en>Jan Spousta: /* See also */ +Quantile regression

2014-12-31T20:31:35Z

See also: +Quantile regression

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	~~The '''forking lemma''' is any~~ of ~~a number of related [[lemma (mathematics)\|lemmas]]~~ in [[cryptography]] research. The lemma states that if an adversary (typically a [[probabilistic Turing machine]]), on inputs drawn from some [[Probability distribution\|distribution]], produces an output that has some property with [[negligible function\|non-negligible]] [[probability]], then with non-negligible probability, if ~~the adversary is re-run on new inputs but with the same [[random tape]], its second output will also have the property~~.		Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. If you beloved this article and you simply would like to get more info relating to [http://aorta.in/WordpressDropboxBackup37844 wordpress backup plugin] kindly visit the webpage. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. This is a service where people write articles using a specific keyword you have given them. If you're using Wordpress and want to make your blog a "dofollow" blog, meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. Understanding how Word - Press works can be a challenge, but it is not too difficult when you learn more about it. <br><br>You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. While direct advertising is limited to few spots in your site and tied to fixed monthly payment by the advertisers, affiliate marketing can give you unlimited income as long as you can convert your traffic to sales. Which is perfect for building a mobile site for business use. They provide many such popular products which you can buy for your baby. Now a days it has since evolved into a fully capable CMS platform which make it, the best platform in the world for performing online business. <br><br>ve labored so hard to publish and put up on their website. When a business benefits from its own domain name and a tailor-made blog, the odds of ranking higher in the search engines and being visible to a greater number of people is more likely. Possibly the most downloaded Word - Press plugin, the Google XML Sitemaps plugin but not only automatically creates a site map linking to everyone your pages and posts, it also notifies Google, Bing, Yahoo, and Ask. You can allow visitors to post comments, or you can even allow your visitors to register and create their own personal blogs. Article Source: Stevens works in Internet and Network Marketing. <br><br>The primary differences are in the plugins that I install, as all sites don't need all the normal plugins. Russell HR Consulting provides expert knowledge in the practical application of employment law as well as providing employment law training and HR support services. Some examples of its additional features include; code inserter (for use with adding Google Analytics, Adsense section targeting etc) Webmaster verification assistant, Link Mask Generator, Robots. Fast Content Update - It's easy to edit or add posts with free Wordpress websites. Fortunately, Word - Press Customization Service is available these days, right from custom theme design, to plugin customization and modifying your website, you can take any bespoke service for your Word - Press development project. <br><br>More it extends numerous opportunities where your firm is at comfort and rest assured of no risks & errors. Automated deal feed integration option to populate your blog with relevant deals. It's not a secret that a lion share of activity on the internet is takes place on the Facebook. Page speed is an important factor in ranking, especially with Google. For your information, it is an open source web content management system.

	~~This concept was first used by [[David Pointcheval]]~~ and [[Jacques Stern]] in "Security proofs for signature schemes," published in the proceedings of [[Eurocrypt]] 1996.<ref>[[Ernest Brickell]], [[David Pointcheval]], [[Serge Vaudenay]], and [[Moti Yung]], "[http://~~www~~.~~springerlink.com/content~~/~~8v8btpfkat5qp3da/?p=2ad4ec3d6e8447a28d44bd3922e75ef8&pi=18 Design Validations for Discrete Logarithm Based Signature Schemes~~]~~", Third International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2000, [[Melbourne]], [[Australia]], January 18–20, 2000, pp~~. ~~276–292.</ref><ref name="YoungYung">Adam Young and Moti Yung, "Malicious Cryptography: Exposing Cryptovirology", Wiley press, 2004, pp. 344.</ref> In their paper,~~ the ~~forking lemma is specified in terms of an adversary that attacks~~ a ~~[[digital signature]] scheme instantiated in the [[random oracle]] model. They show that if an adversary can forge~~ a ~~signature with non~~-~~negligible probability~~, ~~then there~~ is a ~~non-negligible probability that the same adversary with the same random tape can create~~ a ~~second forgery in an attack with a different random oracle~~.<ref>David Pointcheval and [[Jacques Stern]], "[http://www.springerlink.com/content/k0xj74fcvnaj202t/?p=f5b8f4cb35e149ceb402fb89549556f1&pi=32 Security Proofs for Signature Schemes]", Advances in Cryptology — EUROCRYPT '~~96, [[Saragossa]], [[Spain]], May 12–16, 1996, pp. 387–398.</ref> The forking lemma was later generalized by [[Mihir Bellare]]~~ and ~~Gregory Neven.<ref name=~~"~~BellareNeven~~"~~>[[Mihir Bellare]] and Gregory Neven~~, ~~"[http://portal.acm.org/citation.cfm?id=1180453 Multi-Signatures in~~ the ~~Plain Public-Key Model and a General Forking Lemma]"~~, ~~Proceedings~~ of the ~~13th [[Association for Computing Machinery]] (ACM) Conference on Computer and~~
	~~Communications Security (CCS), [[Alexandria, Virginia]], 2006, pp. 390–399~~.~~</ref> The forking lemma has been used to prove the security of a variety of digital signature schemes and other random~~-~~oracle based cryptographic constructions.<ref name="YoungYung" />~~

