s-prf - PSEUDO-RANDOM FUNCTIONS 1 65 Recall We studied...

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Unformatted text preview: PSEUDO-RANDOM FUNCTIONS 1 / 65 Recall We studied security of a block cipher against key recovery. But we saw that security against key recovery is not sufficient to ensure that natural usages of a block cipher are secure. We want to answer the question: What is a good block cipher? where “good” means that natural uses of the block cipher are secure. We could try to define “good” by a list of necessary conditions: • Key recovery is hard • Recovery of M from C = E K ( M ) is hard • . . . But this is neither necessarily correct nor appealing. 2 / 65 Turing Intelligence Test Q: What does it mean for a program to be “intelligent” in the sense of a human? 3 / 65 Turing Intelligence Test Q: What does it mean for a program to be “intelligent” in the sense of a human? Possible answers: • It can be happy • It recognizes pictures • It can multiply • But only small numbers! • • 3 / 65 Turing Intelligence Test Q: What does it mean for a program to be “intelligent” in the sense of a human? Possible answers: • It can be happy • It recognizes pictures • It can multiply • But only small numbers! • • Clearly, no such list is a satisfactory answer to the question. 3 / 65 Turing Intelligence Test Q: What does it mean for a program to be “intelligent” in the sense of a human? Turing’s answer: A program is intelligent if its input/output behavior is indistinguishable from that of a human. 4 / 65 Turing Intelligence Test Behind the wall: • Room 1: The program P • Room 0: A human 5 / 65 Turing Intelligence Test Game: • Put tester in room 0 and let it interact with object behind wall • Put tester in rooom 1 and let it interact with object behind wall • Now ask tester: which room was which? 6 / 65 Turing Intelligence Test Game: • Put tester in room 0 and let it interact with object behind wall • Put tester in rooom 1 and let it interact with object behind wall • Now ask tester: which room was which? The measure of “intelligence” of P is the extent to which the tester fails. 6 / 65 Turing Intelligence Test Game: • Put tester in room 0 and let it interact with object behind wall • Put tester in rooom 1 and let it interact with object behind wall • Now ask tester: which room was which? Clarification: Room numbers are in our head, not written on door! 7 / 65 Real versus Ideal Notion Real object Ideal object Intelligence Program Human PRF Block cipher ? 8 / 65 Real versus Ideal Notion Real object Ideal object Intelligence Program Human PRF Block cipher Random function 8 / 65 Random functions A random function with L-bit outputs is implemented by the following box Fn , where T is initially ⊥ everywhere: Fn Caller x a45 T[ x ] a27 If T[ x ] = ⊥ then T[ x ] $ ←{ , 1 } L Return T[ x ] 9 / 65 Random function Game Rand { , 1 } L procedure Fn (x) if T[ x ] = ⊥ then T[ x ] $ ←{ , 1 } L return T[ x ] Adversary A • Make queries to Fn • Eventually halts with some output We denote by Pr bracketleftBig Rand A { , 1 } l ⇒ d bracketrightBig the probability that A outputs d 10 / 65 Random function...
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This note was uploaded on 10/10/2010 for the course CSE CSE107 taught by Professor Bellare during the Spring '10 term at UCSD.

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s-prf - PSEUDO-RANDOM FUNCTIONS 1 65 Recall We studied...

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