# Lattice-Based Public-Key Cryptography in HardwareCoprocessor for Koblitz Curves

Lattice-Based Public-Key Cryptography in Hardware: Coprocessor for Koblitz Curves [Koblitz curves [20] are a special class of elliptic-curves which enable very efficient point multiplications and, therefore, they are attractive for hardware and software implementations. However, these efficiency gains can be exploited only by representing scalars as specific \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}-adic expansions. Most cryptosystems require the scalar also as an integer (see, e.g., ECDSA [25]). Therefore, cryptosystems utilizing Koblitz curves need both the integer and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}-adic representations of the scalar, which results in a need for conversions between the two domains.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Lattice-Based Public-Key Cryptography in HardwareCoprocessor for Koblitz Curves

17 pages

/lp/springer-journals/lattice-based-public-key-cryptography-in-hardware-coprocessor-for-5TtWIAaBiL
Publisher
Springer Singapore
© Springer Nature Singapore Pte Ltd. 2020
ISBN
978-981-32-9993-1
Pages
25 –42
DOI
10.1007/978-981-32-9994-8_3
Publisher site
See Chapter on Publisher Site

### Abstract

[Koblitz curves [20] are a special class of elliptic-curves which enable very efficient point multiplications and, therefore, they are attractive for hardware and software implementations. However, these efficiency gains can be exploited only by representing scalars as specific \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}-adic expansions. Most cryptosystems require the scalar also as an integer (see, e.g., ECDSA [25]). Therefore, cryptosystems utilizing Koblitz curves need both the integer and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}-adic representations of the scalar, which results in a need for conversions between the two domains.]

Published: Nov 13, 2019