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2014 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

QC-LDPC Code-Based Cryptography

verfasst von: Marco Baldi

Verlag: Springer International Publishing

Buchreihe : SpringerBriefs in Electrical and Computer Engineering

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

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Über dieses Buch

This book describes the fundamentals of cryptographic primitives based on quasi-cyclic low-density parity-check (QC-LDPC) codes, with a special focus on the use of these codes in public-key cryptosystems derived from the McEliece and Niederreiter schemes. In the first part of the book, the main characteristics of QC-LDPC codes are reviewed, and several techniques for their design are presented, while tools for assessing the error correction performance of these codes are also described. Some families of QC-LDPC codes that are best suited for use in cryptography are also presented. The second part of the book focuses on the McEliece and Niederreiter cryptosystems, both in their original forms and in some subsequent variants. The applicability of QC-LDPC codes in these frameworks is investigated by means of theoretical analyses and numerical tools, in order to assess their benefits and drawbacks in terms of system efficiency and security. Several examples of QC-LDPC code-based public key cryptosystems are presented, and their advantages over classical solutions are highlighted. The possibility of also using QC-LDPC codes in symmetric encryption schemes and digital signature algorithms is also briefly examined.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
This chapter introduces the rationale of QC-LDPC code-based cryptography, with focus on the use of QC-LDPC codes in the McEliece and Niederreiter cryptosystems. The organization of the book is also briefly outlined.
Marco Baldi
Chapter 2. Low-Density Parity-Check Codes
Abstract
This chapter provides a brief overview of the basic concepts and definitions concerning Low-Density Parity-Check (LDPC) codes, which will be used in the remainder of the book. The notation concerning LDPC codes which will be used throughout the book is introduced. LDPC encoding and decoding algorithms and their complexity are also discussed.
Marco Baldi
Chapter 3. Quasi-Cyclic Codes
Abstract
In this chapter, we recall the main definitions concerning quasi-cyclic codes, which will be used in the remainder of the book. We introduce the class of circulant matrices, and the special class of circulant permutation matrices, together with their isomorphism with polynomials over finite fields. We characterize the generator and parity-check matrices of quasi-cyclic codes, by defining their “blocks circulant” and “circulants block” forms, and show how they translate into an encoding circuit. We define a special class of quasi-cyclic codes having the parity-check matrix in the form of a single row of circulant blocks, which will be of interest in the following chapters. Finally, we describe how to achieve efficient encoding algorithms based on fast polynomial multiplication and vector-circulant matrix products.
Marco Baldi
Chapter 4. Quasi-Cyclic Low-Density Parity-Check Codes
Abstract
In this chapter, we describe the main characteristics of a hybrid class of codes which are both quasi-cyclic (QC) and low-density parity-check (LDPC) codes. They join the powerful error correcting performance of LDPC codes with the structured nature of QC codes, which allows for very compact representations. This, together with the high number of equivalent codes, makes these codes well suited for cryptographic applications. This chapter addresses the design of these codes, as well as the estimation of the number of different codes having the same parameters.
Marco Baldi
Chapter 5. The McEliece and Niederreiter Cryptosystems
Abstract
This chapter is devoted to the McEliece and Niederreiter cryptosystems, which are the first and best known examples of code-based public-key cryptosystems. The classical instances of the McEliece and Niederreiter cryptosystems are described, together with the class of Goppa codes, which are the codes originally used in these systems and which have best resisted cryptanalysis during years. The main attacks against these systems are reviewed, and their complexity is estimated in order to assess the security level. Some subsequent variants of the McEliece and Niederreiter cryptosystems are briefly reviewed.
Marco Baldi
Chapter 6. QC-LDPC Code-Based Cryptosystems
Abstract
In this chapter, the use of QC-LDPC codes in public key cryptosystems inspired to the McEliece and Niederreiter systems is studied. Both the case in which the private and the public code are permutation equivalent and that in which such an equivalence is absent are considered. It is shown that the use of this kind of codes may expose the system to new attacks, which can be very dangerous if the system is not suitably designed. The countermeasures to be used against these attacks are described, and some practical instances of QC-LDPC code-based public key cryptosystems achieving some specific security levels are provided. The chance to use QC-LDPC codes also in digital signature schemes and symmetric cryptosystems is briefly discussed.
Marco Baldi
Backmatter
Metadaten
Titel
QC-LDPC Code-Based Cryptography
verfasst von
Marco Baldi
Copyright-Jahr
2014
Electronic ISBN
978-3-319-02556-8
Print ISBN
978-3-319-02555-1
DOI
https://doi.org/10.1007/978-3-319-02556-8

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