Evolution of the McEliece Public Key Encryption Scheme

Bucerzan, Dominic; Drăgoi, Vlad; Kalachi, Hervé Talé

doi:10.1007/978-3-319-69284-5_10

Cited by 10 publications

(4 citation statements)

References 80 publications

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“…In parallel to this work in 2017, Bucerzan et al [114] analyzed the evolution of the main encryption variants coming from code-based cryptography field. The authors focus on security issues and Rank-based cryptography.…”

Section: Related Workmentioning

confidence: 98%

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

et al. 2021

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Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or transit. Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems, based on modular arithmetic to the contemporary cryptosystems based on quantum computing. The emergence of quantum computing poses a major threat to the modern cryptosystems based on modular arithmetic, whereby even the computationally hard problems which constitute the strength of the modular arithmetic ciphers could be solved in polynomial time. This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks. This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have been explored. Some potential research directions that are yet to be explored in code-based cryptography research from the perspective of codes is a key contribution of this paper.

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Section: Related Workmentioning

confidence: 98%

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

et al. 2021

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“…More precisely, they are sub-classes of a larger family of algebraic codes called decreasing monomial codes (DMC). The structure underlying DMCs and its algebraic formalism was applied in conjunction with other fields, e.g., in the context of quantum error correcting codes [ 5 , 6 , 7 ], post-quantum cryptography [ 8 , 9 , 10 ] and network reliability [ 11 , 12 , 13 ].…”

Section: Introductionmentioning

confidence: 99%

Bhattacharyya Parameter of Monomial Codes for the Binary Erasure Channel: From Pointwise to Average Reliability

Drăgoi

Cristescu

2021

Sensors

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Monomial codes were recently equipped with partial order relations, a fact that allowed researchers to discover structural properties and efficient algorithm for constructing polar codes. Here, we refine the existing order relations in the particular case of the binary erasure channel. The new order relation takes us closer to the ultimate order relation induced by the pointwise evaluation of the Bhattacharyya parameter of the synthetic channels, which is still a partial order relation. To overcome this issue, we appeal to a related technique from network theory. Reliability network theory was recently used in the context of polar coding and more generally in connection with decreasing monomial codes. In this article, we investigate how the concept of average reliability is applied for polar codes designed for the binary erasure channel. Instead of minimizing the error probability of the synthetic channels, for a particular value of the erasure parameter p, our codes minimize the average error probability of the synthetic channels. By means of basic network theory results, we determine a closed formula for the average reliability of a particular synthetic channel, that recently gain the attention of researchers.

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“…In parallel to this work in 2017, Bucerzan et al,[77] analyzed the evolution of the557 main encryption variants coming from code-based cryptography field. Authors focus on 558 the security issues and Rank based cryptography.…”

mentioning

confidence: 99%

Code-based Post-Quantum Cryptography

Balamurugan¹,

Singh²,

Ganesan³

et al. 2021

Preprint

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Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or in transit. Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems based on modular arithmetic to the contemporary cryptosystems based on quantum computing. The emergence of quantum computing imposes a major threat on the modern cryptosystems based on modular arithmetic whereby, even the computationally hard problems which constitute for the strength of the modular arithmetic ciphers could be solved in deterministic time. This threat triggered post-quantum cryptography research in order to design and develop post-quantum algorithms that can withstand quantum computing attacks. This paper provides a review of the various post-quantum cryptography and, in specific, code-based cryptography research dimensions. The research directions that are yet to be explored in code-based cryptography research is another key contribution of this paper.

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Evolution of the McEliece Public Key Encryption Scheme

Cited by 10 publications

References 80 publications

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Bhattacharyya Parameter of Monomial Codes for the Binary Erasure Channel: From Pointwise to Average Reliability

Code-based Post-Quantum Cryptography

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