A Primitive for Proving the Security of EveryBit and About Universal Hash Functions & Hard Core

Bit and About Universal Hash Functions & Hard Core Bits Eike Kiltz Lehrstuhl Mathematik & Informatik, Fakult at f ur Mathematik, Ruhr-Universit at Bochum, 44780 Bochum, Germany. Fax:+49-234-3214465 [email protected] Abstract. We present a useful primitive, the hidden number problem, which can be exploited to prove that every bit is a hard core of speci c cryptographic functions. Applications are RSA, ElGamal, Rabin and others. We give an e cient construction of a hard core predicate of any one-way function providing an alternative to the famous GoldreichLevin Bit [3]. Furthermore, a conjectured connection between universal hash functions and hard core predicates is disproven.