## Abstract

Raising alpha **x to the yth power over GF(q**n) can be performed by calculating alpha **y modulo the minimum polynomial of alpha **x and then multiplying the result by an n multiplied by n matrix over GF(q). The elements of the matrix are only a function of x and of the generating polynomial of the field. This principle offers a time-memory trade-off when exponentiating a fixed element of GF(q**n), where the multiplications (not the squarings) involved in the standard square-and-multiply process are traded for a reference to a stored n multiplied by n matrix. The operations which make use of the stored data consume time which is equivalent to a single multiplication operation over the field, and are performed continuously, where the time-consuming part of the exponentiation process is performed independently of the stored data. It is then shown how the presented principle enables an efficient implementation over GF(q**n) of some variations of Diffie-Hellman public-key distribution system.

Original language | English |
---|---|

Pages (from-to) | 148-150 |

Number of pages | 3 |

Journal | IEE Proceedings E: Computers and Digital Techniques |

Volume | 131 |

Issue number | 4 |

DOIs | |

State | Published - 1 Jan 1984 |

## ASJC Scopus subject areas

- General Computer Science
- General Engineering

## Fingerprint

Dive into the research topics of 'TIME-MEMORY TRADEOFF IN EXPONENTIATING A FIXED ELEMENT OF GF(q^{n}) REQUIRING A SHORT REFERENCE TO THE MEMORY.'. Together they form a unique fingerprint.