Hardware implementation of elliptic curve cryptosystem over GF(PM)

Ilker Yavuz; Berna Ors

Hardware implementation of elliptic curve cryptosystem over GF(P^M)

Department of Electronics and Communication Engineering

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

Abstract

This paper describes an efficient FPGA implementation for modular multiplication operation in the field GF (p^M) that is suitable for implementing Elliptic Curve Cryptosystems. We have developed a systolic array implementation of a Montgomery modular multiplication (MMM). This implementation is efficient for large finite fields (m =160 - 193 bit) that offer a high security level. Also our implementation is independent of reduction polynomial because of MMM technique. We have specialized to fields GF (3^M) and provide implementation results. We choose m = 97 to compare our results with previous elliptic curve implementations that use different multiplication techniques. In contrast to earlier works, Montgomery multiplication technique has never been used in the field GF (p^M).

Original language	English
Title of host publication	Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007
Publisher	Tafford Publishing
Pages	24-33
Number of pages	10
ISBN (Print)	9781425141097
Publication status	Published - 2008
Event	1st International Conference on Security of Information and Networks, SIN 2007 - Gazimagusa, Turkey Duration: 7 May 2007 → 10 May 2007

Publication series

Name	Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007

Conference

Conference	1st International Conference on Security of Information and Networks, SIN 2007
Country/Territory	Turkey
City	Gazimagusa
Period	7/05/07 → 10/05/07

Keywords

Elliptic Curve
FPGA
Montgomery
Systolic Array

Cite this

Yavuz, I., & Ors, B. (2008). Hardware implementation of elliptic curve cryptosystem over GF(P^M). In Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007 (pp. 24-33). (Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007). Tafford Publishing.

Yavuz, Ilker ; Ors, Berna. / Hardware implementation of elliptic curve cryptosystem over GF(P^M). Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007. Tafford Publishing, 2008. pp. 24-33 (Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007).

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title = "Hardware implementation of elliptic curve cryptosystem over GF(PM)",

abstract = "This paper describes an efficient FPGA implementation for modular multiplication operation in the field GF (pM) that is suitable for implementing Elliptic Curve Cryptosystems. We have developed a systolic array implementation of a Montgomery modular multiplication (MMM). This implementation is efficient for large finite fields (m =160 - 193 bit) that offer a high security level. Also our implementation is independent of reduction polynomial because of MMM technique. We have specialized to fields GF (3M) and provide implementation results. We choose m = 97 to compare our results with previous elliptic curve implementations that use different multiplication techniques. In contrast to earlier works, Montgomery multiplication technique has never been used in the field GF (pM).",

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author = "Ilker Yavuz and Berna Ors",

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booktitle = "Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007",

note = "1st International Conference on Security of Information and Networks, SIN 2007 ; Conference date: 07-05-2007 Through 10-05-2007",

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Yavuz, I & Ors, B 2008, Hardware implementation of elliptic curve cryptosystem over GF(P^M). in Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007. Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007, Tafford Publishing, pp. 24-33, 1st International Conference on Security of Information and Networks, SIN 2007, Gazimagusa, Turkey, 7/05/07.

Hardware implementation of elliptic curve cryptosystem over GF(P^M). / Yavuz, Ilker; Ors, Berna.
Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007. Tafford Publishing, 2008. p. 24-33 (Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007).

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

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AU - Ors, Berna

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N2 - This paper describes an efficient FPGA implementation for modular multiplication operation in the field GF (pM) that is suitable for implementing Elliptic Curve Cryptosystems. We have developed a systolic array implementation of a Montgomery modular multiplication (MMM). This implementation is efficient for large finite fields (m =160 - 193 bit) that offer a high security level. Also our implementation is independent of reduction polynomial because of MMM technique. We have specialized to fields GF (3M) and provide implementation results. We choose m = 97 to compare our results with previous elliptic curve implementations that use different multiplication techniques. In contrast to earlier works, Montgomery multiplication technique has never been used in the field GF (pM).

AB - This paper describes an efficient FPGA implementation for modular multiplication operation in the field GF (pM) that is suitable for implementing Elliptic Curve Cryptosystems. We have developed a systolic array implementation of a Montgomery modular multiplication (MMM). This implementation is efficient for large finite fields (m =160 - 193 bit) that offer a high security level. Also our implementation is independent of reduction polynomial because of MMM technique. We have specialized to fields GF (3M) and provide implementation results. We choose m = 97 to compare our results with previous elliptic curve implementations that use different multiplication techniques. In contrast to earlier works, Montgomery multiplication technique has never been used in the field GF (pM).

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KW - Systolic Array

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Yavuz I, Ors B. Hardware implementation of elliptic curve cryptosystem over GF(P^M). In Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007. Tafford Publishing. 2008. p. 24-33. (Security of Information and Networks - Proceedings of the 1st International Conference on Security of Information and Networks, SIN 2007).