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	Taher Elgamal - Wikipedia, the free encyclopedia
		Taher Elgamal (Arabic: طاهر الجمل) (born 18 August 1955) is an Egyptian-American cryptographer.
		In 1985, Elgamal published a paper titled A Public key Cryptosystem and A Signature Scheme based on discrete Logarithms in which he proposed the design of the ElGamal discrete log cryptosystem and of the ElGamal signature scheme.
		Elgamal's surname has been spelled as two words (the El part is equivalent to "the" in English), and as a single word with an intra-capital.
	en.wikipedia.org /wiki/Taher_ElGamal (337 words)

	ElGamal discrete log cryptosystem
		The ElGamal algorithm is an asymmetric key encryption algorithm for public key cryptography which is based on discrete logarithms.
		ElGamal is a simple example of a semantically secure asymmetric key encryption algorithm.
		Breaking ElGamal is, in most cases, at least as hard as solving the discrete logarithm problem.
	pedia.newsfilter.co.uk /wikipedia/e/el/elgamal_discrete_log_cryptosystem.html (268 words)

	Elgamal encryption - Wikipedia, the free encyclopedia
		The Elgamal algorithm is an asymmetric key encryption algorithm for public key cryptography which is based on Diffie-Hellman key agreement.
		Elgamal consists of three components: the key generator, the encryption algorithm, and the decryption algorithm.
		Elgamal is a simple example of a semantically secure asymmetric key encryption algorithm (under reasonable assumptions).
	www.wikipedia.org /wiki/ElGamal_discrete_log_cryptosystem (741 words)

	Discrete logarithm
		Discrete logarithms are defined in group theory in analogy to ordinary logarithms.
		For some groups, computing discrete logarithms is believed to be difficult, while the inverse problem of discrete exponentiation is not; this asymmetry is exploited in some applications in cryptography.
		The index calculus[?] is another method to compute discrete logarithms in these groups, as is the birthday attack.
	www.ebroadcast.com.au /lookup/encyclopedia/di/Discrete_logarithm.html (258 words)

	Discrete logarithm - Wikipedia, the free encyclopedia
		In abstract algebra and its applications, the discrete logarithms are defined in group theory in analogy to ordinary logarithms.
		For some groups, computing discrete logarithms is believed to be difficult, while the inverse problem of discrete exponentiation is not (it can be efficiently computed for example using exponentiation by squaring); this asymmetry is exploited in some applications in cryptography.
		Newer cryptography applications use discrete logarithms in cyclic subgroups of elliptic curves over finite fields.
	www.wikipedia.org /wiki/Discrete_logarithm (359 words)

	Encyclopedia: Taher ElGamal (Site not responding. Last check: 2007-11-06)
		The ElGamal Signature scheme is a digital signature scheme which is based on the difficulty of computing discrete logarithms.
		In addition, Elgamal sits on the board of FaceTime Communications [1], a company which provides security solutions for instant messaging and peer-to-peer applications.
		Most recently, Elgamal serves as Chairman and CEO of Ektasis Inc., a Silicon Valley startup he founded in late 2004 with co-founders Phil Straw and Mark Chen.
	www.nationmaster.com /encyclopedia/Taher-ElGamal (908 words)

	Read about ElGamal encryption at WorldVillage Encyclopedia. Research ElGamal encryption and learn about ElGamal ... (Site not responding. Last check: 2007-11-06)
		The ElGamal algorithm is used in the free GNU Privacy Guard software, recent versions of
		The Digital Signature Algorithm, even though it is a signature scheme and performs no encryption, is similar to ElGamal in many respects.
		This assumption is often stronger than the discrete log assumption, but is still believed to be true for many classes of groups.
	encyclopedia.worldvillage.com /s/b/ElGamal_discrete_log_cryptosystem (707 words)

	Knowledge King - ElGamal discrete log cryptosystem (Site not responding. Last check: 2007-11-06)
		NSA's Digital Signature Algorithm is based on ElGamal, and is very similar.
		Breaking ElGamal is believed to be, by most informed observers, generally as difficult as solving the discrete logarithm problem.
		NB: When signing a message using the ElGamal algorithm, the per message random value s used may never be made public.
	www.knowledgeking.net /encyclopedia/e/el/elgamal_discrete_log_cryptosystem.html (333 words)

	Taher Elgamal - Encyclopedia, History and Biography
		In 1985, Elgamal published a paper titled A Public key Cryptosystem and A Signature Scheme based on discrete Logarithms in which he proposed the design of the ElGamal discrete log cryptosystem.
		In addition, Elgamal sits on the board of FaceTime Communications [1] (http://www.facetime.com), a company which provides security solutions for instant messaging and peer-to-peer applications.
		Elgamal's surname has been spelled as two words (the El part is equalivant to "the" in English), and as a single word with an intra-capital.
	www.arikah.net /encyclopedia/Taher_ElGamal (315 words)

