High Performance SM2 Elliptic Curve Cryptographic Processor over GF(p)

Hu, Xianghong; Cai, Shuting; Zhan, Ruidian; Xiong, Xiaoming

doi:10.23919/chicc.2019.8865908

Cited by 8 publications

(18 citation statements)

References 20 publications

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“…Mapping occurs when the encoded message is assigned to the parameter x i and there exists a corresponding y i , such that (x i , y i ) ∈ E p (a, b). If there is no corresponding y i , then x i is incremented by 1 until a corresponding y i is identified [53]- [55]. Thus, many schemes append certain bits to the message to avoid changing x i , attempting to find the corresponding y i .…”

Section: ) Mapping the Message To An Elliptic Curvementioning

confidence: 99%

SE-Enc: A Secure and Efficient Encoding Scheme Using Elliptic Curve Cryptography

Almajed

Almogren

2019

IEEE Access

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Many applications use asymmetric cryptography to secure communications between two parties. One of the main issues with asymmetric cryptography is the need for vast amounts of computation and storage. While this may be true, elliptic curve cryptography (ECC) is an approach to asymmetric cryptography used widely in low computation devices due to its effectiveness in generating small keys with a strong encryption mechanism. The ECC decreases power consumption and increases device performance, thereby making it suitable for a wide range of devices, ranging from sensors to the Internet of things (IoT) devices. It is necessary for the ECC to have a strong implementation to ensure secure communications, especially when encoding a message to an elliptic curve. It is equally important for the ECC to secure the mapping of the message to the curve used in the encryption. This work objective is to propose a trusted and proofed scheme that offers authenticated encryption (AE) for both encoding and mapping a message to the curve. In addition, this paper provides analytical results related to the security requirements of the proposed scheme against several encryption techniques. Additionally, a comparison is undertaken between the SE-Enc and other state-of-the-art encryption schemes to evaluate the performance of each scheme.

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Section: ) Mapping the Message To An Elliptic Curvementioning

confidence: 99%

SE-Enc: A Secure and Efficient Encoding Scheme Using Elliptic Curve Cryptography

Almajed

Almogren

2019

IEEE Access

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“…Besides high-speed, our method also supports multi-curve domain parameters. For instance, different standards (e.g., P-256 from NIST [ 8 ], secp256k1 from SECG [ 37 ], SCA-256 from SM2 [ 38 ], and Brainpool256 from the German Brainpool standard [ 39 ]) would be able to be implemented with just a single ECC processor. Moreover, our processor does not incur any additional costs besides BRAMs when adding support for different curves.…”

Section: Hardware Implementation Results and Discussionmentioning

confidence: 99%

High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA

Awaludin

Larasati

Kim

2021

Sensors

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In this paper, we present a high-speed, unified elliptic curve cryptography (ECC) processor for arbitrary Weierstrass curves over GF(p), which to the best of our knowledge, outperforms other similar works in terms of execution time. Our approach employs the combination of the schoolbook long and Karatsuba multiplication algorithm for the elliptic curve point multiplication (ECPM) to achieve better parallelization while retaining low complexity. In the hardware implementation, the substantial gain in speed is also contributed by our n-bit pipelined Montgomery Modular Multiplier (pMMM), which is constructed from our n-bit pipelined multiplier-accumulators that utilizes digital signal processor (DSP) primitives as digit multipliers. Additionally, we also introduce our unified, pipelined modular adder/subtractor (pMAS) for the underlying field arithmetic, and leverage a more efficient yet compact scheduling of the Montgomery ladder algorithm. The implementation for 256-bit modulus size on the 7-series FPGA: Virtex-7, Kintex-7, and XC7Z020 yields 0.139, 0.138, and 0.206 ms of execution time, respectively. Furthermore, since our pMMM module is generic for any curve in Weierstrass form, we support multi-curve parameters, resulting in a unified ECC architecture. Lastly, our method also works in constant time, making it suitable for applications requiring high speed and SCA-resistant characteristics.

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“…s3 � (c14, 0, 0, c14, c14, 0, c14, c14); s4 � (c13, 0, 0, 0, c13, 0, c13, c13); s5 � (c12, 0, c15, 0, 0, 0, c15, c15); s6 � (c11, c11, c13, c13, c11, 0, c11, c11); s7 � (c10, c15, c10, 0, 0, 0, c10, c10); s8 � (c9, c14, c14, c15, c15, 0, c9, c9); s9 � (c8, 0, 0, c9, c8, 0, 0, 0); s10 � (0, 0, 0, c12, c12, 0, c12, c12); s11 � (0, 0, 0, 0, c14, c14, 0, 0); s12 � (0, 0, 0, 0, 0, c9, 0, c8); s13 � (0, 0, 0, 0, 0, c13, c13, 0); s14 � (0, 0, 0, 0, 0, c8, 0, c8); subtraction and two extra half-word additions. While the KO algorithm presented in [11] requires six cycles, the KO algorithm presented in [27] requires only five cycles, shown in Algorithm 4.…”

Section: Integer Multiplicationmentioning

confidence: 99%

“…A series of ECADD and ECDBL operations make up PM. For no-idle cycles, a good ECADD and ECDBL algorithm proposed in [27] is chosen for this architecture, given as Algorithm 5 below. e algorithm has three advantages.…”

Section: Point Addition and Point Doublingmentioning

confidence: 99%

A High-Speed Elliptic Curve Cryptography Processor for Teleoperated Systems Security

Xiao¹,

Lin²,

Zhao³

et al. 2021

Mathematical Problems in Engineering

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Teleoperated robotic systems are those in which human operators control remote robots through a communication network. The deployment and integration of teleoperated robot’s systems in the medical operation have been hampered by many issues, such as safety concerns. Elliptic curve cryptography (ECC), an asymmetric cryptographic algorithm, is widely applied to practical applications because its far significantly reduced key length has the same level of security as RSA. The efficiency of ECC on GF (p) is dictated by two critical factors, namely, modular multiplication (MM) and point multiplication (PM) scheduling. In this paper, the high-performance ECC architecture of SM2 is presented. MM is composed of multiplication and modular reduction (MR) in the prime field. A two-stage modular reduction (TSMR) algorithm in the SCA-256 prime field is introduced to achieve low latency, which avoids more iterative subtraction operations than traditional algorithms. To cut down the run time, a schedule is put forward when exploiting the parallelism of multiplication and MR inside PM. Synthesized with a 0.13 um CMOS standard cell library, the proposed processor consumes 341.98k gate areas, and each PM takes 0.092 ms.

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High Performance SM2 Elliptic Curve Cryptographic Processor over GF(p)

Cited by 8 publications

References 20 publications

SE-Enc: A Secure and Efficient Encoding Scheme Using Elliptic Curve Cryptography

SE-Enc: A Secure and Efficient Encoding Scheme Using Elliptic Curve Cryptography

High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA

A High-Speed Elliptic Curve Cryptography Processor for Teleoperated Systems Security

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