Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards Curve
With the swift evolution of wireless technologies, the demand for the Internet of Things (IoT) security is rising immensely. Elliptic curve cryptography (ECC) provides an attractive solution to fulfill this demand. In recent years, Edwards curves have gained widespread acceptance in digital signatur...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/20/18/5148 |
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| author | Md. Mainul Islam Md. Selim Hossain Moh. Khalid Hasan Md. Shahjalal Yeong Min Jang |
| author_facet | Md. Mainul Islam Md. Selim Hossain Moh. Khalid Hasan Md. Shahjalal Yeong Min Jang |
| author_sort | Md. Mainul Islam |
| collection | DOAJ |
| description | With the swift evolution of wireless technologies, the demand for the Internet of Things (IoT) security is rising immensely. Elliptic curve cryptography (ECC) provides an attractive solution to fulfill this demand. In recent years, Edwards curves have gained widespread acceptance in digital signatures and ECC due to their faster group operations and higher resistance against side-channel attacks (SCAs) than that of the Weierstrass form of elliptic curves. In this paper, we propose a high-speed, low-area, simple power analysis (SPA)-resistant field-programmable gate array (FPGA) implementation of ECC processor with unified point addition on a twisted Edwards curve, namely Edwards25519. Efficient hardware architectures for modular multiplication, modular inversion, unified point addition, and elliptic curve point multiplication (ECPM) are proposed. To reduce the computational complexity of ECPM, the ECPM scheme is designed in projective coordinates instead of affine coordinates. The proposed ECC processor performs 256-bit point multiplication over a prime field in 198,715 clock cycles and takes 1.9 ms with a throughput of 134.5 kbps, occupying only 6543 slices on Xilinx Virtex-7 FPGA platform. It supports high-speed public-key generation using fewer hardware resources without compromising the security level, which is a challenging requirement for IoT security. |
| first_indexed | 2024-03-10T16:26:50Z |
| format | Article |
| id | doaj.art-cf3ed541edbf46ca8788531541ac5066 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T16:26:50Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-cf3ed541edbf46ca8788531541ac50662023-11-20T13:09:36ZengMDPI AGSensors1424-82202020-09-012018514810.3390/s20185148Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards CurveMd. Mainul Islam0Md. Selim Hossain1Moh. Khalid Hasan2Md. Shahjalal3Yeong Min Jang4Department of Electronics Engineering, Kookmin University, Seoul 02707, KoreaDepartment of Electrical and Electronic Engineering, Khulna University of Engineering & Technology (KUET), Khulna 9203, BangladeshDepartment of Electronics Engineering, Kookmin University, Seoul 02707, KoreaDepartment of Electronics Engineering, Kookmin University, Seoul 02707, KoreaDepartment of Electronics Engineering, Kookmin University, Seoul 02707, KoreaWith the swift evolution of wireless technologies, the demand for the Internet of Things (IoT) security is rising immensely. Elliptic curve cryptography (ECC) provides an attractive solution to fulfill this demand. In recent years, Edwards curves have gained widespread acceptance in digital signatures and ECC due to their faster group operations and higher resistance against side-channel attacks (SCAs) than that of the Weierstrass form of elliptic curves. In this paper, we propose a high-speed, low-area, simple power analysis (SPA)-resistant field-programmable gate array (FPGA) implementation of ECC processor with unified point addition on a twisted Edwards curve, namely Edwards25519. Efficient hardware architectures for modular multiplication, modular inversion, unified point addition, and elliptic curve point multiplication (ECPM) are proposed. To reduce the computational complexity of ECPM, the ECPM scheme is designed in projective coordinates instead of affine coordinates. The proposed ECC processor performs 256-bit point multiplication over a prime field in 198,715 clock cycles and takes 1.9 ms with a throughput of 134.5 kbps, occupying only 6543 slices on Xilinx Virtex-7 FPGA platform. It supports high-speed public-key generation using fewer hardware resources without compromising the security level, which is a challenging requirement for IoT security.https://www.mdpi.com/1424-8220/20/18/5148elliptic curve cryptography (ECC)elliptic curve point multiplication (ECPM)twisted Edwards curveunified point additionsimple power analysis (SPA) attacks |
| spellingShingle | Md. Mainul Islam Md. Selim Hossain Moh. Khalid Hasan Md. Shahjalal Yeong Min Jang Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards Curve Sensors elliptic curve cryptography (ECC) elliptic curve point multiplication (ECPM) twisted Edwards curve unified point addition simple power analysis (SPA) attacks |
| title | Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards Curve |
| title_full | Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards Curve |
| title_fullStr | Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards Curve |
| title_full_unstemmed | Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards Curve |
| title_short | Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards Curve |
| title_sort | design and implementation of high performance ecc processor with unified point addition on twisted edwards curve |
| topic | elliptic curve cryptography (ECC) elliptic curve point multiplication (ECPM) twisted Edwards curve unified point addition simple power analysis (SPA) attacks |
| url | https://www.mdpi.com/1424-8220/20/18/5148 |
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