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Design of a Joint Encryption-Encodingscheme using QC-LDPC Codes Based on Finite Geometry

Khayami, Hossein | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47616 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aref, Mohammad Reza; Eghlidos, Taraneh
  7. Abstract:
  8. Code-based cryptosystems could be a suitable alternative to the cryptosystems based on number theory. It is shown that cryptosystems based on descrete logarithm and factoring is vulnerable to the Shor’s algorithm running on quantum computers, while code-based cryptosystemsare thought to be secure against this cryptanalysis. Despite its security, large key size and low transmission rate keep thesecryptosystems impractical. Reliability is one of our inevitable desires in communication systems along with security.In order to fulfill these desires, joint encryption-encoding schemes has been released.Using LDPC codes in joint encryption-encoding schemes, as an alternative to classical linear codes, would shorten the key size as well as improving error correction capability.In this thesis, we present a joint encryption-encoding scheme using QC-LDPC codes based on finite geometry.We observed that our proposed scheme not only outperforms in its key size and transmission rate, but also remains secure against all known cryptanalysis of code-based secret key cryptosystems. We subsequently show that our scheme benefits from low computational complexity.In our proposed joint ecryption-encoding scheme, by taking the advantage of quasi cyclic LDPC codes based on finite geometries, the key size decreases to 1/6 of that of the last known similar system. In addition, using our proposed scheme a plenty of different desirable transmission rates is achievable. In order to achieve a better error performance, we suggest using irregular form of FG-QC-LDPC codes. Moreover, the security of our scheme has been improved by using stream ciphers instead of linear feedback shift registers. The wide variety of codes which is proposed in this thesismakes ourcryptosystemapplicable on a number ofdifferent communication and cryptographic standards
  9. Keywords:
  10. Code-based Cryptosystem ; Joint Encryption-Encoding Scheme ; Quasi Cyclic-Low Density Check Codes (QC-LDPC) ; Finite Euclidean Geometry ; Finite Projective Geometry

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