Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on Recoding
With the development of mobile communication, digital signatures with low latency, low area, and high security are in increasing demand. Elliptic curve cryptography (ECC) is widely used because of its security and lightweight. Elliptic curve scalar multiplication (ECSM) is the basic arithmetic in EC...
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MDPI AG
2024-10-01
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| author | Zhantao Zhang Weijiang Wang Jingqi Zhang Xiang He Mingzhi Ma Shiwei Ren Hua Dang |
| author_facet | Zhantao Zhang Weijiang Wang Jingqi Zhang Xiang He Mingzhi Ma Shiwei Ren Hua Dang |
| author_sort | Zhantao Zhang |
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| description | With the development of mobile communication, digital signatures with low latency, low area, and high security are in increasing demand. Elliptic curve cryptography (ECC) is widely used because of its security and lightweight. Elliptic curve scalar multiplication (ECSM) is the basic arithmetic in ECC. Based on this background information, we propose our own research objectives. In this paper, a low-latency and low-area ECSM architecture based on the comb algorithm is proposed. The detailed methodology is as follows. The recoding-k algorithm and randomization-Z algorithm are used to improve security, which can resist sample power analysis (SPA) and differential power analysis (DPA). A low-area multi-functional architecture for comb is proposed, which takes into account different stages of the comb algorithm. Based on this, the data dependency is considered and the comb architecture is optimized to achieve a uniform and efficient execution pattern. The interleaved modular multiplication algorithm and modified binary inverse algorithm are used to achieve short clock cycle delay and high frequency while taking into account the need for a low area. The proposed architecture has been implemented on Xilinx Virtex-7 series FPGA to perform ECSM on 256-bits prime field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi><mo>(</mo><mi>p</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In the hardware architecture with only 7351 slices of resource usage, a single ECSM only takes 0.74 ms, resulting in an area-time product (ATP) of 5.41. The implementation results show that our design can compete with the existing state-of-the-art engineering in terms of performance and has higher security. Our design is suitable for computing scenarios where security and computing speed are required. The implementation of the overall architecture is of great significance and inspiration to the research community. |
| format | Article |
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| institution | OA Journals |
| issn | 2072-666X |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
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| series | Micromachines |
| spelling | doaj-art-8b3095f7fbb9463e86193c6c05db4ed22025-08-20T02:11:11ZengMDPI AGMicromachines2072-666X2024-10-011510123810.3390/mi15101238Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on RecodingZhantao Zhang0Weijiang Wang1Jingqi Zhang2Xiang He3Mingzhi Ma4Shiwei Ren5Hua Dang6School of Integrated Circuits and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, ChinaSchool of Integrated Circuits and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, ChinaSchool of Integrated Circuits and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, ChinaSchool of Integrated Circuits and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, ChinaSchool of Integrated Circuits and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, ChinaSchool of Integrated Circuits and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, ChinaSchool of Integrated Circuits and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, ChinaWith the development of mobile communication, digital signatures with low latency, low area, and high security are in increasing demand. Elliptic curve cryptography (ECC) is widely used because of its security and lightweight. Elliptic curve scalar multiplication (ECSM) is the basic arithmetic in ECC. Based on this background information, we propose our own research objectives. In this paper, a low-latency and low-area ECSM architecture based on the comb algorithm is proposed. The detailed methodology is as follows. The recoding-k algorithm and randomization-Z algorithm are used to improve security, which can resist sample power analysis (SPA) and differential power analysis (DPA). A low-area multi-functional architecture for comb is proposed, which takes into account different stages of the comb algorithm. Based on this, the data dependency is considered and the comb architecture is optimized to achieve a uniform and efficient execution pattern. The interleaved modular multiplication algorithm and modified binary inverse algorithm are used to achieve short clock cycle delay and high frequency while taking into account the need for a low area. The proposed architecture has been implemented on Xilinx Virtex-7 series FPGA to perform ECSM on 256-bits prime field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi><mo>(</mo><mi>p</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In the hardware architecture with only 7351 slices of resource usage, a single ECSM only takes 0.74 ms, resulting in an area-time product (ATP) of 5.41. The implementation results show that our design can compete with the existing state-of-the-art engineering in terms of performance and has higher security. Our design is suitable for computing scenarios where security and computing speed are required. The implementation of the overall architecture is of great significance and inspiration to the research community.https://www.mdpi.com/2072-666X/15/10/1238elliptic curve cryptography (ECC)elliptic curve scalar multiplication (ECSM)field-programmable gate array (FPGA)prime field (GF)sample power analysis (SPA) |
| spellingShingle | Zhantao Zhang Weijiang Wang Jingqi Zhang Xiang He Mingzhi Ma Shiwei Ren Hua Dang Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on Recoding Micromachines elliptic curve cryptography (ECC) elliptic curve scalar multiplication (ECSM) field-programmable gate array (FPGA) prime field (GF) sample power analysis (SPA) |
| title | Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on Recoding |
| title_full | Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on Recoding |
| title_fullStr | Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on Recoding |
| title_full_unstemmed | Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on Recoding |
| title_short | Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on Recoding |
| title_sort | area time efficient secure comb scalar multiplication architecture based on recoding |
| topic | elliptic curve cryptography (ECC) elliptic curve scalar multiplication (ECSM) field-programmable gate array (FPGA) prime field (GF) sample power analysis (SPA) |
| url | https://www.mdpi.com/2072-666X/15/10/1238 |
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