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# chapter-10 - CS549 Cryptography and Network Security by...

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Cryptography and Network Security 1 CS549: Cryptography and Network Security © by Xiang-Yang Li Department of Computer Science, IIT

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Cryptography and Network Security 2 Notice© This lecture note (Cryptography and Network Security) is prepared by Xiang-Yang Li. This lecture note has benefited from numerous textbooks and online materials. Especially the “Cryptography and Network Security” 2 nd edition by William Stallings and the “Cryptography: Theory and Practice” by Douglas Stinson. You may not modify, publish, or sell, reproduce, create derivative works from, distribute, perform, display, or in any way exploit any of the content, in whole or in part, except as otherwise expressly permitted by the author. The author has used his best efforts in preparing this lecture note. The author makes no warranty of any kind, expressed or implied, with regard to the programs, protocols contained in this lecture note. The author shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these.
Cryptography and Network Security 3 Cryptography and Network Security Pseudo-random Number Xiang-Yang Li

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Cryptography and Network Security 4 Random number, Pseudorandom The outputs of pseudorandom number generators are not truly random they only approximate some of the properties of random numbers. "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.”--- John von Neumann Truely random numbers can be generated using hardware random number generators
Cryptography and Network Security 5 Randomness Definition Chaitin-Kolmogorov randomness (also called algorithmic randomness ) a string of bits is random if and only if it is shorter than any computer program that can produce that string this basically means that random strings are those that cannot be compressed. Statistical Randomness A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal die roll, or the digits of Pi (as far as we can tell) exhibit statistical randomness.

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Cryptography and Network Security 6 Inherent non-randomness Because any PRNG run on a deterministic computer (contrast quantum computer) is deterministic, its output will inevitably have certain properties that a true random sequence would not exhibit. guaranteed periodicity—it is certain that if the generator uses only
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chapter-10 - CS549 Cryptography and Network Security by...

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