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PKC-PC: A variant of the McEliece public-key cryptosystem based on polar codes

Hooshmand, R ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1049/iet-com.2019.0689
  3. Publisher: Institution of Engineering and Technology , 2020
  4. Abstract:
  5. Polar codes are novel and efficient error-correcting codes with low encoding and decoding complexities. These codes have a channel-dependent generator matrix, which is determined by the code dimension, code length and transmission channel parameters. A variant of the McEliece public-key cryptosystem based on polar codes, called the PKC-PC, is studied. Since the structure of the polar codes' generator matrix depends on the parameters of the channel, the authors have used an efficient approach to conceal their generator matrix. The proposed approach is based on a random selection of rows of the matrix by which a random generator matrix is constructed. Using the characteristics of polar codes and introducing an efficient approach, they could reduce the public and secret key sizes, and computational complexity compared to the McEliece cryptosystem. Moreover, they show that PKC-PC yields an increased security level against conventional attacks as well as possible vulnerabilities to the code-based public-key cryptosystems. Furthermore, they prove the security of the authors' cryptosystem and show that its security is reduced to solve NP-complete problems, called polar parameterised syndrome decoding and polar parameterised codeword existence. © The Institution of Engineering and Technology 2020
  6. Keywords:
  7. Computational complexity ; Decoding ; Encoding and decoding ; Error correcting code ; McEliece cryptosystem ; McEliece public-key cryptosystem ; Public key cryptosystems ; Random generator matrices ; Syndrome decoding ; Transmission channels ; Public key cryptography
  8. Source: IET Communications ; Volume 14, Issue 12 , 2020 , Pages 1883-1893
  9. URL: https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/iet-com.2019.0689