advantage

Dictionary: ad·van·tage (ăd-văn'tĭj) pronunciation

A beneficial factor or combination of factors.
Benefit or profit; gain: It is to your advantage to invest wisely.
A relatively favorable position; superiority of means: A better education gave us the advantage.
Sports.
1. The first point scored in tennis after deuce.
2. The resulting score.

tr.v., -taged, -tag·ing, -tag·es.
To afford profit or gain to; benefit.

idioms:

take advantage of

To put to good use; avail oneself of: take advantage of all educational opportunities.
To profit selfishly by; exploit: took advantage of the customer.

to advantage

To good effect; favorably: The roses were displayed to advantage in a blue vase.

[Middle English avantage, from Old French, from avant, before, from Latin abante, from before. See advance.]

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Thesaurus: advantage

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noun

A factor conducive to superiority and success: handicap, head start, odds, start, vantage. See help/harm/harmless.
Something beneficial: avail, benefit, blessing, boon, favor, gain, profit. See help/harm/harmless.
Something that contributes to or increases one's well-being: benefit, good, interest (often used in plural), profit. See help/harm/harmless.
The quality of being suitable or adaptable to an end: account, avail, benefit, profit, use, usefulness, utility. See used/unused.
A dominating position, as in a conflict: better, bulge, draw, drop, edge, superiority, upper hand, vantage. Informal inside track, jump. See over/under.

verb

Archaic

Idioms:

See

help/harm/harmless

Antonyms: advantage

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Definition: benefit, favored position or circumstance
Antonyms: disadvantage, drawback, handicap, hindrance, loss, obstacle, restriction

Word Tutor: advantage

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IN BRIEF: A more favorable position; better chance.

To every disadvantage there is a corresponding advantage. — W. Clement Stone; American entrepreneur

Quotes About: Advantage

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Quotes:

"In life, as in chess, forethought wins." - Charles Buxton

"If we do what is necessary, all the odds are in our favor." - Henry Kissinger

"If eighty percent of your sales come from twenty percent of all of your items, just carry those twenty percent." - Stew Leonard

"He who is in love with himself has at least this advantage -- he won't encounter many rivals." - Georg C. Lichtenberg

"The two big advantages I had at birth were to have been born wise and to have been born in poverty." - Sophia Loren

"It is a great advantage for a system of philosophy to be substantially true." - George Santayana

See more famous quotes about Advantage

Wikipedia: Advantage (cryptography)

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This article may require cleanup to meet Wikipedia's quality standards. Please improve this article if you can. (March 2008)

In cryptography, an adversary's advantage is a measure of how successfully it can attack a cryptographic algorithm, by distinguishing it from an idealized version of that type of algorithm. Note that in this context, the "adversary" is itself an algorithm and not a person. A cryptographic algorithm is considered secure if no adversary has a non-negligible advantage, subject to specified bounds on the adversary's computational resources (see concrete security). "Negligible" usually means "within O(2^-p)" where p is a security parameter associated with the algorithm. For example, p might be the number of bits in a block cipher's key.

1 Description of concept
2 Examples
- 2.1 Example 1: Guess at random
- 2.2 Example 2: Brute force search
3 References

Description of concept

(to be expanded)

Let F be an oracle for the function being studied, and let G be an oracle for an idealized function of that type. The adversary A is a probabilistic algorithm given F or G as input and which outputs 1 or 0. A's job is to distinguish F from G based on making queries to the oracle that it's given. We say: $Adv(A) = |\Pr[A(F)=1] - \Pr[A(G)=1]|$

Examples

Let F be a random instance of the DES block cipher. This cipher has 64-bit blocks and a 56-bit key. The key therefore selects one of a family of 2⁵⁶ permutations on the 2⁶⁴ possible 64-bit blocks. A "random DES instance" means our oracle F computes DES using some key K (which is unknown to the adversary) where K is selected from the 2⁵⁶ possible keys with equal probability.