	Public-key cryptography - Wikipedia, the free encyclopedia
		An asymmetric key cryptosystem was published in 1976 by Whitfield Diffie and Martin Hellman, who, influenced by Ralph Merkle's work on public key distribution, disclosed a method of public key agreement.
		The ElGamal cryptosystem (invented by Taher ElGamal then of Netscape) relies on the (similar, and related) difficulty of the discrete logarithm problem, as does the closely related DSA developed by the NSA and NIST.
		Most are used in hybrid cryptosystems for reasons of efficiency; in such a cryptosystem, a shared secret key ("session key") is generated by one party, this much briefer session key is then encrypted by each recipient's public key.
	en.wikipedia.org /wiki/Asymmetric_key_algorithm (2092 words)

	Taher Elgamal - Encyclopedia Glossary Meaning Explanation Taher Elgamal (Site not responding. Last check: 2007-11-06)
		Taher Elgamal (Arabic: طاهر الجمل) (Born 18 August 1955) (sometimes seen El Gamal and ElGamal, but Elgamal is preferred, see below) is an American-Egyptian cryptographer.
		Presently (2004), Securify is again independent and Elgamal is Chief Technical Officer & Co-Chair of the Board of Directors.
		In addition, Elgamal sits on the board of FaceTime Communications http://www.facetime.com, a company which provides security solutions for instant messaging and peer-to-peer applications.
	www.encyclopedia-glossary.com /en/Taher-Elgamal.html (352 words)

	discrete
		In perception a discrete entity is something that can be percepted individually and not as connected to, or part of something else.
		In mathematics a discrete set is a countable or countably infinite, with a cardinality less than or equal to (See Aleph).
		In mathematics, a discrete space is a topological space in which all sets are open.
	www.fact-library.com /discrete.html (187 words)

	ElGamal encryption - Wikpedia (Site not responding. Last check: 2007-11-06)
		ElGamal can be defined over any cyclic group $G .$
		ElGamal's security rests, in part, on the difficulty of solving the discrete logarithm problem in $G .$
		Note that ElGamal is malleable in an extreme way: for example, given an encryption $(c_1, c_2) of some (possibly unknown) message m, one can easily construct an encryption (c_1, 2 \cdot c_2) of the message 2m .$
	www.bostoncoop.net /~tpryor/wiki/index.php?title=ElGamal_discrete_log_cryptosystem (800 words)

	NTRUEncrypt - Wikipedia, the free encyclopedia
		It was invented in the mid-1990s and is patented and endorsed by NTRU Cryptosystems, Inc..
		It relies on the presumed difficulty of factoring certain polynomials in such rings into a quotient of two polynomials having very small coefficients.
		Breaking the cryptosystem is strongly related, though not equivalent, to the algorithmic problem of lattice reduction (solving the closest vector problem) in certain lattices.
	en.wikipedia.org /wiki/NTRUEncrypt (187 words)

	Knowledge King - Elliptic curve cryptography (Site not responding. Last check: 2007-11-06)
		There are several slightly different versions of elliptic curve cryptography, all of which rely on the widely believed difficulty of solving the discrete logarithm problem for the group of an elliptic curve over some finite field.
		It is believed that the usual discrete logarithm problem over the multiplicative group of a finite field (DLP) and ECDLP are not equivalent problems; and that ECDLP is significantly more difficult than DLP.
		Doing the group operations needed to run the system is slower for an ECC system than for a factorisation system or modulo integer discrete log system of the same size.
	www.knowledgeking.net /encyclopedia/e/el/elliptic_curve_cryptography.html (776 words)

	Discrete logarithm -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		In (Click link for more info and facts about abstract algebra) abstract algebra and its applications, the discrete logarithms are defined in (The branch of mathematics dealing with groups) group theory in analogy to ordinary (The exponent required to produce a given number) logarithms.
		For some groups, computing discrete logarithms is believed to be difficult, while the inverse problem of discrete exponentiation is not; this asymmetry is exploited in some applications in (Act of writing in code or cipher) cryptography.
		Newer cryptography applications use discrete logarithms in cyclic subgroups of (Click link for more info and facts about elliptic curve) elliptic curves over (Click link for more info and facts about finite field) finite fields.
	www.absoluteastronomy.com /encyclopedia/d/di/discrete_logarithm.htm (384 words)

	discrete_log_problem (Site not responding. Last check: 2007-11-06)
		In the discrete log problem is given two elements find the smallest such that.
		However, since in fields of characteristic two the discrete log problem is much easier than it is in prime fields (especially when one uses the Coppersmith...
		For some groups, the discrete log problem is a hard problem that can be used in public-key cryptography.
	discrete_log_problem.networklive.org (355 words)

	Talk:Taher Elgamal - Wikipedia, the free encyclopedia
		See Talk:PGP for a discussion of how Dr Elgamal spells his name.
		Should it then be Elgamal discrete log cryptosystem instead of ElGamal discrete log cryptosystem, too?
		The gentleman should certainly be able to choose how to spell his own name, especially when the differences amongst the various versions is not likely to lead to confusion.
	en.wikipedia.org /wiki/Talk:Taher_ElGamal (176 words)

