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In this paper we consider the one-way function f g;N (X) = g X (modN), where N is a Blum integer. We prove that under the commonly assumed intractability of factoring Blum integers, all its bits are individually hard, and the lower as well as upper halves of them are simultaneously hard. As a result, f g;N can be used in eecient pseudo-random bit generators… (More)

In this paper we consider the one-way function fg,N(X) = gX (modN), where N is a Blum integer. We prove that under the commonly assumed intractability of factoring Blum integers, almost all its bits are individually hard, and half of them are simultaneously hard. As a result, fg,N can be used in efficient pseudo-random bit generators and multi-bit… (More)

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