We want to compare the DES instance with an idealized 64-bit block cipher, meaning a permutation selected at random from the (2⁶⁴)! possible permutations on 64-bit blocks. Call this randomly selected permutation G. Note from Stirling's approximation that (2⁶⁴)! is around $10^{3.47\times 10^{20}}$ , so even specifying which permutation is selected requires writing down a number too large to represent exactly in any real computer. Viewed another way, G is an instance of a "cipher" whose "key length" is about 10²¹ bits, which again is too large to fit in a computer. (We can, however, implement G with storage space proportional to the number of queries, using a random oracle).

Note that because the oracles we're given encrypt plaintext of our choosing, we're modelling a chosen-plaintext attack or CPA, and the advantage we're calculating can be called the CPA-advantage of a given adversary. If we also had decryption oracles available, we'd be doing a chosen-ciphertext attack or CCA and finding the CCA-advantage of the adversary.

We'll look at several different adversaries and see how they perform.

Example 1: Guess at random

We'll call this adversary A₀. It simply flips a coin and returns 1 or 0 with equal probability and without making any oracle calls. Thus, Pr[A₀(F)=1] and Pr[A₀(G)=1] are both 0.5. The difference between these probabilities is zero, so Adv(A₀) is zero. The same thing applies if we always return 0, or always return 1: the probability is the same for both F and G, so the advantage is zero. This adversary can't tell F and G apart. If we're cipher designers, our desire (maybe not achievable) is to make it so that it's computationally infeasible for any adversary to do significantly better than this. We will have succeeded if we can make a cipher for which there's no distinguisher faster than brute force search.

Example 2: Brute force search

This adversary (call it A₁) will attempt to cryptanalyze its input by brute force. It has its own DES implementation. It gives a single query to its oracle, asking for the 64-bit string of all zeroes to be encrypted. Call the resulting ciphertext E₀. It then runs an exhaustive key search. The algorithm looks like this:

 E₀ = oracle_query(0)
 for k in 0,1,...,2⁵⁶-1:
   if DES_k(0) == E₀: 
      return 1
 return 0

This searches the entire 56-bit DES keyspace and returns "1" if it probably finds a matching key. In practice, several plaintexts are required to confirm the key, as two different keys can result in one or more matching plaintext-ciphertext pairs. If no key is found, it returns 0.

If the input oracle is DES, this exhaustive search is certain to find the key, so Pr[A₁(F)=1] = 1. If the input oracle is a random permutation, there are 2⁶⁴ possible values of E₀, and at most 2⁵⁶ of them will get examined in the DES keysearch. So the probability of A₁ returning 1 is at most 2^-8. That is:

Pr[A₁(G)=1] <= 2^-8, so

Adv(A₁) = |Pr[A₁(F)=1] - Pr[A₁(G)=1]| >= 1 - 2^-8

so the advantage is at least about 0.996. This is a near-certain distinguisher, but it's not a security failure because it's no faster than brute force search--because it is brute force search.

References

Phillip Rogaway and Mihir Bellare, Introduction to Modern Cryptography

Oded Goldreich, Foundations of Cryptography (Fragments of a Book)

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

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Translations: Advantage

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Dansk (Danish)
n. - fordel, gunstig, omstændighed
v. tr. - gavne, være til fordel for, være til nytte for

idioms:

take advantage of udnytte, drage fordel af, misbruge
to good advantage fra den mest fordelagtige side
to your advantage til din fordel, i din favør
turn to one's advantage drage fordel af, udnytte, vende til ens egen fordel

Nederlands (Dutch)
voordeel, overwicht, advantage (tennis), bevoordelen, bevorderen het beste tonend ergens van profiteren

Français (French)
n. - avantage, bénéfice, (Sport) avantage (tennis, rugby)
v. tr. - avantager

idioms:

have the advantage of avoir un avantage sur
take advantage of tirer profit de, profiter de
to good advantage à son profit, avantageusement
to your advantage à votre avantage
turn to one's advantage tirer parti de, tourner qch à son advantage

