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Optimizing code-based cryptography for Efficient and Secure Post-Quantum Key Agreement

Procedia Computer Science 2025年 259卷 1034-1048页

作者： Syed Shamikh Iqbal Aasim Zafar Department of Computer Science Aligarh Muslim University Aligarh India

Due to the quantum computing threat, RSA and ECC cryptography are at risk, necessitating the need for post-quantum cryptography. code-based cryptographic schemes, such as the McEliece system, have shown promise due to their resistance to quantum attacks. However, these schemes suffer from large key sizes and high computational complexity, making them unsuitable for resource-constrained devices like IoT. This paper proposes a lightweight key agreement protocol utilizing code-based cryptography optimized for such environments. The protocol reduces key size by 80% (from 1000 KB to 200 KB), computational overhead by 66% (from 15 ms to 5 ms), and energy consumption by 60% (from 2.5 mJ to 1.0 mJ), compared to traditional McEliece-based systems. The inclusion of the Fujisaki-Okamoto transform ensures CCA2 security. Security analysis confirms robustness against classical and quantum adversaries, including Shor’s and Grover’s algorithms. These improvements make the protocol highly suitable for lightweight applications, paving the way for secure post-quantum communication in constrained environments. Future work will address real-world scalability and side-channel attack resistance.

关键词： Post-Quantum cryptography code-based cryptography Key Agreement Lightweight cryptography Secure Communication

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code-based cryptography: State of the Art and Perspectives

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IEEE SECURITY & PRIVACY 2017年第4期15卷 44-50页

作者： Sendrier, Nicolas INRIA Rocquencourt France

code-based cryptography is one of the few mathematical techniques that enables the construction of public-key cryptosystems that are secure against an adversary equipped with a quantum computer. The McEliece public-ke... 详细信息

关键词： Public key cryptography Decoding Encryption Generators Digital signatures Computer security INSPEC: Controlled Indexing public key cryptography quantum computing INSPEC: Non-Controlled Indexing code-based cryptography mathematical techniques public-key cryptosystems quantum computer McEliece public-key encryption scheme postquantum public-key encryption standard Author Keywords cryptography coding theory MDPC codes postquantum cryptography McEliece encryption scheme security

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code-based cryptography With Generalized Concatenated codes for Restricted Error Values

IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY

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IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY 2022年 3卷 1528-1539页

作者： Thiers, Johann-Philipp Freudenberger, Juergen Univ Appl Sci Inst Syst Dynam HTWG Konstanz D-78462 Constance Germany

code-based cryptosystems are promising candidates for post-quantum cryptography. Recently, generalized concatenated codes over Gaussian and Eisenstein integers were proposed for those systems. For a channel model with errors of restricted weight, those q-ary codes lead to high error correction capabilities. Hence, these codes achieve high work factors for information set decoding attacks. In this work, we adapt this concept to codes for the weight-one error channel, i.e., a binary channel model where at most one bit-error occurs in each block of m bits. We also propose a low complexity decoding algorithm for the proposed codes. Compared to codes over Gaussian and Eisenstein integers, these codes achieve higher minimum Hamming distances for the dual codes of the inner component codes. This property increases the work factor for a structural attack on concatenated codes leading to higher overall security. For comparable security, the key size for the proposed code construction is significantly smaller than for the classic McEliece scheme based on Goppa codes.

关键词： code-based cryptography generalized concatenated codes McEliece cryptosystem public-key cryptography restricted error values

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code-based cryptography

Code-based Cryptography

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作者： Jäämeri, Elias Aalto University

学位级别：硕士

Large enough quantum computers could run Shor’s algorithm to solve problems such as the integer factorization problem or the discrete logarithm problem in time frames unattainable by conventional computers. Popular implementations of public-key cryptography rely on brute force computations for such problems being *** threat has motivated the research of post-quantum cryptography, in which code-based cryptography, making use of error-correcting codes, is one promising research direction. The underlying hard problem in code-based cryptography is the syndrome decoding problem, which is known to be NP-complete and believed to resist brute force attack from quantum computers. The original code-based cryptosystem was suggested in 1978 by Robert McEliece and since then extensive analysis on it and later variants has been covered in the literature. Many of the proposed variants have been shown to be insecure due to lack of sufficient concealment of the code structure, which enables attackers to bypass the hard problem and exploit structural vulnerabilities instead. Twisted codes are a relatively new family of codes, with certain explicit constructions potentially being viable for implementation to code-based cryptography, since previously deployed attack are not directly applicable to them. This thesis surveys the literature on linear codes to present concepts necessary to describe twisted codes in their cryptographic environment. The feasibility of twisted codes in code-based cryptography is then discussed through experimental simulation results.

