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One-way Functions
In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient for a function to be called one-way (see Theoretical definition, below). The existence of such one-way functions is still an open conjecture. Their existence would prove that the complexity classes P and NP are not equal, thus resolving the foremost unsolved question of theoretical computer science.Oded Goldreich (2001). Foundations of Cryptography: Volume 1, Basic Tools,draft availablefrom author's site). Cambridge University Press. . (see als The converse is not known to be true, i.e. the existence of a proof that P≠NP would not directly imply the existence of one-way functions. In applied contexts, the terms "easy" and "hard" are usu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Security
Data security means protecting digital data, such as those in a database, from destructive forces and from the unwanted actions of unauthorized users, such as a cyberattack or a data breach. Technologies Disk encryption Disk encryption refers to encryption technology that encrypts data on a hard disk drive. Disk encryption typically takes form in either software (see disk encryption software) or hardware (see disk encryption hardware). Disk encryption is often referred to as on-the-fly encryption (OTFE) or transparent encryption. Software versus hardware-based mechanisms for protecting data Software-based security solutions encrypt the data to protect it from theft. However, a malicious program or a hacker could corrupt the data to make it unrecoverable, making the system unusable. Hardware-based security solutions prevent read and write access to data, which provides very strong protection against tampering and unauthorized access. Hardware-based security or as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapdoor Function
In theoretical computer science and cryptography, a trapdoor function is a function that is easy to compute in one direction, yet difficult to compute in the opposite direction (finding its inverse) without special information, called the "trapdoor". Trapdoor functions are a special case of one-way functions and are widely used in public-key cryptography. In mathematical terms, if ''f'' is a trapdoor function, then there exists some secret information ''t'', such that given ''f''(''x'') and ''t'', it is easy to compute ''x''. Consider a padlock and its key. It is trivial to change the padlock from open to closed without using the key, by pushing the shackle into the lock mechanism. Opening the padlock easily, however, requires the key to be used. Here the key ''t'' is the trapdoor and the padlock is the trapdoor function. An example of a simple mathematical trapdoor is "6895601 is the product of two prime numbers. What are those numbers?" A typical " brute-force" solution wou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptographic Primitive
Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build cryptographic protocols for computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions. Rationale When creating cryptographic systems, designers use cryptographic primitives as their most basic building blocks. Because of this, cryptographic primitives are designed to do one very specific task in a precisely defined and highly reliable fashion. Since cryptographic primitives are used as building blocks, they must be very reliable, i.e. perform according to their specification. For example, if an encryption routine claims to be only breakable with number of computer operations, and it is broken with significantly fewer than operations, then that cryptographic primitive has failed. If a cryptographic primitive is found to fail, almost every protocol that uses it becomes vulnerable. Since creating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bijection
In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. In mathematical terms, a bijective function is a one-to-one (injective) and onto (surjective) mapping of a set ''X'' to a set ''Y''. The term ''one-to-one correspondence'' must not be confused with ''one-to-one function'' (an injective function; see figures). A bijection from the set ''X'' to the set ''Y'' has an inverse function from ''Y'' to ''X''. If ''X'' and ''Y'' are finite sets, then the existence of a bijection means they have the same number of elements. For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-complete
In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # the problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. In this sense, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. If we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. Polynomial time refers to an amount of time that is considered "quick" for a det ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-hard
In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem ''H'' is NP-hard when every problem ''L'' in NP can be reduced in polynomial time to ''H''; that is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve any NP-hard problem would give polynomial time algorithms for all the problems in NP. As it is suspected that P≠NP, it is unlikely that such an algorithm exists. It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven. Moreover, the class P, in which all problems can be solved in polynomial time, is contained in the NP class. Def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Best, Worst And Average Case
In computer science, best, worst, and average cases of a given algorithm express what the resource usage is ''at least'', ''at most'' and ''on average'', respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n. Average case is the function which performs an average number of steps on input data of n elements. In real-time computing, the worst-case execution time is often of particular concern since it is important to know how much time might be needed ''in the worst case'' to guarantee that the algorithm will always finish on time. Average performance and worst-case performance are the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Distribution (discrete)
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of ''n'' values has equal probability 1/''n''. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen". A simple example of the discrete uniform distribution is throwing a fair dice. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform because not all sums have equal probability. Although it is convenient to describe discrete uniform distributions over integers, such as this, one can also consider discrete uniform distributions over any finite set. For instance, a random permutation is a permutation generated uniformly from the permutations of a given length, and a un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kleene Star
In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. In mathematics, it is more commonly known as the free monoid construction. The application of the Kleene star to a set V is written as ''V^*''. It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions". # If V is a set of strings, then ''V^*'' is defined as the smallest superset of V that contains the empty string \varepsilon and is closed under the string concatenation operation. # If V is a set of symbols or characters, then ''V^*'' is the set of all strings over symbols in V, including the empty string \varepsilon. The set ''V^*'' can also be described as the set containing the empty string and all finite-length strings that can be generated by concatenating arbitr ... [...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 r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomized Algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables. One has to distinguish between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite ( Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result ( Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem. In common practice, randomized a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
