Open AccessPKC‐PC: A variant of the McEliece public‐key cryptosystem based on polar codes
Author(s) -
Hooshmand Reza,
Koochak Shooshtari Masoumeh,
Reza Aref Mohammad
Publication year - 2020
Publication title -
iet communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.355
H-Index - 62
eISSN - 1751-8636
pISSN - 1751-8628
DOI - 10.1049/iet-com.2019.0689
Subject(s) - mceliece cryptosystem , polar code , generator matrix , cryptosystem , code word , computer science , decoding methods , theoretical computer science , parity check matrix , code (set theory) , mathematics , encryption , arithmetic , algorithm , computer network , set (abstract data type) , programming language
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.