A Novel and High-Performance Modular Square Scheme for Elliptic Curve Cryptography Over GF(${p}$ )

Li, Bing; Lei, Bingjie; Zhang, Yun-Long; Lei, Shaochong

doi:10.1109/tcsii.2018.2867618

Cited by 5 publications

(6 citation statements)

References 12 publications

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“…The design in [33] reaches good performance in terms of area occupation but lower speed with respect to our work. The modular square method proposed in [23] allows good performance and an AT similar to the one achieved by our crypto-processor. The work in [22] is a low hardware consumption design for ECC.…”

Section: Discussion and Comparisonmentioning

confidence: 96%

“…In this case, no experimental results have been provided to test the SPA resistance, but the authors claim their solution works well. Works in [23,33] do not implement any countermeasure against side-channel attacks. The design in [33] reaches good performance in terms of area occupation but lower speed with respect to our work.…”

Section: Discussion and Comparisonmentioning

confidence: 99%

“…Interleaved Modular Multiplication and Binary Modular Inversion algorithms have been used, and the PM algorithm is claimed to be resistant to SPA attacks, but no experimental results have been provided. The design in [23] presents a novel modular squaring scheme that has been synthesized on a 130 nm CMOS technology. It reaches good performance in terms of area and speed, but no side-channel attacks resistance is guaranteed.…”

Section: Related Workmentioning

confidence: 99%

“…The work in [19] is a review paper that shows some guidelines to aid hardware designers in choosing the combination of methods and algorithms for different application classes. Works like [20][21][22][23][24] focus on the acceleration of ECC.…”

Section: Introductionmentioning

confidence: 99%

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Secure Elliptic Curve Crypto-Processor for Real-Time IoT Applications

et al. 2021

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Cybersecurity is a critical issue for Real-Time IoT applications since high performance and low latencies are required, along with security requirements to protect the large number of attack surfaces to which IoT devices are exposed. Elliptic Curve Cryptography (ECC) is largely adopted in an IoT context to provide security services such as key-exchange and digital signature. For Real-Time IoT applications, hardware acceleration for ECC-based algorithms can be mandatory to meet low-latency and low-power/energy requirements. In this paper, we propose a fast and configurable hardware accelerator for NIST P-256/-521 elliptic curves, developed in the context of the European Processor Initiative. The proposed architecture supports the most used cryptography schemes based on ECC such as Elliptic Curve Digital Signature Algorithm (ECDSA), Elliptic Curve Integrated Encryption Scheme (ECIES), Elliptic Curve Diffie-Hellman (ECDH) and Elliptic Curve Menezes-Qu-Vanstone (ECMQV). A modified version of Double-And-Add-Always algorithm for Point Multiplication has been proposed, which allows the execution of Point Addition and Doubling operations concurrently and implements countermeasures against power and timing attacks. A simulated approach to extract power traces has been used to assess the effectiveness of the proposed algorithm compared to classical algorithms for Point Multiplication. A constant-time version of the Shamir’s Trick has been adopted to speed-up the Double-Point Multiplication and modular inversion is executed using Fermat’s Little Theorem, reusing the internal modular multipliers. The accelerator has been verified on a Xilinx ZCU106 development board and synthesized on both 45 nm and 7 nm Standard-Cell technologies.

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Section: Discussion and Comparisonmentioning

confidence: 96%

Section: Discussion and Comparisonmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Secure Elliptic Curve Crypto-Processor for Real-Time IoT Applications

et al. 2021

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“…In [ 16 , 17 ], the fast partial Montgomery reduction algorithm achieved better performance and a more balanced area. In contrast to the majority of works centered on modular multiplication, the authors in [ 18 ] presented a low-complexity modular squaring scheme to decrease the cycle time required for point multiplication. Additionally, some studies focused on binary field curves [ 19 , 20 ], but the NIST- p 256 curve is a better choice because it is a widely adopted and standardized elliptic curve, offering strong security and compatibility with various cryptographic protocols.…”

Section: Introductionmentioning

confidence: 99%

FPGA Implementation for Elliptic Curve Cryptography Algorithm and Circuit with High Efficiency and Low Delay for IoT Applications

Wang

Lin

et al. 2023

Micromachines

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The Internet of Things requires greater attention to the security and privacy of the network. Compared to other public-key cryptosystems, elliptic curve cryptography can provide better security and lower latency with shorter keys, rendering it more suitable for IoT security. This paper presents a high-efficiency and low-delay elliptic curve cryptographic architecture based on the NIST-p256 prime field for IoT security applications. A modular square unit utilizes a fast partial Montgomery reduction algorithm, demanding just a mere four clock cycles to complete a modular square operation. The modular square unit can be computed simultaneously with the modular multiplication unit, consequently improving the speed of point multiplication operations. Synthesized on the Xilinx Virtex-7 FPGA platform, the proposed architecture completes one PM operation in 0.08 ms using 23.1 k LUTs at 105.3 MHz. These results show significantly better performance compared to that in previous works.

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