distinguish it from the use of the latter as ''media access control address'' (''MAC address''). However, some authors use MIC to refer to a message digest, which aims only to uniquely but opaquely identify a single message. RFC 4949 recommends avoiding the term ''message integrity code'' (MIC), and instead using ''checksum'', ''error detection code'', '' hash'', ''keyed hash'', ''message authentication code'', ... [...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 product of two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collision Resistance
In cryptography, collision resistance is a property of cryptographic hash functions: a hash function ''H'' is collision-resistant if it is hard to find two inputs that hash to the same output; that is, two inputs ''a'' and ''b'' where ''a'' ≠ ''b'' but ''H''(''a'') = ''H''(''b''). Goldwasser, S. and Bellare, M.br>"Lecture Notes on Cryptography" Summer course on cryptography, MIT, 1996-2001 The pigeonhole principle means that any hash function with more inputs than outputs will necessarily have such collisions; the harder they are to find, the more cryptographically secure the hash function is. The "birthday paradox" places an upper bound on collision resistance: if a hash function produces ''N'' bits of output, an attacker who computes only 2''N''/2 (or \scriptstyle \sqrt) hash operations on random input is likely to find two matching outputs. If there is an easier method than this brute-force attack, it is typically considered a flaw in the hash function.Pass, R"Lecture 21: Col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Logarithm
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b''''k'' can be defined for all integers ''k'', and the discrete logarithm log''b'' ''a'' is an integer ''k'' such that . In number theory, the more commonly used term is index: we can write ''x'' = ind''r'' ''a'' (mod ''m'') (read "the index of ''a'' to the base ''r'' modulo ''m''") for ''r''''x'' ≡ ''a'' (mod ''m'') if ''r'' is a primitive root of ''m'' and gcd(''a'',''m'') = 1. Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. Several important algorithms in public-key cryptography, such as ElGamal base their security on the assumption that the discrete logarithm problem over carefully chosen groups has no efficient solution. Definition Let ''G'' be any group. Denote its group operation by mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis Of Algorithms
In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small, or grow slowly compared to a growth in the size of the input. Different inputs of the same size may cause the algorithm to have different behavior, so best, worst and average case descriptions might all be of practical interest. When not otherwise specified, the function describing the performance of an algorithm is usually an upper bound, determined from the worst case inputs to the algorithm. The term "analysis of algorithms" was coined by Donald Knuth. Algorithm analysis is an important part of a broader ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ciphertext Indistinguishability
Ciphertext indistinguishability is a property of many encryption schemes. Intuitively, if a cryptosystem possesses the property of indistinguishability, then an adversary will be unable to distinguish pairs of ciphertexts based on the message they encrypt. The property of indistinguishability under chosen plaintext attack is considered a basic requirement for most provably secure public key cryptosystems, though some schemes also provide indistinguishability under chosen ciphertext attack and adaptive chosen ciphertext attack. Indistinguishability under chosen plaintext attack is equivalent to the property of semantic security, and many cryptographic proofs use these definitions interchangeably. A cryptosystem is considered ''secure in terms of indistinguishability'' if no adversary, given an encryption of a message randomly chosen from a two-element message space determined by the adversary, can identify the message choice with probability significantly better than that of rand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collision-resistant
In cryptography, collision resistance is a property of cryptographic hash functions: a hash function ''H'' is collision-resistant if it is hard to find two inputs that hash to the same output; that is, two inputs ''a'' and ''b'' where ''a'' ≠ ''b'' but ''H''(''a'') = ''H''(''b''). Goldwasser, S. and Bellare, M.br>"Lecture Notes on Cryptography" Summer course on cryptography, MIT, 1996-2001 The pigeonhole principle means that any hash function with more inputs than outputs will necessarily have such collisions; the harder they are to find, the more cryptographically secure the hash function is. The "birthday paradox" places an upper bound on collision resistance: if a hash function produces ''N'' bits of output, an attacker who computes only 2''N''/2 (or \scriptstyle \sqrt) hash operations on random input is likely to find two matching outputs. If there is an easier method than this brute-force attack, it is typically considered a flaw in the hash function.Pass, R"Lecture 21: Col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negligible Function
In mathematics, a negligible function is a function \mu:\mathbb\to\mathbb such that for every positive integer ''c'' there exists an integer ''N''''c'' such that for all ''x'' > ''N''''c'', :, \mu(x), 0 such that for all ''x'' > ''N''poly : , \mu(x), 0, there exists a positive number \delta>0 such that , x-x_0, N_\varepsilon ::, \mu(x), 0 by the functions 1/x^c where c>0 or by 1/\operatorname(x) where \operatorname(x) is a positive polynomial. This leads to the definitions of negligible functions given at the top of this article. Since the constants \varepsilon>0 can be expressed as 1/\operatorname(x) with a constant polynomial this shows that negligible functions are a subset of the infinitesimal functions. Use in cryptography In complexity-based modern cryptography, a security scheme is ''provably secure'' if the probability of security failure (e.g., inverting a one-way function, distinguishing cryptographically strong pseudorandom bits from truly ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PP (complexity)
In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances. The abbreviation PP refers to probabilistic polynomial time. The complexity class was defined by Gill in 1977. If a decision problem is in PP, then there is an algorithm for it that is allowed to flip coins and make random decisions. It is guaranteed to run in polynomial time. If the answer is YES, the algorithm will answer YES with probability more than 1/2. If the answer is NO, the algorithm will answer YES with probability less than 1/2. In more practical terms, it is the class of problems that can be solved to any fixed degree of accuracy by running a randomized, polynomial-time algorithm a sufficient (but bounded) number of times. Turing machines that are polynomially-bound and probabilistic are characterized as PPT, which stands for probabilistic polynomial-time machines. This characterization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
