### Abstract

New FPGA architectures for the ordinary Montgomery multiplication algorithm and the FIOS modular multiplication algorithm are presented. The embedded 18×18-bit multipliers and fast carry look-ahead logic located on the Xilinx Virtex2 Pro family of FPGAs are used to perform the ordinary multiplications and additions/subtractions required by these two algorithms. The architectures are developed for use in Elliptic Curve Cryptosystems over GF(p), which require modular field multiplication to perform elliptic curve point addition and doubling. Field sizes of 128-bits and 256-bits are chosen but other field sizes can easily be accommodated, by rapidly reprogramming the FPGA. Overall, the larger the word size of the multiplier, the more efficiently it performs in terms of area/time product. Also, the FIOS algorithm is flexible in that one can tailor the multiplier architecture is to be area efficient, time efficient or a mixture of both by choosing a particular word size. It is estimated that the computation of a 256-bit scalar point multiplication over GF(p) would take about 4.8 ms.

Original language | English |
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Pages | 509-512 |

Number of pages | 4 |

Publication status | Published - 01 Jan 2004 |

Event | IEEE International Symposium on Circuits and Systems - Vancouver, Canada Duration: 01 May 2004 → 01 May 2004 |

### Conference

Conference | IEEE International Symposium on Circuits and Systems |
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Country | Canada |

City | Vancouver |

Period | 01/05/2004 → 01/05/2004 |

### Bibliographical note

Copyright 2008 Elsevier B.V., All rights reserved.## Fingerprint Dive into the research topics of 'FPGA montgomery modular multiplication architectures suitable for ECCs over GF(p)'. Together they form a unique fingerprint.

## Cite this

McIvor, C., McLoone, M., & McCanny, J. V. (2004).

*FPGA montgomery modular multiplication architectures suitable for ECCs over GF(p)*. 509-512. Paper presented at IEEE International Symposium on Circuits and Systems, Vancouver, Canada.