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Secret Key Cryptosystem Based on Non-systematic Polar Codes

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Abstract

Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is assumed that an attacker with a restricted processing power has unlimited access to the transmission media. Therefore, the attacker can construct the generator matrix of polar codes, especially in the case of binary erasure channels, on which this matrix can be easily constructed. In this paper, we introduce a novel method to keep the generator matrix of polar codes in secret in a way that the attacker cannot access the required information to decode the intended polar code. With the help of this method, a secret key cryptosystem is proposed based on non-systematic polar codes. In fact, the main objective of this study is to achieve an acceptable level of security and reliability through taking advantage of the special properties of polar codes. The analyses revealed that our scheme resists the typical attacks on the secret key cryptosystems based on linear block codes. In addition, by employing some efficient methods, the key length of the proposed scheme is decreased compared to that of the previous cryptosystems. Moreover, this scheme enjoys other advantages including high code rate, and proper error performance as well.

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Acknowledgments

The authors would like to thank Masoumeh Kootchak Shooshtari, Mahdi Alaghband and Behnam Mafakheri for their helpful discussions and suggestions. This work was supported in part by Iranian National Science Foundation (INSF) Cryptography Chair under Grant No. 92.32575.

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Authors and Affiliations

  1. Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Reza Hooshmand

  2. Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran

    Mohammad Reza Aref

  3. Electronics Research Institute, Sharif University of Technology, Tehran, Iran

    Taraneh Eghlidos

Authors
  1. Reza Hooshmand
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  2. Mohammad Reza Aref
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  3. Taraneh Eghlidos
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Correspondence to Reza Hooshmand.

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Hooshmand, R., Aref, M.R. & Eghlidos, T. Secret Key Cryptosystem Based on Non-systematic Polar Codes. Wireless Pers Commun 84, 1345–1373 (2015). https://doi.org/10.1007/s11277-015-2691-9

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