Quasi-twisted codes: decoding and applications in code-based cryptography
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911033220661248 |
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| author | S, Bhagyalekshmy Kshirsagar, Rutuja |
| author_facet | S, Bhagyalekshmy Kshirsagar, Rutuja |
| contents | Quasi-twisted (QT) codes generalize several important families of linear codes, including cyclic, constacyclic, and quasi-cyclic codes. Despite their potential, to the best of our knowledge, there exists no efficient decoding algorithm for QT codes. In this work, we propose a syndrome-based decoding method capable of efficiently correcting up to (d* - 1)/2 errors, where d* denotes an HT-like lower bound on the minimum distance of QT codes, which we formalize here. Additionally, we introduce a Niederreiter-like cryptosystem constructed from QT codes. This cryptosystem is resistant to some classical attacks as well as some quantum attacks based on Quantum Fourier Sampling. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_01118 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-twisted codes: decoding and applications in code-based cryptography S, Bhagyalekshmy Kshirsagar, Rutuja Cryptography and Security Information Theory Quasi-twisted (QT) codes generalize several important families of linear codes, including cyclic, constacyclic, and quasi-cyclic codes. Despite their potential, to the best of our knowledge, there exists no efficient decoding algorithm for QT codes. In this work, we propose a syndrome-based decoding method capable of efficiently correcting up to (d* - 1)/2 errors, where d* denotes an HT-like lower bound on the minimum distance of QT codes, which we formalize here. Additionally, we introduce a Niederreiter-like cryptosystem constructed from QT codes. This cryptosystem is resistant to some classical attacks as well as some quantum attacks based on Quantum Fourier Sampling. |
| title | Quasi-twisted codes: decoding and applications in code-based cryptography |
| topic | Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2507.01118 |