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In [[computational complexity]], if <math>\scriptstyle\{ D_n \}_{n \in \mathbb{N}}</math> and <math>\scriptstyle\{ E_n \}_{n \in \mathbb{N}}</math> are two [[distribution ensemble]]s indexed by a [[security parameter]] ''n'' (which usually refers to the length of the input), then we say they are '''computationally indistinguishable''' if for any [[Uniformity (complexity)|non-uniform]] probabilistic [[polynomial time]] [[algorithm]] ''A'', the following quantity is a [[negligible function (cryptography)|negligible function]] in ''n'':
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: <math>\delta(n) = \left| \Pr_{x \gets D_n}[ A(x) = 1] - \Pr_{x \gets E_n}[ A(x) = 1] \right|.</math>
 
denoted <math>D_n \approx E_n\!\,</math>.<ref>[http://www.cs.princeton.edu/courses/archive/spr10/cos433/lec4.pdf Lecture 4 - Computational Indistinguishability, Pseudorandom Generators]</ref> In other words, every efficient algorithm ''A'''s behavior does not significantly change when given samples according to ''D''<sub>''n''</sub> or ''E''<sub>''n''</sub> in the limit as <math>n\to \infty</math>. Another interpretation of computational indistinguishability, is that polynomial-time algorithms actively trying to distinguish between the two ensembles cannot do so: That any such algorithm will only perform negligibly better than if one were to just guess.
 
Implicit in the definition is the condition that the algorithm, <math>A</math>, must decide based on a single sample from one of the distributions. One might conceive of a situation in which the algorithm trying to distinguish between two distributions, could access as many samples as it needed. Hence two ensembles that cannot be distinguished by polynomial-time algorithms looking at multiple samples are deemed '''indistinguishable by polynomial-time sampling'''<ref name=Goldreich>[[Oded Goldreich|Goldreich, O.]] (2003). Foundations of cryptography. Cambridge, UK: Cambridge University Press.</ref>{{rp|107}}. It turns out that if the polynomial-time algorithm can generate samples in polynomial time, or has access to [[random oracle]] that generates samples for it, then indistinguishable by polynomial-time sampling is equivalent to computational indistinguishability<ref name=Goldreich></ref>{{rp|108}}.
 
== References ==
<references/>
* Donald Beaver and [[Silvio Micali]] and [[Phillip Rogaway]], The Round Complexity of Secure Protocols (Extended Abstract), 1990, pp.&nbsp;503—513
* [[Shafi Goldwasser]] and [[Silvio Micali]]. Probabilistic Encryption. JCSS, 28(2):270–299, 1984
* [[Oded Goldreich]]. Foundations of Cryptography: Volume 2 – Basic Applications. Cambridge University Press, 2004.
* [[Jonathan Katz]], [[Yehuda Lindell]], "Introduction to Modern Cryptography: Principles and Protocols," Chapman & Hall/CRC, 2007
 
==External links==
* [[Yehuda Lindell]]. [http://u.cs.biu.ac.il/~lindell/89-656/main-89-656.html Introduction to Cryptography]
 
{{PlanetMath attribution|id=3457|title=computationally indistinguishable}}
 
[[Category:Algorithmic information theory]]
 
{{comp-sci-theory-stub}}
{{crypto-stub}}

Latest revision as of 08:17, 1 October 2014

However, your blood pressure can also affect other major organs in your body from your kidneys to your eyes to your brain. In August, he has introduced the three places will be new work, Li Ao said that the title a bit vulgar - "American impotence", "impotence" as a verb. Other symptoms of allergic reaction include difficulty breathing, swelling of the lips, face, mouth, and tongue. The patient will have to wait for some time, to experience positive results. So, there is still some kind of way out of the problem.

Fortunately, several non-drug treatments are available as well. Tadalafil works by inhibiting the enzyme PDE-5, and helps to increase the blood supply to the penis. It increases libido and strengthens reproducing organs. His soul is as hellish as his form, full of treachery and fiendlike malice. Eric strongly recommends the use of supplements to improve your overall health.

There are preventative actions that one can take such as regular exercise, adequate sleep, reducing levels of stress and consulting your doctor as soon as possible. In the case of impotence, herbal remedies may seem more attractive than other treatment methods because the source is natural. With the prospects of L-Arginine supplementation being as promising as they are the hardening of the arteries and build up on the arterial lining, the two most common factors in heart disease, could be reversed. Your physician is the best person to guide you regarding the treatment of impotence as he knows your health better than anyone else. An anti-aging effect can be achieved from many herbs as lots of them contain certain antioxidants that help with this effect.

Men will typically need more zinc than females to provide enough zinc content to seminal fluids, but neither should ever go overboard. Unfortunately, few of them deliver the promised benefits. These dangerous workouts are also the causes of impotence. You should also be eliminating your body and your bloodstream. There are also drugs associated with causing impotence such as marijuana, heroin, cocaine and prescription ulcer medications such as Cimetidine (Tagamet), hypertension medicines such as beta-blockers and diuretics.

Mutations in the HFE, SLC40A1, HAMP, TFR2, and HFE2 genes cause this genetic disorder. Often feed walnut porridge, can not only, still can prevent kidney impotence, spermatorrhea, have delayed failure anti-ageing effect. Generic online pharmacy provides prescription drugs including ED Medicine which is now reaching distinctive horizons by effectively treating male impotence. Therefore, cheap generic Viagra have become famous. It is also the official gemstone of the Zodiac sign Aries.

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