	~~==Statement of the lemma==~~

	~~The generalized version of the lemma is stated as follows.<ref name="BellareNeven" /> Let ''A''~~ be a ~~probabilistic algorithm, with inputs (''x'', ''h''<sub>1</sub>~~, .~~.., ''h''~~<~~sub~~>~~''q''~~<~~/sub~~>~~; ''r'') that outputs~~ a ~~pair (''J'', ''y''), where ''r'' refers to~~ the ~~random tape of ''A'' (that is, the random choices A will make)~~. ~~Suppose '''further''' that ''IG''~~ is ~~a probability distribution from which ''x'' is drawn,~~ and ~~that ''H'' is a set of size ''h'' from which each of the ''h<sub>i</sub>'' values are drawn according~~ to the ~~[[Uniform distribution (discrete)\|uniform distribution]]. Let acc be the probability that on inputs distributed~~ as ~~described, the ''J'' output by ''A'' is greater than or equal~~ to 1.

	~~We can then define~~ a ~~"forking algorithm" ''F<sub>A</sub>'' that proceeds as follows, on input ''x'':~~
	~~# Pick a random tape ''r''~~ for ~~''A''.~~
	~~# Pick ''h''<sub>1</sub>, .~~.., ~~''h''<sub>''q''</sub> uniformly from ''H''~~.
	~~# Run ''A'' on input (''x'', ''h''~~<~~sub~~>1<~~/sub~~>~~, ..., ''h''<sub>''q''</sub>; ''r'')~~ to ~~produce (''J'', ''y'')~~.
	~~# If ''J'' = 0, then return (0, 0, 0).~~
	~~# Pick ''h'<sub>J</sup>, ..., h'<sub>q</sub>'' uniformly~~ from ~~''H''.~~
	# Run ''A'' on input (''x'', ''h''<sub>1</sub>, ..., ''h''<sub>''J''−1</sub>, ''h''<nowiki>'</nowiki><sub>''J''</sub>, ..., ''h''<nowiki>'</nowiki><sub>''q''</sub>; ''r'') to produce (''J''<nowiki>'</nowiki>, ''y''<nowiki>'</nowiki>).
	~~# If ''J' '' = ''J''~~ and ~~''h<sub>J</sub>'' ≠ ''h'<sub>J</sub>'' then return (1~~, ~~''y'', ''y''<nowiki>'</nowiki>), otherwise, return (0, 0, 0).~~

	~~Let frk be~~ the ~~probability that ''F<sub>A</sub>'' outputs a triple starting with 1, given an input ''x'' chosen randomly from ''IG''. Then~~

	~~: <math>\text{frk} \geq \text{acc} \cdot \left ( \frac\text{acc}{q} - \frac{1}{h} \right).</math>~~

	~~===Intuition===~~

	~~The idea here is to think~~ of ~~''A'' as running two times~~ in ~~related executions, where~~ the ~~process "[[Fork (software development)\|forks]]" at~~ a ~~certain point, when some but not all~~ of ~~the input has been examined~~. In the ~~alternate version~~, the ~~remaining inputs are re-generated~~ but ~~are generated in the normal way. The point at which the process forks may be something we~~ only ~~want~~ to ~~decide later~~, possibly based on the behavior of ''A'' the first time around: this is why the lemma statement chooses the branching point (''J'') based on the output of ''A''. The requirement that ''h<sub>J</sub>'' ≠ ''h'<sub>J</sub>'' is a technical one required by many uses of the lemma. (Note that since both ''h<sub>J</sub>'' and ''h'<sub>J</sub>'' are chosen randomly from ''H'', ~~then if ''h'' is large~~, ~~which would be normal~~, ~~the probability of the two values not being distinct is extremely small~~.)