Deutsch (German)
n. - Vorteil
v. - nutzen, fördern, (einer Sache) dienen

idioms:

have the advantage of (jmdm. gegenüber) in der besseren Position sein
take advantage of ausnutzen
to good advantage vorteilhaft
to your advantage zu Ihrem Vorteil
turn to one's advantage in einen Vorteil wandeln

Ελληνική (Greek)
n. - πλεονέκτημα, αβαντάζ, όφελος, ωφέλεια, υπεροχή, κέρδος, προτέρημα

idioms:

take advantage of εκμεταλλεύομαι, επωφελούμαι, καταχρώμαι, εξαπατώ, αποπλανώ
to good advantage με κέρδος
to your advantage προς όφελός σου, για το καλό σου
turn to one's advantage επωφελούμαι από, μεταστρέφω σε όφελός μου

Italiano (Italian)
vantaggio

idioms:

take advantage of approfittare di, sfruttare
to good advantage nella luce migliore
to your advantage a tuo/vostro vantaggio
turn to his advantage mettere a suo profitto

Português (Portuguese)
n. - vantagem (f), superioridade (f), circunstância (f) favorável, benefício (m)

idioms:

take advantage of aproveitar, tirar partido ou vantagem
to good advantage destacar as melhores características
to your advantage para sua vantagem
turn to his advantage explorar algo para seu benefício

Русский (Russian)
преимущество

idioms:

take advantage of воспользоваться
to good advantage на пользу дела
to your advantage в твою пользу
turn to his advantage повернуть в свою пользу

Español (Spanish)
n. - ventaja, beneficio, provecho
v. tr. - adelantar, beneficiar, promover

idioms:

have the advantage of tener la ventaja de, contar con la ventaja de
take advantage of aprovecharse de, sacar ventaja de, valerse de
to good advantage para provecho de
to your advantage a su favor, para su bien
turn to one's advantage dar vuelta un suceso a nuestro favor

Svenska (Swedish)
n. - fördel, företräde, övertag

中文（简体）(Chinese (Simplified))
优势, 优点, 有利条件, 利益, 有利于, 使处于优势, 有助于

idioms:

take advantage of 利用, 占...的便宜, 欺骗
to good advantage 使优点突出
to your advantage 对你有利
turn to one's advantage 使...转为有利

中文（繁體）(Chinese (Traditional))
n. - 優勢, 優點, 有利條件, 利益
v. tr. - 有利於, 使處於優勢, 有助於

idioms:

take advantage of 利用, 占...的便宜, 欺騙
to good advantage 使優點突出
to your advantage 對你有利
turn to one's advantage 使...轉為有利

한국어 (Korean)
n. - 유리, 이익, 강점, 듀스 후 1점의 득점
v. tr. - 이롭게 하다

idioms:

take advantage of ~을 이용하다, 허를 찌르다, 유혹하다
to good advantage 매우 유리하게
to your advantage 너에게 유리한
turn to one's advantage 유리하게 이끌다

日本語 (Japanese)
n. - 有利な点, 利点, 優位, 利益, 便宜, 好都合, アドバンテージ, 優越
v. - 利する

idioms:

take advantage of 利用する, …に付け込む
to your advantage 有利に

العربيه (Arabic)
‏(الاسم) أفضليه, فائده, مصلحه إنقلب لصالحه‏

עברית (Hebrew)
n. - ‮יתרון, תועלת, רווח‬
v. tr. - ‮הועיל ל-, עזר ל-, קידם‬

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		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved. Read more
		Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved. Read more
		Antonyms. © 1999-2009 by Answers Corporation. All rights reserved. Read more
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		Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Advantage (cryptography)". Read more
		Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved. Read more

advantage

Contents

Description of concept

Examples

Example 1: Guess at random

Example 2: Brute force search

References