Title: PKC-SPE: a variant of the McEliece cryptosystem based on systematic polar encoding

Authors: Ritu Redhu; Ekta Narwal

Addresses: Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, 124001, India ' Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, 124001, India

Abstract: The public key cryptosystem (PKC), including Rivest, Shamir, Adleman (RSA) and elliptic curve cryptography can be deciphered with the development of quantum computers. As a result, we must find a replacement for these algorithms, and post-quantum cryptography (PQC) is the best solution to this problem. This paper examines public key cryptosystem based on systematic polar encoding (PKC-SPE), the McEliece cryptosystem variant based on systematic polar encoding. A highly reliable and effective cryptosystem based on systematic polar encoding (SPE) is designed using the properties of polar codes. Here, we also examine the error performance, upper bound on error probability, bit error rate (BER) performance for a fixed code rate of 0.85 on various blocklengths with varying bit energy to noise power spectral density ratio (EbNo) and its comparison with non-systematic counterparts. The findings show that this technique has better error performance and a higher encryption rate.

Keywords: PKC; public key cryptosystem; polar codes; PQC; post-quantum cryptography; AWGN channel; BER; bit error rate.

DOI: 10.1504/IJCSM.2024.139923

International Journal of Computing Science and Mathematics, 2024 Vol.20 No.1, pp.32 - 45

Received: 19 Apr 2023
Accepted: 18 Jan 2024
Published online: 11 Jul 2024 *

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