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Topic: Blum Blum Shub

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	Blum Blum Shub - Wikipédia
		Blum Blum Shub (BBS) est un algorithme capable de générer des nombres pseudo-aléatoires.
		Il fut proposé en 1986 par Lenore Blum, Manuel Blum et Michael Shub, d'où son nom.
		GMPBBS - une implémentation GNU de l'algorithme Blum Blum Shub.
	fr.wikipedia.org /wiki/Blum_Blum_Shub (256 words)

	Blum Blum Shub (Site not responding. Last check: 2007-10-21)
		The Weather Channel: Blum Local forecast, current conditions, and radar.
		The Antenna Conspiracy Government conspiracies and bizarre events of animal mutilations, unexplained pregnancies and birth defects from covert tower construction project in Blum, Texas.
		Rechtsanwalt Dr. Andreas M. Blum Die Rechtsanwaltskanzlei Dr. Blum ist rechtsberatend, rechtsgestaltend und forensisch auf dem Gebiet des Arbeitsrechts mit dem Schwerpunkt Allgemeiner und Besonderer Kündigungsschutz tätig.
	www.serebella.com /encyclopedia/article-Blum_Blum_Shub.html (516 words)

	Encyclopedia: Blum Blum Shub
		A pseudorandom number generator (PRNG) is an algorithm that generates a sequence of numbers, the elements of which are approximately independent of each other.
		Some of his work includes the Blum Blum Shub pseudorandom number generator, the...
		Categories: Pseudorandom number generators The GNU Multiple-Precision Library, also known as GMP, is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers.
	www.nationmaster.com /encyclopedia/Blum-Blum-Shub (745 words)

	Encyclopedia: Integer factorization
		A fast integer factorization algorithm would mean that the RSA public-key algorithm was insecure.
		Some cryptographic systems, such as the Rabin public-key algorithm and the Blum Blum Shub pseudo-random number generator can make a stronger guarantee - any means of breaking them can be used to build a fast integer factorization algorithm, so if integer factorization is hard then they are strong.
		In contrast, it may turn out that there are attacks on the RSA problem more efficient than integer factorization, though none are currently known.
	www.nationmaster.com /encyclopedia/Integer-factorization (2355 words)

	Re: Blum Blum Shub RNG in gmp
		Blum Blum Shub RNG in gmp, Gary Wong,
		Re: Blum Blum Shub RNG in gmp, Torbjorn Granlund,
		Re: Blum Blum Shub RNG in gmp, Gary Wong
	lists.gnu.org /archive/html/bug-gmp/2001-12/msg00044.html (200 words)

	Encyclopedia: Integer factorisation (Site not responding. Last check: 2007-10-21)
		If a fast method were found for solving the integer factorization problem, then several important cryptographic systems would be broken, including the RSA public-key algorithm and the Blum Blum Shub pseudo-random number generator.
		A rare exception is the Blum Blum Shub generator.
		It has been proved to be exactly as hard as integer factorization: if you can break the generator in polynomial time then you can factorize integers in polynomial time, and vice versa.
	www.nationmaster.com /encyclopedia/Integer-factorisation (848 words)

	Citations: A simple Unpredictable Pseudo-Random Number Generator - Blum, Blum, Shub (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		Blum, M. Blum, and M. Shub, "A simple unpredictable pseudo-random number generator," SIAM J. Cornput., 15(2) (1986).
		Recall the notion of a Blum Blum Shub (BBS) sequence x 0 ; x 1 ; Delta Delta Delta ; x n, with x 0 = g (mod N) for a random g 2 ZN, and x i = x i Gamma1 (mod N) 1 i n.
		Blum, M., L. Blum and Shub, "A simple unpredictable pseudo-random number generator", SIAM J. Computing, 15(2):364--383, May 1986.
	citeseer.ist.psu.edu /context/54357/0 (1704 words)

