Abstract
Most cipher systems designed thus far are binary-valued or integer-valued cipher systems. Their security relies on the assumption that one-way functions exist. Though the existence of one-way functions has not been proved yet, most cryptographic researchers believe that one-way functions exist. In addition, many candidates for one-way functions have been proposed. Therefore, the key step for developing real-valued cipher systems is to define real one-way functions and to propose candidates for them. In this paper, based on computational complexity theory over the real field, we give two definitions of real one-way functions; one is for digital one-way functions and the other is for general one-way functions. Candidates for these two classes of one-way functions are also proposed. Moreover, we present two examples to demonstrate that the candidates for both digital one-way functions and general one-way functions can be applied to construct secure real-valued cipher systems.
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