Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Articles

MATHEMATICAL ANALYSIS OF QC-MDPC STRUCTURES IN BIKE V5.2 POST-QUANTUM KEY ENCAPSULATION SCHEME

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  • Rosa Rosa,
  • Sa'aadah Sajjana Carita,
  • Nadia Paramita Retno Adiati,
  • Sri Rosdiana
Rosa Rosa
Department of Cryptographic Engineering, Politeknik Siber dan Sandi Negara, Indonesia
Sa'aadah Sajjana Carita
Department of Cryptographic Engineering, Politeknik Siber dan Sandi Negara, Indonesia
Nadia Paramita Retno Adiati
Department of Cryptographic Engineering, Politeknik Siber dan Sandi Negara, Indonesia
Sri Rosdiana
Department of Cryptographic Engineering, Politeknik Siber dan Sandi Negara, Indonesia
DOI: https://doi.org/10.30598/barekengvol20iss2pp1061-1076
Published January 26, 2026
Keywords
  • BIKE v5.2,
  • QC-MDPC,
  • Key encapsulation,
  • Mechanism,
  • Post-quantum cryptography
How to Cite
[1]
R. Rosa, S. S. Carita, N. P. R. Adiati, and S. Rosdiana, “MATHEMATICAL ANALYSIS OF QC-MDPC STRUCTURES IN BIKE V5.2 POST-QUANTUM KEY ENCAPSULATION SCHEME”, BAREKENG: J. Math. & App., vol. 20, no. 2, pp. 1061-1076, Jan. 2026.

Copyright (c) 2026 Rosa Rosa, Sa'aadah Sajjana Carita, Nadia Paramita Retno Adiati, Sri Rosdiana

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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

The security of the BIKE scheme depends on a complex mathematical structure built upon QC-MDPC codes. This scheme is constructed using the Niederreiter framework and the application of  transformation. Its security is based on the complexity of two main mathematical problems: the QCSD Problem and the QCCF Problem. The BIKE v5.2 scheme is the latest version of this scheme. This study aims to mathematically analyze the characteristics forming the BIKE v5.2, focusing on QC-MDPC codes, the Niederreiter framework, and the  transformation, as well as the QCSD and QCCF problems. The method used in this study is a systematic literature review combined with theoretical analysis. The study highlights how the interplay of these three components forms a rational and resilient design. Although the BIKE v5.2 scheme was not selected for standardization by NIST, it is still capable of producing an efficient, secure, and relevant KEM for post-quantum cryptography. Through mathematical analysis of the QC-MDPC construction, the formulation of the complex computational problems QCCF and QCSD, and the rational design of the Niederreiter framework with the  transformation, this study demonstrates that BIKE has a strong security foundation and resistance to both classical and quantum attacks.

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