On the Power of the Randomized Iterate
SIAM Journal on Computing
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Many of the results in Modern Cryptography are actually transformations of a basic computational phenomenon (i.e., a basic primitive, tool or assumption) to a more complex phenomenon (i.e., a higher level primitive or application). The transformation is explicit and is always accompanied by an explicit reduction of the violation of the security of the former phenomenon to the violation of the latter. A key aspect is the efficiency of the reduction. We discuss and slightly modify the hierarchy of reductions originally suggested by Levin.