### Abstract

For every prime p, there are AT^{2}-optimal VLSI multipliers for Galois fields GF(p^{n}) in standard notation. In fact, the lower bound AT^{2} = Ω(n^{2}) is matched for every computation time T in the range [Ω(log n), 0(√n)]. Similar results hold for variable primes p too. The designs are based on the DFT on a structure similar to Fermat rings. For p=2 the DFT uses 3^{ℓ}-th instead of 2^{ℓ}-th rotts of unity.

Original language | English (US) |
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Title of host publication | VLSl Algorithms and Architectures - Aegean Workshop on Computing, Proceedings |

Editors | Kurt Mehlhorn, Fillia Makedon, T. Papatheodorou, P. Spirakis |

Publisher | Springer Verlag |

Pages | 217-225 |

Number of pages | 9 |

ISBN (Print) | 9783540167662 |

DOIs | |

State | Published - Jan 1 1986 |

Event | Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 1986 - Loutrak, Greece Duration: Jul 8 1986 → Jul 11 1986 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 227 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 1986 |
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Country | Greece |

City | Loutrak |

Period | 7/8/86 → 7/11/86 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

^{2}-optimal galois field multiplier for VLSI. In K. Mehlhorn, F. Makedon, T. Papatheodorou, & P. Spirakis (Eds.),

*VLSl Algorithms and Architectures - Aegean Workshop on Computing, Proceedings*(pp. 217-225). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 227 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-16766-8_19

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^{2}-optimal galois field multiplier for VLSI. in K Mehlhorn, F Makedon, T Papatheodorou & P Spirakis (eds),

*VLSl Algorithms and Architectures - Aegean Workshop on Computing, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 227 LNCS, Springer Verlag, pp. 217-225, Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 1986, Loutrak, Greece, 7/8/86. https://doi.org/10.1007/3-540-16766-8_19

**At ^{2}-optimal galois field multiplier for VLSI.** / Furer, Martin; Mehlhorn, Kurt.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - At2-optimal galois field multiplier for VLSI

AU - Furer, Martin

AU - Mehlhorn, Kurt

PY - 1986/1/1

Y1 - 1986/1/1

N2 - For every prime p, there are AT2-optimal VLSI multipliers for Galois fields GF(pn) in standard notation. In fact, the lower bound AT2 = Ω(n2) is matched for every computation time T in the range [Ω(log n), 0(√n)]. Similar results hold for variable primes p too. The designs are based on the DFT on a structure similar to Fermat rings. For p=2 the DFT uses 3ℓ-th instead of 2ℓ-th rotts of unity.

AB - For every prime p, there are AT2-optimal VLSI multipliers for Galois fields GF(pn) in standard notation. In fact, the lower bound AT2 = Ω(n2) is matched for every computation time T in the range [Ω(log n), 0(√n)]. Similar results hold for variable primes p too. The designs are based on the DFT on a structure similar to Fermat rings. For p=2 the DFT uses 3ℓ-th instead of 2ℓ-th rotts of unity.

UR - http://www.scopus.com/inward/record.url?scp=84919773602&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919773602&partnerID=8YFLogxK

U2 - 10.1007/3-540-16766-8_19

DO - 10.1007/3-540-16766-8_19

M3 - Conference contribution

SN - 9783540167662

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 217

EP - 225

BT - VLSl Algorithms and Architectures - Aegean Workshop on Computing, Proceedings

A2 - Mehlhorn, Kurt

A2 - Makedon, Fillia

A2 - Papatheodorou, T.

A2 - Spirakis, P.

PB - Springer Verlag

ER -

^{2}-optimal galois field multiplier for VLSI. In Mehlhorn K, Makedon F, Papatheodorou T, Spirakis P, editors, VLSl Algorithms and Architectures - Aegean Workshop on Computing, Proceedings. Springer Verlag. 1986. p. 217-225. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-16766-8_19