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Birthday paradox: Meaning (information, definition, explanation, facts)

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Encyclopedia: Birthday paradox

In probability theory, the birthday paradox states that given a group of 23 (or more) randomly chosen people, the probability is more than 50% that some pair of them will have the same birthday. For 57 or more people, the probability is greater than 99%, although it cannot actually be 100% unless there are at least 366 people.^[1] This is not a paradox in the sense of leading to a logical contradiction; it is described as a paradox because mathematical truth contradicts naive intuition: most people estimate that the chance is much lower than 50%. Calculating this probability (and related ones) is the birthday problem. The mathematics behind it have been used to devise a well-known cryptographic attack named the birthday attack.

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Translations

How to say "Birthday paradox" in other languages:

	(Chinese)	生日悖论
	(Japanese)	誕生日のパラドックス
	(German)	Geburtstagsparadoxon
	(Spanish)	Paradoja del cumpleaños
	(French)	Paradoxe des anniversaires
	(Italian)	Paradosso del compleanno

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Birthday attack

A birthday attack is a mathematical and cryptographic attack which makes use of a space-time tradeoff. It exploits the mathematics behind the birthday paradox. Specifically, if a function yields any... signature can be susceptible to a birthday attack. A message m is typically signed by first computing...

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Block size (cryptography)

the example of the DES in using a block size of 64 bits (8 bytes). However the Birthday paradox...

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Intuition

called a paradox (a paradox can also be a logical self-contradiction). An example of this is the Birthday paradox. In the philosophy of Immanuel Kant, intuition is one of the basic cognitive faculties...

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Large number

...

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List of combinatorics topics

algorithm Divide and conquer Akra-Bazzi Method Dynamic programming Branch and bound Birthday attack, birthday paradox Reduction to linear algebra Umbral calculus Minimax algorithm Alpha-beta pruning...

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List of probability topics

gambling strategy) Coincidence Birthday paradox Index of coincidence Bible code Spurious... Thompson Jaynes Bayesianism Prior probability Posterior probability Borel's paradox Bertrand's paradox Coherence (philosophical gambling strategy) Dutch book Random variables Discrete random variable...

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Paradox

are equal. For example, the Birthday paradox is more of a surprise than a paradox, while the..., both of equal size to the first. Birthday paradox: What is the chance that two people in a room have the same birthday? Borel's paradox: Conditional probability density functions are not invariant...

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Cryptographic hash function

2 such that hash( m1 )�=�hash( m2 ). Because of the birthday paradox this means the hash function...

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List of mathematical topics (A-C)

Birthday attack -- Birthday paradox Birthday paradox -- Bisection Bisection -- Bisection method Bisection... theorem -- Arrow's paradox Arrow's paradox -- Art of Problem Solving Art of Problem Solving -- Artin... paradox Banach-Tarski paradox -- Barbier's theorem Barbier's theorem -- Barber paradox Barber paradox...