关键词： error-correcting codes post-quantum cryptography code-based cryptography Gabidulin codes twisted codes

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Compact Constant Weight Coding Engines for the code-based cryptography

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2017年第9期64卷 1092-1096页

作者： Hu, Jingwei Cheung, Ray C. C. Gueneysu, Tim City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China Univ Bremen Dept Math & Comp Sci D-28359 Bremen Germany

We present here a more memory efficient method for encoding binary information into words of prescribed length and weight. Existing solutions either require complicated float point arithmetic or additional memory overhead, making it a challenge for resource constrained computing environment. The solution we propose here solves these problems yet obtains better coding efficiency by a memory efficient approximation of the critical intermediate value in constant weight coding. For the time being, the design presented in this brief is the most compact one for any code-based encryption schemes.

关键词： code-based cryptography McEliece/Niederreiter cryptosystem constant weight coding FPGA implementation

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Probabilistic root finding in code-based cryptography

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JOURNAL OF CRYPTOGRAPHIC ENGINEERING 2024年第1期14卷 71-85页

作者： Marchiori, Dunia Custodio, Ricardo Panario, Daniel Moura, Lucia Univ Fed Santa Catarina Programa Posgrad Ciencia Comp Florianopolis Brazil Carleton Univ Sch Math & Stat Ottawa ON Canada Univ Ottawa Sch Elect Engn & Comp Sci Ottawa ON Canada

Probabilistic algorithms for finding roots of polynomials have not been applied to code-based cryptography before. One obstacle is their non-constant execution time, since runtime variations can be exploited by side-channel attack techniques. We aim to create a constant-time approach to probabilistic algorithms, so cryptosystems can benefit from these algorithms' efficiency, especially when considering larger parameters. Our countermeasure prevents that the execution time of a probabilistic root-finding algorithm be dependent on the degree of the input polynomial and makes it dependent only on the cryptosystem parameters. We compare the performance of our proposal to other root-finding algorithms already used in code-based cryptography and related works. We also show that our countermeasure can be applied to other root-finding algorithms successfully. In general, our method is faster than a variant of the Berlekamp Trace Algorithm, the exhaustive algorithm in Classic McEliece and the additive Fast Fourier Transform algorithm for plausible parameters with larger finite fields.

关键词： Post-quantum cryptography code-based cryptography Root-finding algorithms Probabilistic root finding Timing side-channel attack Constant-time algorithm

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Rank-metric Encryption on Arm-Cortex M0 Porting code-based cryptography to lightweight devices 6

Rank-metric Encryption on Arm-Cortex M0 Porting code-based c...

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6th ACM ASIA Public-Key cryptography Workshop (APKC) / 3rd ACM Workshop on Blockchains, Cryptocurrencies and Contracts (BCC) / ACM International Symposium on Blockchain and Secure Critical Infrastructure (BSCI)

作者： al Abdouli, A. Bellini, Emanuele Caullery, Florian Manzano, Marcos Mateu, Victor DarkMatter LLC Dubai U Arab Emirates

ISBN: (纸本)9781450367844

Since its invention by McEliece in 1978, cryptography based on Error Correcting codes (ECC) has suffered from the reputation of not being suitable for constrained devices. Indeed, McEliece's scheme and its variants have large public keys and relatively long ciphertexts. Recent works on these downsides explored the possible use of ECC based on rank metric instead of Hamming metric. These codes were introduced in the late 80's to eliminate errors with repeating patterns, regardless of their Hamming weight. Numerous proposals for the NIST Post-Quantum cryptography (PQC) competition rely on these codes. It has been proven that lattice-based cryptography and even hash-based signatures can run on lightweight devices, but the question remains for code-based cryptography. In this work, we demonstrate that this is actually possible for rank metric: we have implemented the encryption operation of 5 schemes based on ECC in rank metric and made them run on an Arm Cortex-M0 processor, the smallest Arm processor available. We describe the technical difficulties of porting rank-based cryptography to a resource-constrained device while maintaining decent performance and a suitable level of security against side-channel attacks, especially timing attacks.

关键词： Post-quantum cryptography code-based cryptography Rank metric Lightweight cryptography

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The Tightness of Security Reductions in code-based cryptography

The Tightness of Security Reductions in Code-based Cryptogra...

