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Accelerating Square Root Computations Over Large GF (2m)

Topics: Applied Cryptography; Data Integrity; Data Protection; Database Security and Privacy; Formal Methods for Security; Identification, Authentication and Non-Repudiation; Network Security; Network Security; Privacy; Security and Privacy in Web Services; Security in Distributed Systems; Security Metrics and Measurement; Security Protocols; Security Verification and Validation; Sensor and Mobile Ad Hoc Network Security; Service and Systems Design and Qos Network Security; Software Security; Wireless Network Security

Authors: Salah Harb and Moath Jarrah

Affiliation: Jordan University of Science and Technology, Jordan

ISBN: 978-989-758-259-2

Keyword(s): Cryptosystems, computation, elliptic curve cryptography, Galois field, hardware implementation, square root.

Related Ontology Subjects/Areas/Topics: Applied Cryptography ; Cloud Computing ; Cryptographic Techniques and Key Management ; Data and Application Security and Privacy ; Data Engineering ; Data Integrity ; Data Protection ; Database Security and Privacy ; Databases and Data Security ; Formal Methods for Security ; Identification, Authentication and Non-Repudiation ; Information and Systems Security ; Network Security ; Privacy ; Security and Privacy in Web Services ; Security in Distributed Systems ; Security in Information Systems ; Security Metrics and Measurement ; Security Protocols ; Security Verification and Validation ; Sensor and Mobile Ad Hoc Network Security ; Service and Systems Design and Qos Network Security ; Services Science ; Software Security ; Wireless Network Security

Abstract: The communication networks of low-resources applications require implementing cryptographic protocols and operations with less computational and architectural complexities. In this paper, an efficient method for high speed calculations of square (SQR) root is proposed over Galois Fields GF (2m). The method is based on using the results of certain pre-computations, and transforming the SQR root calculations into a system of linear equations. The computational complexity of our proposed method for computing the SQR root in GF (2m) is O(m) which is significantly better than existing methods such as Tonelli-Shanks and Cipolla. Our proposed method was implemented using different types of multipliers over several polynomial degrees. Software and hardware implementations were developed in NTL-C++ and VHDL, respectively. Our software experimental results show up to 38 times faster than Doliskani & Schost method. Moreover, our method is 840 times faster than Tonelli-Shanks method. In terms of hardware implementation and since Tonelli-Shanks requires less resources than Doliskani & Schost, we compare our method with Tonelli-Shanks. The hardware experimental results show that up to 50% less LUTs with a speedup of 18% that can be obtained compared to Tonelli-Shanks method. (More)

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Paper citation in several formats:
Harb, S. and Jarrah, M. (2017). Accelerating Square Root Computations Over Large GF (2m).In Proceedings of the 14th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2017) ISBN 978-989-758-259-2, pages 229-236. DOI: 10.5220/0006386702290236

@conference{secrypt17,
author={Salah Harb. and Moath Jarrah.},
title={Accelerating Square Root Computations Over Large GF (2m)},
booktitle={Proceedings of the 14th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2017)},
year={2017},
pages={229-236},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006386702290236},
isbn={978-989-758-259-2},
}

TY - CONF

JO - Proceedings of the 14th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2017)
TI - Accelerating Square Root Computations Over Large GF (2m)
SN - 978-989-758-259-2
AU - Harb, S.
AU - Jarrah, M.
PY - 2017
SP - 229
EP - 236
DO - 10.5220/0006386702290236

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