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Lattice-Based Public-Key Cryptography in Hardware

verfasst von: Sujoy Sinha Roy, Prof. Ingrid Verbauwhede

Verlag: Springer Singapore

Buchreihe : Computer Architecture and Design Methodologies

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book describes the efficient implementation of public-key cryptography (PKC) to address the security challenges of massive amounts of information generated by the vast network of connected devices, ranging from tiny Radio Frequency Identification (RFID) tags to powerful desktop computers. It investigates implementation aspects of post quantum PKC and homomorphic encryption schemes whose security is based on the hardness of the ring-learning with error (LWE) problem. The work includes designing an FPGA-based accelerator to speed up computation on encrypted data in the cloud computer. It also proposes a more practical scheme that uses a special module called recryption box to assist homomorphic function evaluation, roughly 20 times faster than the implementation without this module.

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Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

Since the advent of the internet, our world has become more and more connectedevery day. The International Telecommunications Union reports that the number of internet users has increased from 400 million in 2000 to 3.2 billionin 2015. This growth rate is expected to be faster in the future as a result ofinternet penetration in the developing nations. The Internet of Things (IoT)is a network of connected devices ranging from powerful personal computersand smart phones to low-cost passive RFID tags. These devices are capable of computing together and exchanging information with or without humanintervention and are present in many areas of our life such as smart homes, smart grids, intelligent transportation, smart cities.

Sujoy Sinha Roy, Ingrid Verbauwhede

Chapter 2. Background

Abstract

In this chapter we review the concept of public-key cryptography (PKC) and then describe two PKC schemes namely, elliptic-curve cryptography and lattice-based cryptography.

Sujoy Sinha Roy, Ingrid Verbauwhede

Chapter 3. Coprocessor for Koblitz Curves

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 \(\tau \)-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 \(\tau \)-adic representations of the scalar, which results in a need for conversions between the two domains.

Sujoy Sinha Roy, Ingrid Verbauwhede

Chapter 4. Discrete Gaussian Sampling

Abstract

In this chapter we propose an efficient hardware implementation of a discrete Gaussian sampler for ring-LWE encryption schemes. The proposed sampler architecture is based on the Knuth-Yao sampling Algorithm [10]. It has high precision and large tail-bound to keep the statistical distance below \(2^{-90}\) to the true Gaussian distribution for the secure parameter sets [6] that are used in the public key encryption schemes [12, 17].

Sujoy Sinha Roy, Ingrid Verbauwhede

Chapter 5. Ring-LWE Public Key Encryption Processor

Abstract

In this chapter we analyze the \(\mathtt {LPR}\) ring-LWE public key encryption scheme of Sect. 2.4.1 and design a compact hardware architecture of the encryption processor. From Fig. 2.4 of Sect. 2.4.1, we see that the \(\mathtt {LPR}\) encryption scheme is composed of a discrete Gaussian sampler, a polynomial arithmetic (addition/multiplication) unit, a message encoder and a message decoder. In the last chapter we described how to design the discrete Gaussian sampler efficiently. In this chapter we first design a novel polynomial arithmetic unit and integrate it with the discrete Gaussian sampler to realize the ring-LWE public key encryption processor.

Sujoy Sinha Roy, Ingrid Verbauwhede

Chapter 6. Conclusions and Future Work

Abstract

In this chapter we summarize the contributions of this work and point out some of the possible future directions.

Sujoy Sinha Roy, Ingrid Verbauwhede

Backmatter

Titel: Lattice-Based Public-Key Cryptography in Hardware
verfasst von: Sujoy Sinha Roy
Prof. Ingrid Verbauwhede
Copyright-Jahr: 2020
Verlag: Springer Singapore
Electronic ISBN: 978-981-329-994-8
Print ISBN: 978-981-329-993-1
DOI: https://doi.org/10.1007/978-981-32-9994-8