	Blum Blum Shub - Wikipedia, the free encyclopedia
		Blum Blum Shub (BBS) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub (Blum et al, 1986).
		GMPBBS - a GMP-based implementation of Blum Blum Shub.
		This page was last modified 02:35, 30 September 2005.
	en.wikipedia.org /wiki/Blum_Blum_Shub (318 words)

	Is a BB&S System "Proven Secure"?
		Subject: Re: small subgroups in Blum Blum Shub Date: Fri, 16 Jun 2000 17:13:09 GMT From: sarnold_intertrust@my-deja.com Message-ID: <8idn6h$vvf$1@nnrp1.deja.com> References: <39499DD2.3E39F0F7@zetnet.co.uk> Newsgroups: sci.crypt Lines: 18 In article <39499DD2.3E39F0F7@zetnet.co.uk>, hopwood@zetnet.co.uk wrote: > AFAICS from Theorem 4 of the BBS paper, lordcow77's argument > is correct.
		Subject: Re: small subgroups in Blum Blum Shub Date: 18 Jun 2000 16:12:23 -0700 From: daw@blowfish.isaac.cs.berkeley.edu (David A. Wagner) Message-ID: <8ijl0n$ltg$1@blowfish.isaac.cs.berkeley.edu> References: <394c7e0b.7556651@news.io.com> Newsgroups: sci.crypt Lines: 16 In article <394c7e0b.7556651@news.io.com>, Terry Ritter <ritter@io.com> wrote: > You attempt to make the issue the same as the usual key selection, but > that is a false analogy.
		Subject: Re: small subgroups in Blum Blum Shub Date: 21 Jun 2000 08:38:10 GMT From: pom@imsd.uni-mainz.de (Klaus Pommerening) Message-ID: <8iputi$o3o$3@bambi.zdv.Uni-Mainz.DE> References: <394ec029.4137859@news.io.com> Newsgroups: sci.crypt Lines: 36 In <394fa7b6.6164415@news.io.com> Terry Ritter wrote: > I do have a different model, but it is not a model of computation.
	www.ciphersbyritter.com /NEWS5/SUBGPBBS.HTM (18410 words)

	Blum Blum Shub - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-10-21)
		Blum Blum Shub - Encyclopedia, History, Geography and Biography
		GMPBBS (http://firefly.is-a-geek.org/gmpbbs/) - a GMP-based implementation of Blum Blum Shub.
		The article about Blum Blum Shub contains information related to Blum Blum Shub, Security, References and External links.
	www.arikah.net /encyclopedia/Blum_Blum_Shub (345 words)

	MANUEL BLUM (Site not responding. Last check: 2007-10-21)
		Manuel Blum (26 de abril de 1938) es profesor de Ciencias de la Computación.
		Recibió el Premio Turing en 1995 por sus contribuciones a la teoría de Complejidad computacional y sus aplicaciones a la criptografía y "program checking".
		Blum asistió al MIT, en donde recibió su B.S. en 1959, su "master" en 1961, y su PhD en 1964.
	www.espnuevomilenio.org /encyclopedia/M/Manuel_Blum (132 words)

	Lenore Blum's Home Page
		Lenore Blum’s research, from her early work in model theory and differential fields (logic and algebra) to her more recent work with Shub and Smale in developing a theory of computation and complexity over the real numbers (mathematics and computer science), has focused on merging seemingly unrelated areas.
		Blum is well known for her work in increasing the participation of girls and women in mathematics and scientific fields.
		In 1979 Blum was elected Fellow of the AAAS.
	www.cs.cmu.edu /~lblum (1335 words)

	Mersenne twister - Wikipedia, the free encyclopedia
		The "twist" is a transformation which assures equidistribution of the generated numbers in 623 dimensions (linear congruential generators can at best manage reasonable distribution in 5 dimensions).
		Unlike Blum Blum Shub, the algorithm in its native form is not suitable for cryptography.
		For many other applications, however, it is fast becoming the random number generator of choice.
	en.wikipedia.org /wiki/Mersenne_Twister (373 words)

