Abstract. We show that given a PRFG (pseudo-random function generator) G that is (1/nc) -partially secure there exists a polynomial p such that the construction g 1 (x ⊕ r1) ⊕ · ⊕ g p(n) (x ⊕ r p(n) ) produces a strongly secure PRFG, where g i ∈ G and r i are strings of random bits, and the key for the new PRFG is composed of the r i 's and keys for the g i 's. This is the first ``natural'' construction of a (totally secure) PRFG from a partially secure PRFG. Using results of Luby and Rackoff, this result also demonstrates how to construct a PRPG ``naturally'' from a partially secure PRPG.
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Myers, . Efficient Amplification of the Security of Weak Pseudo-Random Function Generators . J. Cryptology 16, 1–24 (2003). https://doi.org/10.1007/s00145-002-0007-1
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DOI: https://doi.org/10.1007/s00145-002-0007-1
- Key words. Pseudo-randomness, Security amplification, Function generators, XOR Lemma.