	~~===Example===~~

	~~For example~~, ~~let ''A'' be an algorithm for breaking a [[digital signature]] scheme in the [[random oracle]] model~~. ~~Then ''x'' would be the public parameters (including the public key) ''A'' is attacking,~~ and ~~''h~~<~~sub~~>i<~~/sub~~>~~'' would be the output of the random oracle on its ''i''th distinct input.~~ The ~~forking lemma is of use when it would be possible, given two different random signatures of~~ the ~~same message, to solve some underlying hard problem. An adversary~~ that ~~forges once~~, ~~however, gives rise to one that forges twice on~~ the ~~same message with non-negligible probability through~~ the ~~forking lemma~~. ~~When ''A'' attempts to forge on a message ''m'', we consider the output~~ of ~~''A'' to be~~ (~~''J''~~, ~~''y''~~) ~~where ''y'' is the forgery~~, ~~and ''J'' is such that ''m'' was the ''J''th unique query to the random oracle (it may be assumed that ''A'' will query ''m'' at some point~~, if '~~'A'' is~~ to ~~be successful~~ with ~~non-negligible probability)~~. ~~(If ''A'' outputs an incorrect forgery~~, ~~we consider the output to be (0~~, ~~''y'').)~~

	~~By the forking lemma~~, ~~the probability (''frk'') of obtaining two good forgeries ''y''~~ and ~~''y' '' on the same message but with different random oracle outputs (that is~~, ~~with ''h~~<~~sub~~>J<~~/sub~~> ~~≠ h'<sub>J</sub>'')~~ is ~~non-negligible when ''acc'' is also non-negligible~~. ~~This allows us~~ to ~~prove~~ that ~~if the underlying hard problem is indeed hard, then no adversary can forge signatures.~~

	~~This is the essence of the proof given by Pointcheval and Stern for~~ a ~~modified [[ElGamal signature scheme]] against an adaptive adversary.~~

	~~==Known issues with application~~ of ~~forking lemma==~~
	~~The reduction provided by~~ the ~~forking lemma~~ is not a tight reduction. Pointcheval and Stern proposed security arguments for Digital Signatures and Blind Signature using Forking Lemma.<ref>David Pointcheval and Jacques Stern, "Security Arguments for Digital Signatures and Blind Signatures," ''JOURNAL OF CRYPTOLOGY'', Volume 13, pp 361--396, 2000. [http://www.di.ens.fr/~pointche/pub.php Available on ~~Internet]~~.~~</ref> [[Claus P. Schnorr]] provided~~ an ~~attack on blind Schnorr signatures schemes~~,~~<ref>C~~.~~P.Schnorr~~, ~~"Security of Blind Discrete Log Signatures Against Interactive Attacks," ''Proceedings of ICICS 2001,'' [http://www.springerlink.com/~~content~~/wtykch59xl2r/ LNCS Vol. 2229], pp 1-13, 2001. [http://www.mi.informatik~~.uni-frankfurt.de/research/papers.html Available on Internet].</ref> which were argued to be secure by Pointcheval and Stern. Schnorr also suggested enhancements for securing blind signatures schemes based on [[discrete logarithm]] problem.<ref>C.P. Schnorr, "Enhancing the security of perfect blind DL-signatures," Information Sciences, Elsevier, Vol. 176, pp 1305--1320, 2006. [http://www.mi.informatik.uni-frankfurt.de/research/papers.html Available on Internet]</ref>

	~~==References==~~
	~~{{reflist}}~~

	~~{{DEFAULTSORT:Forking Lemma}}~~
	~~[[Category:Cryptography]]~~

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-24T12:13:20Z

Fix CS1 deprecated date parameter errors

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en>Duoduoduo: /* Variations, extensions, specializations */ fixing, defining, and rendering standard the notation

2012-05-12T03:45:41Z

Variations, extensions, specializations: fixing, defining, and rendering standard the notation

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Least absolute deviations - Revision history

en>Jan Spousta: /* See also */ +Quantile regression

en>Monkbot: Fix CS1 deprecated date parameter errors

en>Duoduoduo: /* Variations, extensions, specializations */ fixing, defining, and rendering standard the notation