Validation of Multipliers for Elements of Extended Galois Fields GF(pn) and Multipliers VHDL-descriptions Generator

This article discusses a VHDL-description (IPcore generator, IP - intellectual property) generator developed by the authors for multiplication of elements in extended Galois fields \mathrm{GF(p^{n}}). Such multipliers are used in information security systems based on elliptic curves. This generator...

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Bibliographic Details
Main Authors: Zholubak, Ivan, Hlukhov, Valeriy
Format: Conference Proceeding
Language:English
Subjects:
Computer science
Elliptic curves
field characteristic
GaloisCPP
Generators
Information security
Intellectual property
IP-core generator
Libraries
multiplier
the order of the generating polynomial
VHDL
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Summary:This article discusses a VHDL-description (IPcore generator, IP - intellectual property) generator developed by the authors for multiplication of elements in extended Galois fields \mathrm{GF(p^{n}}). Such multipliers are used in information security systems based on elliptic curves. This generator simplifies the process of generating VHDL-descriptions for multipliers utilizing modified Guild cells that are interconnected. The count of modified Guild cells can reach 2^{999}. The evaluation of the generated multipliers' performance is presented for Galois fields: GF(3^{30}),GF(7^{17}),GF(23^{10}), and GF(53^{8}), which exhibit similar orders. The testing procedure involved simulations within the Active HDL environment, with the simulation outcomes being compared to the multiplication results obtained through the GaloisCPP C++ library.
ISSN:2766-3639
DOI:10.1109/CSIT61576.2023.10324200