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QC-LDPC Code-Based Cryptography
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This book describes the fundamentals of the use of quasi-cyclic low-density parity-check (QC-LDPC) codes within the framework of the McEliece cryptosystem. In the first part, different design techniques for QC-LDPC codes are examined, and the error correction performance of these codes is assessed through numerical simulations of transmission systems. Within this context, novel design techniques are proposed for particular families of QC-LDPC codes. The second part of the book focuses on the McEliece cryptosystem, both in its original form, based on Goppa codes, and in some subsequent variants. The applicability of QC-LDPC codes in the McEliece cryptosystem is investigated by means of theoretical analyses and numerical tools in order to assess the benefits and drawbacks in terms of system efficiency and security. On this basis, a particular family of codes is presented that is able to ensure suitable system robustness and overcomes two major drawbacks of the original McEliece cryptosystem: its large public key and its low transmission rate.
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