	Manuel Blum (Site not responding. Last check: 2007-10-21)
		Manuel Blum is a profound thinker, said ACM President...
		NORFOLK -- Margot Manuel Blum, 81, died March 18, 1997, in her daughter's residence in St. Louis, Mo. Mrs.
		Blum was a retired partner with Fraoli, Blum and Yesselman which was responsible...
	enciclopedia.cc /Manuel_Blum (384 words)

	Décomposition en produit de facteurs premiers - Wikipédia
		Ceci s'applique pour les systèmes modernes en cryptologie.
		Si une méthode rapide a été trouvée pour résoudre le problème de la factorisation des nombres entiers, alors plusieurs systèmes cryptologiques importants seraient cassés, incluant l'algorithme à clé publique RSA et le générateur de nombres pseudo-aléatoires Blum Blum Shub.
		Une exception rare est le générateur Blum Blum Shub.
	fr.wikipedia.org /wiki/Factorisation_en_nombres_premiers (938 words)

	Citations: a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and ... (Site not responding. Last check: 2007-10-21)
		Blum, L., M. Shub, S. Smale, On a Theory of Computation and Complexity over the Real Numbers; NP Completeness, Recursive Functions and Universal Machines, Bull.
		Blum, M. Shub, S. Smale, A theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines, Bulletin of the American Mathematical Society 21 (1989) 1-46.
		Blum, M. Shub, S. Smale, A theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines, Bulletin of the American Mathematical Society 21 (1989) 1--46.
	citeseer.lcs.mit.edu /context/5445/0 (4598 words)

	iqexpand.com (Site not responding. Last check: 2007-10-21)
		Recent instances of algorithms include Blum Blum Shub, Fortuna, and the Mersenne Twister.
		Because any PRNG run on a deterministic computer (contrast quantum computer) is a deterministic algorithm, its output will inevitably have one property that a true random sequence would not exhibit: guaranteed periodicity.
		For example Blum Blum Shub has a strong conditional security proof, though it is slow.
	pseudorandom_number_generator.iqexpand.com (1049 words)

	Manuel Blum (Site not responding. Last check: 2007-10-21)
		Manuel Blum (de llevado el 26 de abril de 1938) es un informático que recibió la concesión de Turing en 1995 "en el reconocimiento de sus contribuciones a las fundaciones la teoría de complejidad de cómputo y su aplicación la criptografía y programa que comprobaba".
		Algo de su trabajo incluye el generador del número pseudaleatorio de Blum Blum Shub, el cypher de la corriente de Blum-Goldwasser, y más recientemente Captchas.
		Blum atendió al MIT, en donde él recibieron su licenciatura en 1959, su masters en 1961, y su PhD en 1964.
	www.yotor.net /wiki/es/ma/Manuel%20Blum.htm (151 words)

	Cryptographically secure pseudo-random number generator - Wikipedia, the free encyclopedia
		Initialization: Compute I = DES_k (D) Output: Each time a random number is required, output x=DES_k(I xor s), and update the seed s to DES_k(x xor I) edit]
		Blum Blum Shub has a strong security proof, based on the difficulty of integer factorization.
		However, implementations are slow compared to some other designs.
	en.wikipedia.org /wiki/CSPRNG (902 words)

	Cryptography-Digest Digest #78
		And in this particular case, I deny that increasing the keyspace and so reducing the probability of using a short cycle is the same as absolutely removing that possibility, since we do have that alternative.
		Consider a Blum >integer n, and an adversary A who is unable to factor n.
		If one determines that there are more than one variants that are appropriate for the application, then one can advantageously exploit the variability of using these variants.
	www.mail-archive.com /cryptography-digest@senator-bedfellow.mit.edu/msg03270.html (2845 words)

	Blum Drawer Slide (Site not responding. Last check: 2007-10-21)
		Find results for blum drawer slide and anything else you are looking for instantly!
		Your support is critical to those that have been impacted by this national disaster.
		Blum Blum Shub Articles and Information - Current Article Blum Blum Shub Blum Blum Shub (BBS) is form: xn+1 = (xn)2 mod M where M is...
	www.meridian-tt.com /Blum-Drawer-Slide.html (528 words)

