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نتیجه جستجو - Finite field arithmetic

تعداد مقالات یافته شده: 2
ردیف عنوان نوع
1 Efficient Hardware Implementation of Finite Field Arithmetic AB + C for Binary Ring-LWE Based Post-Quantum Cryptography
اجرای سخت افزار کارآمد محاسبات میدان محدود AB + C برای رمزنگاری پس کوانتومی مبتنی بر حلقه باینری-LWE-2022
Post-quantum cryptography (PQC) has gained significant attention from the community recently as it is proven that the existing public-key cryptosystems are vulnerable to the attacks launched from the well-developed quantum computers. The finite field arithmetic AB þ C, where A and C are integer polynomials and B is a binary polynomial, is the key component for the binary Ring-learning-with-errors (BRLWE)- based encryption scheme (a low-complexity PQC suitable for emerging lightweight applications). In this paper, we propose a novel hardware implementation of the finite field arithmetic AB þ C through three stages of interdependent efforts: (i) a rigorous mathematical formulation process is presented first; (ii) an efficient hardware architecture is then presented with detailed description; (iii) a thorough implementation has also been given along with the comparison. Overall, (i) the proposed basic structure (u ¼ 1) outperforms the existing designs, e.g., it involves 55.9% less area-delay product (ADP) than [13] for n ¼ 512; (ii) the proposed design also offers very efficient performance in time-complexity and can be used in many future applications.
INDEX TERMS: Binary ring-learning-with-errors | finite field arithmetic | FPGA platform | hardware design | post-quantum cryptography
مقاله انگلیسی
2 An area-efficient bit-serial sequential polynomial basis finite field GF(2m) multiplier
An area-efficient bit-serial sequential polynomial basis finite field GF(2m) multiplier-2019
Many cryptographic and error control coding algorithms rely on finite field arithmetic. Hardware implementation of these algorithms requires an efficient realization of finite field GF(2m) arithmetic operations. Finite field multiplication is complex among the basic arithmetic operations, and it is employed in field exponentiation and inversion operations. Various algorithms and architectures are proposed in the literature for hardware implementation of finite field multiplication to achieve a reduction in area and delay. In this paper, a modified interleaved modular reduction multiplication algorithm and its bit-serial sequential architecture are proposed. It is observed from the comparison of analytical results that the proposed architecture achieves the reduction in area and area-delay product compared to the existing multipliers. The proposed multiplier achieves an improvement of 39% in area and 17% in area-delay product estimations for field order of 409 when compared with the best sequential multiplier available in the literature. Application specific integrated circuit (ASIC) implementation of the proposed multiplier together with the two most comparable multipliers confirms that the proposed multiplier outperforms in terms of area and area-delay product. The proposed multiplier is suitable for implementation of security in Internet of Things (IoT) gateways and edge-devices.
Keywords: Finite field arithmetic | Polynomial basis | Bit-serial multiplier | Elliptic curve cryptography | Internet of Things (IoT)
مقاله انگلیسی
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بازدید امروز: 12877 :::::::: بازدید دیروز: 0 :::::::: بازدید کل: 12877 :::::::: افراد آنلاین: 87