## Abstract

In this paper we discuss the relation between a one-way group homomorphism and a one-way ring homomorphism. Let U, V be finite abelian groups with #U = n. We show that if there exists a one-way group homomorphism f: U → V, then there exists a one-way ring homomorphism F: Z_{n} ⊕ U → Z_{n} ⊕ Im f. We also give examples of such ring homomorphisms which are one-way under a standard cryptographic assumption. This implies that there is an affirmative solution to an extended version of the open question raised by Feigenbaum and Merrit: Is there an encryption function f such that both f(x + y) and f(x · y) can be efficiently computed from f(x) and f(y) ? A multiple signature scheme is also given as an application of one-way ring homomorphisms.

Original language | English |
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Pages (from-to) | 54-60 |

Number of pages | 7 |

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

Volume | E79-A |

Issue number | 1 |

Publication status | Published - 1996 Jan 1 |

## Keywords

- Cryptography
- Homomorphism
- One-way function

## ASJC Scopus subject areas

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