A popular methodology for designing cryptographic protocols consists of the following two steps. One first designs an ideal system in which all parties (including the adversary) have oracle access to a truly random function, and proves the security of this ideal system. Next, one replaces the random oracle by a “good cryptographic hashing function” (such as MD5 or SHA), providing all parties (including the adversary) with a succinct description of this function. Thus, one obtains an implementation of the ideal system in a “real-world” where random oracles do not exist. This methodology, explicitly formulated by Bellare and Rogaway [5] and hereafter referred to as the random oracle methodology, has been used in many works (see, for example, [14, 35, 23, 32, 5, 27,6, 33]).
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