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Area-Time Efficient Computation of Niederreiter Encryption on QC-MDPC codes for Embedded Hardware

IEEE TRANSACTIONS ON COMPUTERS 2017年第8期66卷 1313-1325页

作者： Hu, Jingwei Cheung, Ray C. C. City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China

In this paper, we present a fast implementation for QC-MDPC Niederreiter encryption. Existing high-speed implementations are considerably resource involving but the solution we propose here mitigates such situation while maintaining the high throughputs. In particular, new arithmetic for lightweight Hamming weight computation and a fast sorting network for MDPC decoding are proposed. A novel constant weight coding unit is proposed to enable standard asymmetric encryptions. For now, the design presented in this work is the fastest one of existing QC-MDPC code based encryptions in the public domain. The area-time product of this work drops by at least 53 percent compared to previous fast speed designs of QC-MDPC based encryptions. It is shown for instance that our implementation of encrypting engine can sign one encryption in 3.86 mu s on a Xilinx Virtex-6 FPGA with 3371 slices. Our iterative decrypting engine can decrypt one ciphertext in 114.64 mu s with 5271 slices and our faster non-iterative decrypting engine can decrypt in 65.76 mu s with 8781 slices.

关键词： code-based cryptography niederreiter encryption scheme QC-MDPC code FPGA implementation

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A code-based signature scheme from the Lyubashevsky framework

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THEORETICAL COMPUTER SCIENCE 2020年 835卷 15-30页

作者： Song, Yongcheng Huang, Xinyi Mu, Yi Wu, Wei Wang, Huaxiong Fujian Normal Univ Coll Math & Informat Fujian Prov Key Lab Network Secur & Cryptol Fuzhou 350117 Peoples R China Nanyang Technol Univ Sch Phys & Math Sci Div Math Sci Singapore 639798 Singapore

We propose a new method to construct code-based signature scheme following the Lyubashevsky's lattice-based framework. Our technique ensures that the Hamming weight of each row of the private key matrix is below the GV bound instead of fixed weight. Our scheme can generate signatures whose maximum Hamming weight is below the GV bound of random linear codes with the public key matrix as parity-check matrix. We argue that our scheme can resist existing attacks on code-based signatures. We provide a detailed security analysis and prove that our scheme is existentially unforgeable under adaptive chosen-message attacks (EUF-CMA) in the random oracle model through exploiting and expanding code-based complex problems. Our scheme enjoys the shorter signature size than the Durandal signature scheme (EUROCRYPT 2019) and the Wave signature scheme (ASIACRYPT 2019) for security level of 128 bits. We also show that there is a generic method to construct Weight Restricted Hash (WRH) functions which can produce hash value with a given Hamming weight. (C) 2020 Elsevier B.V. All rights reserved.

关键词： code-based cryptography Hamming metric Digital signatures

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A toolbox for software optimization of QC-MDPC code-based cryptosystems

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JOURNAL OF CRYPTOGRAPHIC ENGINEERING 2019年第4期9卷 341-357页

作者： Drucker, Nir Gueron, Shay Univ Haifa Haifa Israel Amazon Web Serv Inc Seattle WA 98109 USA

The anticipated emergence of quantum computers in the foreseeable future drives the cryptographic community to start considering cryptosystems, which are based on problems that remain intractable even with large-scale quantum computers. One example is the family of code-based cryptosystems that relies on the syndrome decoding problem. Recent work by Misoczki et al. (in: 2013 IEEE international symposium on information theory, pp 2069-2073, 2013. https://***/10.1109/ISIT.2013.6620590) showed a variant of McEliece encryption which is based on quasi cyclic moderate density parity check (QC-MDPC) codes and has significantly smaller keys than the original McEliece encryption. It was followed by the newly proposed QC-MDPC-based cryptosystems CAKE (Barreto et al. in: IMA international conference on cryptography and coding, Springer, Berlin, pp 207-226, 2017) and Ouroboros (Deneuville et al. in Ouroboros: a simple, secure and efficient key exchange protocol based on coding theory, Springer, Cham, pp 18-34, 2017. https://***/10.1007/978-3-319-59879-62). These motivate dedicated new software optimizations. This paper lists the cryptographic primitives that QC-MDPC cryptosystems commonly employ, studies their software optimizations on modern processors, and reports the achieved speedups. It also assesses methods for side channel protection of the implementations and their performance costs. These optimized primitives offer a useful toolbox that can be used, in various ways, by designers and implementers of QC-MDPC cryptosystems. Indeed, we applied our methods to generate a platform-specific additional implementation of "BIKE"-a QC-MDPC key encapsulation mechanism (KEM) proposal submitted to the NIST Post-Quantum Project (NIST:Post-Quantum cryptography-call for proposals, https://***/Projects/Post-Quantum-cryptography, 2017). This gave a 5x speedup compared to the reference implementation.