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IEEE Information Theory Workshop (ITW)

作者： Sendrier, Nicolas Project Team SECRET Inria Rocquencourt France

ISBN: (纸本)9781457704376

code-based cryptography allows the construction of primitives with various functionalities. Those designs are in general secure and possess no undesirable features that cannot be corrected by a proper choice of parameters and a careful implementation (i.e. semantically secure conversion). Their security reduction is, for the systems who do not require a trapdoor decoder, as good as possible as we have an exact reduction to the syndrome decoding problem, the hardness of which conveys an extreme confidence. For public-key systems (encryption, signature) there exists no really threatening (non exponential) attacks but the security reduction involves other problems (indistinguishability of families of codes) which offer some confidence but which also need to be considered with more hindsight, in particular for variants with reduced key size (typically using quasi-cyclic or quasi-dyadic codes). The security reductions of code-based cryptosystems rely on well identified problems and in that sense are well founded. We hope that the problems we expose here will attract some attention and eventually help to produce even better reductions.

关键词： Conferences Decoding Parity check codes Public key code-based cryptography cyclic codes decoding public key cryptography public-key systems quasicyclic codes quasidyadic codes security reductions syndrome decoding problem telecommunication security trapdo

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Survey on Cryptanalysis of code-based cryptography: from Theoretical to Physical Attacks 7

Survey on Cryptanalysis of Code-Based Cryptography: from The...

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7th International Conference on Computers Communications and Control (ICCCC)

作者： Dragoi, Vlad Richmond, Tania Bucerzan, Dominic Legay, Axel Aurel Vlaicu Univ Arad Fac Exact Sci Arad Romania Inria Rennes Bretagne Atlantique TAMIS Team Rennes France

ISBN: (纸本)9781538619346

Nowadays public-key cryptography is based on number theory problems, such as computing the discrete logarithm on an elliptic curve or factoring big integers. Even though these problems are considered difficult to solve with the help of a classical computer, they can be solved in polynomial time on a quantum computer. Which is why the research community proposed alternative solutions that are quantum-resistant. The process of finding adequate post-quantum cryptographic schemes has moved to the next level, right after NIST's announcement for post-quantum standardization. One of the oldest quantum-resistant proposition goes back to McEliece in 1978, who proposed a public-key cryptosystem based on coding theory. It benefits of really efficient algorithms as well as a strong mathematical background. Nonetheless, its security has been challenged many times and several variants were cryptanalyzed. However, some versions remain unbroken. In this paper, we propose to give some background on coding theory in order to present some of the main flawless in the protocols. We analyze the existing side-channel attacks and give some recommendations on how to securely implement the most suitable variants. We also detail some structural attacks and potential drawbacks for new variants.

关键词： Post-quantum cryptography code-based cryptography McEliece scheme coding theory side-channel analysis

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Introducing Arithmetic Failures to Accelerate QC-MDPC code-based cryptography 1

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7th International Workshop on code-based cryptography (CBC)

作者： Guimaraes, Antonio Borin, Edson Aranha, Diego F. Univ Estadual Campinas Inst Comp Sao Paulo Brazil Aarhus Univ Dept Engn Aarhus Denmark

ISBN: (数字)9783030259228

ISBN: (纸本)9783030259228;9783030259211

In this work, we optimize the performance of QC-MDPC code-based cryptosystems through the insertion of configurable failure rates in their arithmetic procedures. We present constant time algorithms with a configurable failure rate for multiplication and inversion over binary polynomials, the two most expensive subroutines used in QC-MDPC implementations. Using a failure rate negligible compared to the security level (2(-128)), our multiplication is 2 times faster than NTL on sparse polynomials and 1.6 times faster than a naive constant-time sparse polynomial multiplication. Our inversion algorithm, based on Wu et al., is 2 times faster than the original algorithm and 12 times faster than Itoh-Tsujii using the same modulus polynomial (x(32749) - 1). By inserting these algorithms in a version of QcBits at the 128-bit quantum security level, we were able to achieve a speedup of 1.9 on the key generation and up to 1.4 on the decryption time. Comparing with variant 2 of the BIKE suite, which also implements the Niederreiter Cryptosystem using QC-MDPC codes, our final version of QcBits performs the uniform decryption 2.7 times faster.

关键词： code-based cryptography QC-MDPC Polynomial inversion Polynomial multiplication Failure insertion

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