Efficient Hardware Implementation of Finite Field Arithmetic AB+CAB+C for Binary Ring-LWE Based Post-Quantum Cryptography

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 <inline-formula><tex-math not...

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Vydáno v:IEEE transactions on emerging topics in computing Ročník 10; číslo 2; s. 1222 - 1228
Hlavní autoři: Xie, Jiafeng, He, Pengzhou, Wang, Xiaofang, Imana, Jose L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.04.2022
Témata:
Binary ring-learning-with-errors
Complexity theory
Computer architecture
Computers
Encryption
finite field arithmetic
FPGA platform
Hardware
hardware design
Lead
post-quantum cryptography
Time complexity
ISSN:2168-6750
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Shrnutí: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 <inline-formula><tex-math notation="LaTeX">AB+C</tex-math> <mml:math><mml:mrow><mml:mi>A</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="xie-ieq3-3091982.gif"/> </inline-formula>, where <inline-formula><tex-math notation="LaTeX">A</tex-math> <mml:math><mml:mi>A</mml:mi></mml:math><inline-graphic xlink:href="xie-ieq4-3091982.gif"/> </inline-formula> and <inline-formula><tex-math notation="LaTeX">C</tex-math> <mml:math><mml:mi>C</mml:mi></mml:math><inline-graphic xlink:href="xie-ieq5-3091982.gif"/> </inline-formula> are integer polynomials and <inline-formula><tex-math notation="LaTeX">B</tex-math> <mml:math><mml:mi>B</mml:mi></mml:math><inline-graphic xlink:href="xie-ieq6-3091982.gif"/> </inline-formula> 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 <inline-formula><tex-math notation="LaTeX">AB+C</tex-math> <mml:math><mml:mrow><mml:mi>A</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="xie-ieq7-3091982.gif"/> </inline-formula> 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 (<inline-formula><tex-math notation="LaTeX">u=1</tex-math> <mml:math><mml:mrow><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="xie-ieq8-3091982.gif"/> </inline-formula>) outperforms the existing designs, e.g., it involves 55.9% less area-delay product (ADP) than [13] for <inline-formula><tex-math notation="LaTeX">n=512</tex-math> <mml:math><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>512</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="xie-ieq9-3091982.gif"/> </inline-formula>; (ii) the proposed design also offers very efficient performance in time-complexity and can be used in many future applications.
ISSN:2168-6750
DOI:10.1109/TETC.2021.3091982