	ElGamal discrete log cryptosystem: Definition and Links by Encyclopedian.com - All about ElGamal discrete log ... (Site not responding. Last check: 2007-11-06)
		ElGamal discrete log cryptosystem: Definition and Links by Encyclopedian.com - All about ElGamal discrete log cryptosystem
		To sign the message m with the secret key (p, g, k) choose a random s with 1 < s < p-1 and s coprime to p-1 (in order that s has a multiplicative inverse modulo p-1).
		Nor may the same s value be used to sign two different messages; doing so will enable an opponent to easily recover the secret key.
	www.encyclopedian.com /el/ElGamal-discrete-log-cryptosystem.html (407 words)

	ElGamal encryption (Site not responding. Last check: 2007-11-06)
		ElGamal can be defined over any cyclic group
		ElGamal's security rests, in part, on the difficulty of solving the discrete logarithm problem in
		Note that ElGamal is malleable in an extreme way: for example, given an encryption
	www.worldhistory.com /wiki/E/ElGamal-encryption.htm (921 words)

	FaceTime Communications Board of Directors
		Elgamal currently serves as the organization's Chief Technology Officer and member of the Board of Directors.
		Prior to Netscape, Elgamal served as the director of Engineering at RSA Data Security, Inc. where he built and ran the engineering department that developed the industry standard RSA cryptographic toolkits.
		In 1985 Dr. Elgamal published a paper entitled A Public Key Cryptosystem and A Signature Scheme Based on Discrete Logarithms in which he proposed the design of the ElGamal discrete log cryptosystem.
	www.facetime.com /company/board.aspx (1124 words)

	ElGamal discrete log cryptosystem Definition / ElGamal discrete log cryptosystem Research (Site not responding. Last check: 2007-11-06)
		The ElGamal algorithm is an asymmetric key encryption algorithmIn cryptography, an asymmetric key algorithm uses a pair of cryptographic keys to encrypt and decrypt.
		[click for more] for public key cryptography which is based on discrete logarithmsIn abstract algebra and its applications, the discrete logarithms are defined in group theory in analogy to ordinary logarithms.
		The ElGamal algorithm is used in the free GNU Privacy GuardThe GNU Privacy Guard (GnuPG or GPG) is a free software replacement for the PGP suite of cryptographic software, released under the GNU General Public License.
	www.elresearch.com /ElGamal_discrete_log_cryptosystem (453 words)

	Auto-recoverable and auto-certifiable cryptostem using zero-knowledge proofs for key escrow in general exponential ... (Site not responding. Last check: 2007-11-06)
		The ARC Cryptosystem is based on a key generation mechanism that outputs a public/private key pair, and a certificate of proof that the key is recoverable by the escrow authorities.
		The first solution is based on the discrete log problem, and the second solution is based on the difficulty of factoring.
		The users of such a cryptosystem employ the public key system in a way that is identical to a typical PKI based on discrete logs, for secure communications.
	www.freepatentsonline.com /6282295.html (7769 words)

	Read about Discrete logarithm at WorldVillage Encyclopedia. Research Discrete logarithm and learn about Discrete ... (Site not responding. Last check: 2007-11-06)
		group isomorphism, called the discrete logarithm to base b.
		For some groups, computing discrete logarithms is believed to be difficult, while the inverse problem of discrete exponentiation is not; this asymmetry is exploited in some applications in
		Newer cryptography applications use discrete logarithms in cyclic subgroups of
	encyclopedia.worldvillage.com /s/b/Discrete_logarithm_problem (340 words)

	Cryptosystem discreto del registro de ElGamal (Site not responding. Last check: 2007-11-06)
		ElGamal es un ejemplo simple de un algoritmo dominante asimétrico semántico asegurado del cifrado.
		Romper ElGamal está, en la mayoría de los casos, por lo menos tan difícilmente como solucionando el problema discreto del logaritmo.
		Taher ElGamal, "un cryptosystem de la Pu'blico-Llave y un esquema de la firma basado en logaritmos discretos", las transacciones de IEEE en teoría de información, v.
	www.yotor.net /wiki/es/cr/Cryptosystem%20discreto%20del%20registro%20de%20ElGamal.htm (345 words)

	ElGamal discrete log cryptosystem : Elgamal discrete logarithm cryptosystem
		ElGamal discrete log cryptosystem : Elgamal discrete logarithm cryptosystem
		terms defined : ElGamal discrete log cryptosystem : Elgamal discrete logarithm cryptosystem
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	www.termsdefined.net /el/elgamal-discrete-logarithm-cryptosystem.html (537 words)

	Asymmetric cryptography (Site not responding. Last check: 2007-11-06)
		Well after RSA's publication, Taher Elgamal invented the Elgamal discrete log cryptosystem which relies on the difficulty of inverting logs in afinite field.
		While it is more complex computationally, it is believed by manyto represent a more difficult mathematical problem than either the factorisation or discrete logarithm problems.
		One drawback of asymmetric key algorithms is that they are much slower (factors of 1000+ are typical) than 'comparably' secure symmetric key algorithms.
	www.therfcc.org /asymmetric-cryptography-79738.html (946 words)

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