Padding Techniques for Identifying Decodable Syndrome in Post-Quantum Digital Signature Schemes
Rupali Khurana, Ekta Narwal, Deepika Deepika · Indian Journal of Science and Technology · 2023
Objectives: The aim of this study is to design a MATLAB algorithm that will identify decodable syndromes easily. Methods: The most time-consuming step in developing code-based digital signature schemes is to identify a decodable syndrome. So, to find a decodable syndrome in a short period of time several padding techniques are presented in this paper. Our study uses a polar code with blocklength 16 with a rate of 0.5, and its Successive Cancellation (SC) decoding algorithm is used to decode the syndrome. The techniques suggested in this paper can be used to generate polar code-based digital signatures more quickly. Findings: Our study evaluates the effectiveness of padding techniques by simulating random syndromes 10,000 times over Binary Symmetric Channel (BSC) and Additive White Gaussian Noise (AWGN) channel by calculating the success rate, failure rate, and mean failure count for each channel. Novelty: In this paper, we present graphs showing the number of syndromes that failed to decode in the BSC and AWGN channels when simulating a predefined number of times. Additionally, we calculate the success rate, failure rate, and mean failure count of decoding for both channels, which demonstrate that the proposed padding techniques are highly effective in decoding syndromes in AWGN. Keywords: Quantum computing, Post-Quantum digital signature, Decodable syndromes, Padding, Polar codes, Successive cancellation decoding