	Blum Blum Shub -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Blum Blum Shub -- Facts, Info, and Encyclopedia article
		Blum Blum Shub (BBS) is a (Click link for more info and facts about pseudorandom number generator) pseudorandom number generator proposed in 1986 by (Click link for more info and facts about Lenore Blum) Lenore Blum, (Click link for more info and facts about Manuel Blum) Manuel Blum and Michael Shub (Blum et al, 1986).
		- a (Click link for more info and facts about GMP) GMP-based implementation of Blum Blum Shub.
	www.absoluteastronomy.com /encyclopedia/b/bl/blum_blum_shub.htm (408 words)

	Blum Hinge (Site not responding. Last check: 2007-10-21)
		Find results for blum hinge and anything else you are looking for instantly!
		[1] In 2002, Blum was appointed by California Governor Gray Davis to California.
		Léon Blum Articles and Information - Current Article Léon Blum Léon Blum Léon Blum Léon Blum (9 April 1872 - 30 March 1950), French socialist leader France'...
	www.meridian-tt.com /Blum-Hinge.html (586 words)

	Learn more about Blum Blum Shub in the online encyclopedia. (Site not responding. Last check: 2007-10-21)
		Learn more about Blum Blum Shub in the online encyclopedia.
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	www.onlineencyclopedia.org /b/bl/blum_blum_shub.html (345 words)

	FoRK Archive: Intel (was Re: TBTF for 11/10/97: Blum Blum Shub) (Site not responding. Last check: 2007-10-21)
		FoRK Archive: Intel (was Re: TBTF for 11/10/97: Blum Blum Shub)
		Intel (was Re: TBTF for 11/10/97: Blum Blum Shub)
		In reply to: Robert Harley: "Re: TBTF for 11/10/97: Blum Blum Shub"
	www.xent.com /FoRK-archive/oct97/0315.html (289 words)

	Randomness Tests; Blum, Blum & Shub
		1994-06-17 Robert I. Eachus: AFAIK the only algorithmic RNG that can be considered secure and has reasonable performance is Blum, Blum, and Shub.
		The original Blum, Blum and Shub paper proved that at least one secure bit could be generated each iteration.
		1995-10-06 Robert I. Eachus: The Blum, Blum and Shub algorithm is at least as difficult to predict as it is to factor the modulus.
	www.ciphersbyritter.com /NEWS2/TESTSBBS.HTM (1727 words)

	New Sources of Random Numbers (Site not responding. Last check: 2007-10-21)
		Six Lava Lites in different colors are set up in front of a digital camera, which takes a snapshot of them periodically.
		The digital image is run through a one-way hash-function to produce an 800-bit seed, which is used as the starting value for the "Blum Blum Shub" pseudorandom generator.
		According to the article, which was dated well in advance of 1 April, the authors are attempting to patent the ideas behind the technology.
	www.ieee-security.org /Cipher/Newsbriefs/1997/970325.RNs.html (195 words)

	Shub (Site not responding. Last check: 2007-10-21)
		Et un peu plus pour les curieux de Shub, Marvin et Glen or Glenda.
		Shub Niggurath: discographie et commentaire OPPOSITION DE PHASE
		Quoique conseiller Shub Niggurath relève peut-être de l'irresponsabilité...
	www.focus.fr /q.asp?Keywords=Shub (151 words)

	Cryptographically Secure Pseudo Random Number Generator (Site not responding. Last check: 2007-10-21)
		There are a number of examples of CSPRNGs.
		Blum Blum Shub has the strongest security proofs, although it is slow..
		Most stream ciphers work by generating a pseudorandom stream of bits that are XORed with the message; this stream can be used as a good CSPRNG (thought not always: see RC4 cipher).
	www.wikiverse.org /cryptographically-secure-pseudo-random-number-generator (342 words)

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