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Low area-time complexity point multiplication architecture for ECC over GF(\(2^{\textrm{m}}\)) using polynomial basis

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Abstract

In the present day, billions of devices communicate over the wireless networks. The massive information transmitted over open ended, and unsecured Internet architecture results in eavesdropping of private, sensitive and confidential information. Therefore, it is necessary to incorporate some data encryption techniques while communicating any sensitive information. Public key cryptography is one of the widely used data encryption technique, and elliptic curve cryptography (ECC) is the most-sought after public key cryptographic algorithm. The efficiency of ECC depends on a series of hierarchical finite field operations, and point multiplication is one of the most time-critical and resource-consuming ECC operation. Point multiplication involves a substantial number of multiplications, additions and inversion operations over finite fields of higher orders. In this article, we present a point multiplication architecture developed for a modified Montgomery-ladder algorithm. A digit-serial multiplier is employed to perform multiplication in the realization of the modified Montgomery-ladder algorithm. The area and time complexities of the proposed elliptic curve point multiplication (ECPM) architecture are computed for irreducible pentanomial GF(2\(^{163}\)) and irreducible trinomial GF(2\(^{233}\)) targeting Virtex-5(XC5VLX110) FPGA and compared with the similar architectures available in the literature.

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The authors have no financial or proprietary interests in any material discussed in this article.

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Authors and Affiliations

  1. Electronics and Communication Engineering, National Institute of Technology, Warangal, Telangana, 506001, India

    Pradeep Kumar Goud Nadikuda & Lakshmi Boppana

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  1. Pradeep Kumar Goud Nadikuda
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  2. Lakshmi Boppana
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by all the authors. The first draft of the manuscript was written by PKG Nadikuda, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Pradeep Kumar Goud Nadikuda.

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Nadikuda, P.K.G., Boppana, L. Low area-time complexity point multiplication architecture for ECC over GF(\(2^{\textrm{m}}\)) using polynomial basis. J Cryptogr Eng 13, 107–123 (2023). https://doi.org/10.1007/s13389-022-00302-0

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