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Elliptic Curve Cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGamal cryptosystem. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic-curve factorization. History The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor S. Miller in 1985. Elliptic curve cryptography algorithms entered wide use in 2004 to 2005. In 1999, NIST recommended fifteen elliptic curves. Specifically, FIPS 186 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Public-key Cryptography
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. There are many kinds of public-key cryptosystems, with different security goals, including digital signature, Diffie–Hellman key exchange, Key encapsulation mechanism, public-key key encapsulation, and public-key encryption. Public key algorithms are fundamental security primitives in modern cryptosystems, including applications and protocols that offer assurance of the confidentiality and authenticity of electronic communications and data storage. They underpin numerous Internet standards, such as Transport Layer Security, T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Finite Field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are the integers mod n, integers mod p when p is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number p and every positive integer k there are fields of order p^k. All finite fields of a given order are isomorphism, isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set that is a fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Transport Layer Security
Transport Layer Security (TLS) is a cryptographic protocol designed to provide communications security over a computer network, such as the Internet. The protocol is widely used in applications such as email, instant messaging, and voice over IP, but its use in securing HTTPS remains the most publicly visible. The TLS protocol aims primarily to provide security, including privacy (confidentiality), integrity, and authenticity through the use of cryptography, such as the use of certificates, between two or more communicating computer applications. It runs in the presentation layer and is itself composed of two layers: the TLS record and the TLS handshake protocols. The closely related Datagram Transport Layer Security (DTLS) is a communications protocol that provides security to datagram-based applications. In technical writing, references to "(D)TLS" are often seen when it applies to both versions. TLS is a proposed Internet Engineering Task Force (IETF) standard, fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Proxy Re-encryption
Proxy re-encryption (PRE) schemes are cryptosystems which allow third parties ( proxies) to alter a ciphertext which has been encrypted for one party, so that it may be decrypted by another. Examples of use A proxy re-encryption is generally used when one party, say Bob, wants to reveal the contents of messages sent to him and encrypted with his public key to a third party, Charlie, without revealing his private key to Charlie. Bob does not want the proxy to be able to read the contents of his messages. Bob could designate a proxy to re-encrypt one of his messages that is to be sent to Charlie. This generates a new key that Charlie can use to decrypt the message. Now if Bob sends Charlie a message that was encrypted under Bob's key, the proxy will alter the message, allowing Charlie to decrypt it. This method allows for a number of applications such as e-mail forwarding, law-enforcement monitoring, and content distribution. A weaker re-encryption scheme is one in which the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Signcryption
In cryptography, signcryption is a public-key primitive that simultaneously performs the functions of both digital signature and encryption. Background Encryption and digital signature are two fundamental cryptographic tools that can guarantee the confidentiality, integrity, and non-repudiation. Until 1997, they were viewed as important but distinct building blocks of various cryptographic systems. In public key schemes, a traditional method is to digitally sign a message then followed by an encryption (signature-then-encryption) that can have two problems: Low efficiency and high cost of such summation, and the case that any arbitrary scheme cannot guarantee security. Signcryption is a relatively new cryptographic technique that is supposed to perform the functions of digital signature and encryption in a single logical step and can effectively decrease the computational costs and communication overheads in comparison with the traditional signature-then-encryption schemes. Sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Identity-based Encryption
Identity-based encryption (IBE), is an important primitive of identity-based cryptography. As such it is a type of public-key encryption in which the public key of a user is some unique information about the identity of the user (e.g. a user's email address). This means that a sender who has access to the public parameters of the system can encrypt a message using e.g. the text-value of the receiver's name or email address as a key. The receiver obtains its decryption key from a central authority, which needs to be trusted as it generates secret keys for every user. Identity-based encryption was proposed by Adi Shamir in 1984. He was however only able to give an instantiation of Identity-based cryptography, identity-based signatures. Identity-based encryption remained an open problem for many years. The pairing-based cryptography, pairing-based Boneh–Franklin scheme and Cocks IBE scheme, Cocks's encryption scheme based on quadratic residues both solved the IBE problem in 2001. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Tate Pairing
