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ElGamal Signature Scheme
The ElGamal signature scheme is a digital signature scheme which is based on the difficulty of computing discrete logarithms. It was described by Taher Elgamal in 1985. (conference version appeared in CRYPTO'84, pp. 10–18) The ElGamal signature algorithm is rarely used in practice. A variant developed at the NSA and known as the Digital Signature Algorithm is much more widely used. There are several other variants. The ElGamal signature scheme must not be confused with ElGamal encryption which was also invented by Taher Elgamal. Overview The ElGamal signature scheme is a digital signature scheme based on the algebraic properties of modular exponentiation, together with the discrete logarithm problem. The algorithm uses a key pair consisting of a public key and a private key. The private key is used to generate a digital signature for a message, and such a signature can be verified by using the signer's corresponding public key. The digital signature provides message authenticatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Signature
A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient very high confidence that the message was created by a known sender (authenticity), and that the message was not altered in transit (integrity). Digital signatures are a standard element of most cryptographic protocol suites, and are commonly used for software distribution, financial transactions, contract management software, and in other cases where it is important to detect forgery or tampering. Digital signatures are often used to implement electronic signatures, which includes any electronic data that carries the intent of a signature, but not all electronic signatures use digital signatures. [...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] |
Taher Elgamal
Taher Elgamal (Arabic: طاهر الجمل) (born 18 August 1955) is an Egyptian cryptographer and entrepreneur. He has served as the Chief Technology Officer (CTO) of Security at Salesforce since 2013. Prior to that, he was the founder and CEO of Securify and the director of engineering at RSA Security. From 1995 to 1998, he was the chief scientist at Netscape Communications. He has been described as the "father of SSL" for the work he did in computer security while working at Netscape, which helped in establishing a private and secure communications on the Internet. Elgamal's 1985 paper entitled "A Public Key Cryptosystem and A Signature Scheme Based on Discrete Logarithms" proposed the design of the ElGamal discrete log cryptosystem and of the ElGamal signature scheme. The latter scheme became the basis for Digital Signature Algorithm (DSA) adopted by National Institute of Standards and Technology (NIST) as the Digital Signature Standard (DSS). Biography Early life Acc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CRYPTO
Crypto commonly refers to: * Cryptocurrency, a type of digital currency secured by cryptography and decentralization * Cryptography, the practice and study of hiding information Crypto or Krypto may also refer to: Cryptography * Cryptanalysis, the study of methods for obtaining the meaning of encrypted information * CRYPTO (conference), an annual cryptographical and cryptoanalytic conference * Crypto++, a free, open source library of cryptographic algorithms and schemes *'' Crypto: How the Code Rebels Beat the Government—Saving Privacy in the Digital Age'', a book about cryptography by Steven Levy * Crypto AG, a Swiss manufacturer of encrypted communications products Finance * crypto.com, a cryptocurrency online News platform. Biology and medicine * ''Cryptococcus'' (fungus), a genus of fungus that can cause lung disease, meningitis, and other illnesses in humans and animals ** Cryptococcosis (also called cryptococcal disease), a disease caused by ''Cryptococcus'' * ''Cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Signature Algorithm
The Digital Signature Algorithm (DSA) is a Public-key cryptography, public-key cryptosystem and Federal Information Processing Standards, Federal Information Processing Standard for digital signatures, based on the mathematical concept of modular exponentiation and the Discrete logarithm, discrete logarithm problem. DSA is a variant of the Schnorr signature, Schnorr and ElGamal signature scheme, ElGamal signature schemes. The National Institute of Standards and Technology (NIST) proposed DSA for use in their Digital Signature Standard (DSS) in 1991, and adopted it as FIPS 186 in 1994. Four revisions to the initial specification have been released. The newest specification isFIPS 186-4 from July 2013. DSA is patented but NIST has made this patent available worldwide royalty-free. A draft version of the specificatioFIPS 186-5indicates DSA will no longer be approved for digital signature generation, but may be used to verify signatures generated prior to the implementation date of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ElGamal Encryption
In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1985. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. The Digital Signature Algorithm (DSA) is a variant of the ElGamal signature scheme, which should not be confused with ElGamal encryption. ElGamal encryption can be defined over any cyclic group G, like multiplicative group of integers modulo ''n''. Its security depends upon the difficulty of a certain problem in G related to computing discrete logarithms. The algorithm ElGamal encryption consists of three components: the key generator, the encryption algorithm, and the decryption algorithm. Key generation The first party, Alice, generates a key pair as follows: * Generate an efficient description of a cyclic group G\, of order q\, with g ... [...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 always pr ... [...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 messa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generating Set Of A Group
In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses. In other words, if ''S'' is a subset of a group ''G'', then , the ''subgroup generated by S'', is the smallest subgroup of ''G'' containing every element of ''S'', which is equal to the intersection over all subgroups containing the elements of ''S''; equivalently, is the subgroup of all elements of ''G'' that can be expressed as the finite product of elements in ''S'' and their inverses. (Note that inverses are only needed if the group is infinite; in a finite group, the inverse of an element can be expressed as a power of that element.) If ''G'' = , then we say that ''S'' ''generates'' ''G'', and the elements in ''S'' are called ''generators'' or ''group generators''. If ''S'' is the empty set, then is the trivial group , since we consider th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Group Of Integers Modulo N
In modular arithmetic, the integers coprime (relatively prime) to ''n'' from the set \ of ''n'' non-negative integers form a group under multiplication modulo ''n'', called the multiplicative group of integers modulo ''n''. Equivalently, the elements of this group can be thought of as the congruence classes, also known as ''residues'' modulo ''n'', that are coprime to ''n''. Hence another name is the group of primitive residue classes modulo ''n''. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo ''n''. Here ''units'' refers to elements with a multiplicative inverse, which, in this ring, are exactly those coprime to ''n''. This quotient group, usually denoted (\mathbb/n\mathbb)^\times, is fundamental in number theory. It is used in cryptography, integer factorization, and primality testing. It is an abelian, finite group whose order is given by Euler's totient function: , (\mathbb/n\mathbb)^\times, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Hardness Assumption
In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where ''efficiently'' typically means "in polynomial time"). It is not known how to prove (unconditional) hardness for essentially any useful problem. Instead, computer scientists rely on reductions to formally relate the hardness of a new or complicated problem to a computational hardness assumption about a problem that is better-understood. Computational hardness assumptions are of particular importance in cryptography. A major goal in cryptography is to create cryptographic primitives with provable security. In some cases, cryptographic protocols are found to have information theoretic security; the one-time pad is a common example. However, information theoretic security cannot always be achieved; in such cases, cryptographers fall back to computational security. Roughly speaking, this means that these systems are secure ''assuming th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Forgery
In a cryptographic digital signature or MAC system, digital signature forgery is the ability to create a pair consisting of a message, m, and a signature (or MAC), \sigma, that is valid for m, but has not been created in the past by the legitimate signer. There are different types of forgery. To each of these types, security definitions can be associated. A signature scheme is secure by a specific definition if no forgery of the associated type is possible. Types The following definitions are ordered from lowest to highest achieved security, in other words, from most powerful to the weakest attack. The definitions form a hierarchy, meaning that an attacker able to do mount a specific attack can execute all the attacks further down the list. Likewise, a scheme that reaches a certain security goal also reaches all prior ones. Total break More general than the following attacks, there is also a ''total break'': when adversary can recover the private information and keys used by t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
