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<p>In the realm of modern cryptography, error-correcting codes emerge as a robust approach to secure communication. Polar codes, harnessing the power of channel polarization, offer near-linear encoding and decoding complexity while achieving Shannon capacity. Thus, polar codes are useful for Code-based Secret Sharing (CSS), Quantum Key Distribution (QKD), and Code-Based Cryptography (CBC). Therefore, the analysis of polar codes’ potential is imperative for several reasons: polar codes garner substantial attention due to error-correction capability, cryptography plays a pivotal role in securing communications and data, making it crucial to assess the efficacy of polar codes in encryption, secret sharing, and QKD, and polar codes help to identify vulnerabilities and weaknesses when incorporated into cryptographic schemes. Our survey represents the first comprehensive analysis of polar codes in CBC, CSS, and QKD. We delve into the practical implementation of polar codes within McEliece’s system and key reconciliation protocols, conducting detailed simulations to assess their strengths and weaknesses. We consider decoding attack cost, maximum Frame Error Rate (<i>FER</i>), and the efficiency of the key reconciliation protocol. Moreover, we offer insights into designing efficient polar code-based cryptographic algorithms for post-quantum security, making this survey a valuable resource for academia and industries alike.</p>

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Analyzing the Potential of Polar Codes in Modern Cryptography: A Survey

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Belkacem Imine,
  • Rahul Saha,
  • Mauro Conti,
  • Maryam Ehsanpour

摘要

In the realm of modern cryptography, error-correcting codes emerge as a robust approach to secure communication. Polar codes, harnessing the power of channel polarization, offer near-linear encoding and decoding complexity while achieving Shannon capacity. Thus, polar codes are useful for Code-based Secret Sharing (CSS), Quantum Key Distribution (QKD), and Code-Based Cryptography (CBC). Therefore, the analysis of polar codes’ potential is imperative for several reasons: polar codes garner substantial attention due to error-correction capability, cryptography plays a pivotal role in securing communications and data, making it crucial to assess the efficacy of polar codes in encryption, secret sharing, and QKD, and polar codes help to identify vulnerabilities and weaknesses when incorporated into cryptographic schemes. Our survey represents the first comprehensive analysis of polar codes in CBC, CSS, and QKD. We delve into the practical implementation of polar codes within McEliece’s system and key reconciliation protocols, conducting detailed simulations to assess their strengths and weaknesses. We consider decoding attack cost, maximum Frame Error Rate (FER), and the efficiency of the key reconciliation protocol. Moreover, we offer insights into designing efficient polar code-based cryptographic algorithms for post-quantum security, making this survey a valuable resource for academia and industries alike.