In mathematics, Tate pairing is any of several closely related bilinear pairings involving elliptic curves or abelian varieties, usually over local or finite fields, based on the Tate duality pairings introduced by and extended by . applied the Tate pairing over finite fields to cryptography. See also * Weil pairing In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing ''n'' of an elliptic curve ''E'', taking values in ''n''th roots of unity. More generally there is a similar Weil ... References * * * * Pairing-based cryptography Elliptic curve cryptography Elliptic curves {{Crypto-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Weil Pairing
In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing ''n'' of an elliptic curve ''E'', taking values in ''n''th roots of unity. More generally there is a similar Weil pairing between points of order ''n'' of an abelian variety and its dual. It was introduced by André Weil (1940) for Jacobians of curves, who gave an abstract algebraic definition; the corresponding results for elliptic functions were known, and can be expressed simply by use of the Weierstrass sigma function. Formulation Choose an elliptic curve ''E'' defined over a field ''K'', and an integer ''n'' > 0 (we require ''n'' to be coprime to char(''K'') if char(''K'') > 0) such that ''K'' contains a primitive nth root of unity. Then the ''n''-torsion on E(\overline) is known to be a Cartesian product of two cyclic groups of order ''n''. The Weil pairing produces an ''n''-th root of unity :w(P,Q) \in \mu_n by mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Classified Information In The United States
The United States government classification system is established under Executive Order 13526, the latest in a long series of executive orders on the topic of classified information beginning in 1951. Issued by President Barack Obama in 2009, Executive Order 13526 replaced earlier executive orders on the topic and modified the regulations codified to 32 C.F.R. 2001. It lays out the system of classification, declassification, and handling of national security information generated by the U.S. government and its employees and contractors, as well as information received from other governments. The desired degree of secrecy about such information is known as its sensitivity. Sensitivity is based upon a calculation of the damage to national security that the release of the information would cause. The United States has three levels of classification: Confidential, Secret, and Top Secret. Each level of classification indicates an increasing degree of sensitivity. Thus, if one holds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Elliptic Curve Digital Signature Algorithm
In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography. Key and signature sizes As with elliptic-curve cryptography in general, the bit size of the private key believed to be needed for ECDSA is about twice the size of the security level, in bits. For example, at a security level of 80 bits—meaning an attacker requires a maximum of about 2^ operations to find the private key—the size of an ECDSA private key would be 160 bits. On the other hand, the signature size is the same for both DSA and ECDSA: approximately 4 t bits, where t is the exponent in the formula 2^, that is, about 320 bits for a security level of 80 bits, which is equivalent to 2^ operations. Signature generation algorithm Suppose Alice wants to send a signed message to Bob. Initially, they must agree on the curve parameters (\textrm, G, n). In addition to the field and equation of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Elliptic-curve Diffie–Hellman
Elliptic-curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an Elliptic curve, elliptic-curve public–private key pair, to establish a shared secret over an insecure channel. This shared secret may be directly used as a key, or to Key derivation function, derive another key. The key, or the derived key, can then be used to encrypt subsequent communications using a Symmetric-key algorithm, symmetric-key cipher. It is a variant of the Diffie–Hellman key exchange, Diffie–Hellman protocol using elliptic-curve cryptography. Key establishment protocol The following example illustrates how a shared key is established. Suppose Alice and Bob, Alice wants to establish a shared key with Alice and Bob, Bob, but the only channel available for them may be eavesdropped by a third party. Initially, the Elliptic curve cryptography#Domain parameters, domain parameters (that is, (p, a, b, G, n, h) in the prime case or (m, f(x), a, b, G, n, h) in the bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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National Institute Of Standards And Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into Outline of physical science, physical science laboratory programs that include Nanotechnology, nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement. From 1901 to 1988, the agency was named the National Bureau of Standards. History Background The Articles of Confederation, ratified by the colonies in 1781, provided: The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective states—fixing the standards of weights and measures throughout the United States. Article 1, section 8, of the Constitution of the United States, ratified i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |