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Advances in quantum computing have urged the need for cryptographic algorithms that are low-power, low-energy, and secure against attacks that can be potentially enabled. For this post-quantum age, different solutions have been studied. Code-based cryptography is one feasible solution whose hardware architectures have become the focus of research in the NIST standardization process and has been advanced to the final round (to be concluded by 2022–2024). Nevertheless, although these constructions, e.g., McEliece and Niederreiter public key cryptography, have strong error correction properties, previous studies have proved the vulnerability of their hardware implementations against faults product of the environment and intentional faults, i.e., differential fault analysis. It is previously shown that depending on the codes used, i.e., classical or reduced (using either quasi-dyadic Goppa codes or quasi-cyclic alternant codes), flaws in error detection could be observed. In this work, efficient fault detection constructions are proposed for the first time to account for such shortcomings. Such schemes are based on regular parity, interleaved parity, and two different cyclic redundancy checks (CRC), i.e., CRC-2 and CRC-8. Without losing the generality, we experiment on the McEliece variant, noting that the presented schemes can be used for other code-based cryptosystems. We perform error detection capability assessments and implementations on field-programmable gate array Kintex-7 device xc7k70tfbv676-1 to verify the practicality of the presented approaches. To demonstrate the appropriateness for constrained embedded systems, the performance degradation and overheads of the presented schemes are assessed.
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Reproducible families of codes and cryptographic applications
Abstract Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography. Some well known families of structured linear block codes have been separately and intensively studied, without searching for possible bridges between them. In this article, we start from well known examples of this type and generalize them into a wider class of codes that we call ℱ-reproducible codes. Some families of ℱ-reproducible codes have the property that they can be entirely generated from a small number of signature vectors, and consequently admit matrices that can be described in a very compact way. We denote these codes as compactly reproducible codes and show that they encompass known families of compactly describable codes such as quasi-cyclic and quasi-dyadic codes. We then consider some cryptographic applications of codes of this type and show that their use can be advantageous for hindering some current attacks against cryptosystems relying on structured codes. This suggests that the general framework we introduce may enable future developments of code-based cryptography.
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- Award ID(s):
- 1906360
- PAR ID:
- 10444153
- Date Published:
- Journal Name:
- Journal of Mathematical Cryptology
- Volume:
- 16
- Issue:
- 1
- ISSN:
- 1862-2984
- Page Range / eLocation ID:
- 20 to 48
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1515/jmc-2020-0003
