One-Way Functions over Finite Near-Rings

概要

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A near-ring is an extended notion of a usual ring. Therefore a ring is a near-ring, but the converse does not necessarily hold. We investigate in this paper one-way functions associated with finite near-rings, and show that if there exists a one-way group homomorphism, there exists a one-way non-ring near-ring homomorphism (Theorem 1) ; if there exists a one-way ring homomorphism, there exists a one-way non-ring near-ring homomorphism (Theorem 2). Further, we introduce a discrete logarithm problem over a finite near-ring, and show that the integer factoring is probabilistic polynomial-time Turing equivalent to a modified version of this problem (Theorem 3). Theorem 1 implies that under some standard cryptographic assumption, there is an affirmative but trivial solution to the extended version of the open question : Is there an encryption function f such that both f(x+y) and f(xy) are efficiently computed from given f(x) and f(y)?
社団法人電子情報通信学会の論文
1995-01-25