|
Secret Sharing
Secret sharing (also called secret splitting) refers to methods for distributing a secrecy, secret among a group, in such a way that no individual holds any intelligible information about the secret, but when a sufficient number of individuals combine their 'shares', the secret may be reconstructed. Whereas ''insecure'' secret sharing allows an attacker to gain more information with each share, ''secure'' secret sharing is 'all or nothing' (where 'all' means the necessary number of shares). In one type of secret sharing scheme there is one ''dealer'' and ''n'' ''players''. The dealer gives a share of the secret to the players, but only when specific conditions are fulfilled will the players be able to reconstruct the secret from their shares. The dealer accomplishes this by giving each player a share in such a way that any group of ''t'' (for ''threshold'') or more players can together reconstruct the secret but no group of fewer than ''t'' players can. Such a system is called a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secrecy
Secrecy is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals. That which is kept hidden is known as the secret. Secrecy is often controversial, depending on the content or nature of the secret, the group or people keeping the secret, and the motivation for secrecy. Secrecy by government entities is often decried as excessive or in promotion of poor operation; excessive revelation of information on individuals can conflict with virtues of privacy and confidentiality. It is often contrasted with social transparency. Secrecy can exist in a number of different ways: encoding or encryption (where mathematical and technical strategies are used to hide messages), true secrecy (where restrictions are put upon those who take part of the message, such as through government security classification) and obfuscation, where secrets are hidden in plain sight behind complex idiosyncrat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problem (mathematics education), word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tal Rabin
Tal Rabin (; born 1962) is a computer scientist and Professor of Computer and Information Science at the University of Pennsylvania and a Director at Amazon Web Services (AWS). She was previously the head of research at the Algorand Foundation and the head of the cryptography research group at IBM's Thomas J. Watson Research Center. Biography Rabin was born in Massachusetts and grew up in Jerusalem, Israel. As a child, she enjoyed solving riddles and playing strategic games. Her father, Michael Rabin, is a celebrated computer scientist who is responsible for many breakthroughs in the fields of computability and cryptography. She and her father have co-authored a paper together. She is the mother of two daughters. Career In 1986, she received her BSc from the Hebrew University of Jerusalem. She continued her studies there for her MSc (1988) and PhD (1994) degrees under the supervision of Professor Michael Ben-Or. Between 1994 and 1996, she was an National Science Foundation pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adversary (cryptography)
In cryptography, an adversary (rarely opponent, enemy) is an entity whose aim is to prevent the users of the cryptosystem from achieving their goal (primarily privacy, integrity, and availability of data), often with malicious intent. An adversary's efforts might take the form of attempting to discover secret data, corrupting some of the data in the system, spoofing the identity of a message sender or receiver, or forcing system downtime. Actual adversaries, as opposed to idealized ones, are referred to as ''attackers''. The former term predominates in the cryptographic and the latter in the computer security literature. Eavesdropper Eve, malicious attacker Mallory, opponent Oscar, and intruder Trudy are all adversarial characters widely used in both types of texts. This notion of an adversary helps both intuitive and formal reasoning about cryptosystems by casting security analysis of cryptosystems as a 'game' between the users and a ''centrally co-ordinated'' enemy. The notion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pairwise Coprime
In number theory, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. One says also ''is prime to'' or ''is coprime with'' . The numbers 8 and 9 are coprime, despite the fact that neither—considered individually—is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition. Notation and testing When the integers and are coprime, the standard way of expressing this fact in mathematical notation is to indicate that their greatest common divisor is one, by the formula or . In their 1989 textbook '' Concrete Mathematics'', Ronald Graham, Donald Knuth, and Oren Patashnik proposed an alternat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Remainder Theorem
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer ''n'' by several integers, then one can determine uniquely the remainder of the division of ''n'' by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). The theorem is sometimes called Sunzi's theorem. Both names of the theorem refer to its earliest known statement that appeared in '' Sunzi Suanjing'', a Chinese manuscript written during the 3rd to 5th century CE. This first statement was restricted to the following example: If one knows that the remainder of ''n'' divided by 3 is 2, the remainder of ''n'' divided by 5 is 3, and the remainder of ''n'' divided by 7 is 2, then with no other information, one can determine the remainder of ''n'' divided by 105 (the product of 3, 5, and 7) without knowing the value of ''n''. In this example, the remainder is 23. More ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line (mathematics)
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher. The word ''line'' may also refer, in everyday life, to a line segment, which is a part of a line delimited by two points (its ''endpoints''). Euclid's ''Elements'' defines a straight line as a "breadthless length" that "lies evenly with respect to the points on itself", and introduced several postulates as basic unprovable properties on which the rest of geometry was established. ''Euclidean line'' and ''Euclidean geometry'' are terms introduced to avoid confusion with generalizations introduced since the end of the 19th century, such as non-Euclidean, projective, and affine geometry. Properties In the Greek deductive geometry of Euclid's ''Elements'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersecting Planes 2
In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. Unlike the Euclidean definition, this does not presume that the objects under consideration lie in a common space. It simply means the overlapping area of two or more objects or geometries. Intersection is one of the basic concepts of geometry. An intersection can have various geometric shapes, but a point is the most common in a plane geometry. Incidence geometry defines an intersection (usually, of flats) as an object of lower dimension that is incident to each of the original objects. In this approach an intersection can be sometimes undefined, such as for parallel l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theoretic Security
A cryptosystem is considered to have information-theoretic security (also called unconditional security) if the system is secure against adversaries with unlimited computing resources and time. In contrast, a system which depends on the computational cost of cryptanalysis to be secure (and thus can be broken by an attack with unlimited computation) is called computationally secure or conditionally secure. Overview An encryption protocol with information-theoretic security is impossible to break even with infinite computational power. Protocols proven to be information-theoretically secure are resistant to future developments in computing. The concept of information-theoretically secure communication was introduced in 1949 by American mathematician Claude Shannon, one of the founders of classical information theory, who used it to prove the one-time pad system was secure. Information-theoretically secure cryptosystems have been used for the most sensitive governmental communica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperplane
In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like a plane in space, a hyperplane is a flat hypersurface, a subspace whose dimension is one less than that of the ambient space. Two lower-dimensional examples of hyperplanes are one-dimensional lines in a plane and zero-dimensional points on a line. Most commonly, the ambient space is -dimensional Euclidean space, in which case the hyperplanes are the -dimensional "flats", each of which separates the space into two half spaces. A reflection across a hyperplane is a kind of motion ( geometric transformation preserving distance between points), and the group of all motions is generated by the reflections. A convex polytope is the intersection of half-spaces. In non-Euclidean geometry, the ambient space might be the -dimensional sphere or hyperbolic space, or more generally a pseudo-Riemannian space form, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
