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QC-LDPC Code-Based Cryptography

Part of the SpringerBriefs in Electrical and Computer Engineering Book Series

DOI: 10.1007/978-3-319-02556-8

ISBN: 978-3-319-02555-1

Publisher: Springer International Publishing - Springer Journals

May 3, 2014

Available

Introduction

Baldi, Marco

Pages: 1 –3

[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.]
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Low-Density Parity-Check Codes

Baldi, Marco

Pages: 5 –21

[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...
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Quasi-Cyclic Codes

Baldi, Marco

Pages: 23 –40

[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...
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Quasi-Cyclic Low-Density Parity-Check Codes

Baldi, Marco

Pages: 41 –63

[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...
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The McEliece and Niederreiter Cryptosystems

Baldi, Marco

Pages: 65 –89

[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...
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QC-LDPC Code-Based Cryptosystems

Baldi, Marco

Pages: 91 –117

[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...

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