R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from any one-way function. In 21st Annual ACM Symposium on Theory of Computing, pages 12-24, 1989. 60  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to encrypt a message m, one can 38 expand the key K using a pseudo random bit generator to obtain a one time pad of length jmj, and then compute m . A pseudo random bit generator can be built from an arbitrary one way permutation [GL89] or even from an arbitrary one way function [ILL89, HILL99]. These constructions, however, are not very practical. In a practical implementation, it is perfectly reasonable to stretch the key K by using it as the key to a dedicated block cipher, and then evaluate the block cipher at successive points (so called counter mode ) to obtain a sequence of ....

.... all 2 Z 0 , for all [ G; G; g; q] 2 [S ] for all a; b; b 0 2 G with b 6= b 0 , the distribution f(KDF ; dk (a; b) KDF ; dk (a; b 0 ) dk R KDF.KeySpace ; g is the uniform distribution over all pairs of bits strings of length KDF.OutLen( By the Leftover Hash Lemma [ILL89, IZ89], it follows that if KDF is pair wise independent, then for all 0 1 valued, probabilistic, polynomial time algorithms A, for all 2 Z 0 , and all [ G; G; g; q] 2 [S ] AdvDist KDF;A ( j ) 2 k ; where k = b blog 2 qc KDF.OutLen( 2 c: We also point out that fairly ecient pair wise ....

R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from any one-way function. In 21st Annual ACM Symposium on Theory of Computing, pages 12-24, 1989. 60

....the same length as m that is computationally indistinguishable from a random bit string of the same length. One way to implement F is as follows. First, hash the 1024 bit encoding of h r down to, say, 56 bits using a random but publicly known 2 universal hash function. The left over hash lemma [9] would imply that these 56 bits are fairly close to random. We can then use these 56 bits as a DES key, and generate as many pseudo random bits as we need using DES in counter mode. The security proof would then require the assumption that DES is a good pseudo random permutation, which is quite ....

R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from any one-way function. In 21st Annual ACM Symposium on Theory of Computing, pages 12--24, 1989.

....h r to an l bit string with a public 2 universal hash function. For the hash function H used in the encryption scheme, something like SHA 1, possibly keyed, would be appropriate. The security of this variant is easily proved using the techniques of this paper, along with the left over hash lemma [15], assuming the cipher C is semantically secure. 5.3 A hash free variant We can actually eliminate the hash function H from the scheme, so that the security can be based strictly on the Diffie Hellman decision problem for an arbitrary group G. Suppose the strings we need to hash in the original ....

R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from any one-way function. In 21st Annual ACM Symposium on Theory of Computing, pages 12--24, 1989.

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Impagliazzo, R., L.A. Levin and M. Luby, "Pseudorandom Number Generation from any OneWay Function", Proc. 21st ACM Symp. on Theory of Computing, 1989, pp. 12--24.

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R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from any one-way function. In 21st Annual ACM Symposium on Theory of Computing, pages 12-24, 1989. 60

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