## Abstract

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)?

Original language | English |
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Pages (from-to) | 4-10 |

Number of pages | 7 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E78-A |

Issue number | 1 |

Publication status | Published - 1995 Jan 1 |

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics