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

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