关键词： QC-MDPC code-based cryptography Post-Quantum cryptography

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Efficient Encryption From Random Quasi-Cyclic codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第5期64卷 3927-3943页

作者： Aguilar-Melchor, Carlos Blazy, Olivier Deneuville, Jean-Christophe Gaborit, Philippe Zemor, Gilles Univ Toulouse INP ENSEEIHT F-31000 Toulouse France Univ Toulouse ISAE SUPAERO F-31000 Toulouse France Univ Limoges XLIM F-87060 Limoges France Univ Orleans LIFO F-18000 Bourges France INSA CVL F-18000 Bourges France Univ Bordeaux UMR 5251 IMB F-33405 Talence France

We propose a framework for constructing efficient code-based encryption schemes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based on the difficulty of decoding random linear codes from random errors of low weight. We depart somewhat from Alekhnovich's approach and propose an encryption scheme based on the difficulty of decoding random quasi-cyclic codes. We propose two new cryptosystems instantiated within our framework: the hamming quasi-cyclic cryptosystem (HQC), based on the hamming metric, and the rank quasi-cyclic cryptosystem (RQC), based on the rank metric. We give a security proof, which reduces the indistinguishability under chosen plaintext attack security of our systems to a decision version of the well-known problem of decoding random families of quasi-cyclic codes for the hamming and rank metrics (the respective QCSD and RQCSD problems). We also provide an analysis of the decryption failure probability of our scheme in the Hamming metric case: for the rank metric there is no decryption failure. Our schemes benefit from a very fast decryption algorithm together with small key sizes of only a few thousand bits. The cryptosystems are very efficient for low encryption rates and are very well suited to key exchange and authentication. Asymptotically, for lambda the security parameter, the public key sizes are respectively in O(lambda(2)) for HQC and in O(lambda(4/3)) for RQC. Practical parameter compares well to the systems based on ring-learning parity with noise or the recent moderate density parity check codes system.

关键词： code-based cryptography public-key encryption post-quantum cryptography provable security

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Integer syndrome decoding in the presence of noise

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cryptography AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2024年第5期16卷 1103-1134页

作者： Dragoi, Vlad-Florin Colombier, Brice Cayrel, Pierre-Louis Grosso, Vincent Aurel Vlaicu Univ Arad Fac Exact Sci Arad Romania Univ Rouen Normandy LITIS Ave Univ F-76800 St Etienne Du Rouvray France Univ Lyon UJM St Etienne Lab Hubert Curien UMR 5516 CNRS F-42023 St Etienne France

code-based cryptography received attention after the NIST started the post-quantum cryptography standardization process in 2016. A central NP-hard problem is the binary syndrome decoding problem, on which the security of many code-based cryptosystems lies. The best known methods to solve this problem all stem from the information-set decoding strategy, first introduced by Prange in 1962. A recent line of work considers augmented versions of this strategy, with hints typically provided by side-channel information. In this work, we consider the integer syndrome decoding problem, where the integer syndrome is available but might be noisy. We study how the performance of the decoder is affected by the noise. First we identify the noise model as being close to a centered in zero binomial distribution. Second we model the probability of success of the ISD-score decoder in presence of a binomial noise. Third, we demonstrate that with high probability our algorithm finds the solution as long as the noise parameter d is linear in t (the Hamming weight of the solution) and t is sub-linear in the code-length. We provide experimental results on cryptographic parameters for the BIKE and Classic McEliece cryptosystems, which are both candidates for the fourth round of the NIST standardization process.

关键词： code-based cryptography Syndrome decoding problem Information-set decoding

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LowMS: a new rank metric code-based KEM without ideal structure

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DESIGNS codeS AND cryptography 2024年第4期92卷 1075-1093页

作者： Aragon, Nicolas Dyseryn, Victor Gaborit, Philippe Loidreau, Pierre Renner, Julian Wachter-Zeh, Antonia NAQUIDIS Ctr Talence France Univ Limoges XLIM Limoges France Univ Rennes DGA MI CNRS IRMAR Rennes France Tech Univ Munich Inst Commun Engn Munich Germany

We propose and analyze LowMS, a new rank-based key encapsulation mechanism (KEM). The acronym stands for Loidreau with Multiple Syndromes, since our work combines the cryptosystem of Loidreau (presented at PQCrypto 2017) together with the multiple syndromes approach, that allows to reduce parameters by sending several syndromes with the same error support in one ciphertext. Our scheme is designed without using ideal structures. Considering cryptosystems without such an ideal structure, like the FrodoKEM cryptosystem, is important since structure allows to compress objects, but gives reductions to specific problems whose security may potentially be weaker than for unstructured problems. For 128 bits of security, we propose parameters with a public key size of 4.8 KB and a ciphertext size of 1.1 KB. To the best of our knowledge, our scheme is the smallest among all existing unstructured post-quantum lattice or code-based algorithms, when taking into account the sum of the public key size and the ciphertext size. In that sense, our scheme is for instance about 4 times shorter than FrodoKEM. Our system relies on the hardness of the Rank Support Learning problem, a well-known variant of the Rank Syndrome Decoding problem, and on the problem of indistinguishability of distorted Gabidulin codes, i.e., Gabidulin codes multiplied by a homogeneous matrix of given rank. The latter problem was introduced by Loidreau in his paper.

关键词： Rank-based cryptography code-based cryptography Post-quantum cryptography Rank support learning

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A New Sieving-Style Information-Set Decoding Algorithm

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第11期70卷 8303-8319页

作者： Guo, Qian Johansson, Thomas Nguyen, Vu Lund Univ Dept Elect & Informat Technol Lund Sweden

The problem of decoding random codes is a fundamental problem for code-based cryptography, including recent code-based candidates in the NIST post-quantum standardization process. In this paper, we present a novel Sieving-style Information-set Decoding algorithm, addressing the task of solving the syndrome decoding problem. Our approach involves maintaining a list of weight- $2p$ solution vectors to a partial syndrome decoding problem and then creating new vectors by identifying pairs of vectors that collide in p positions. By gradually increasing the parity-check condition by one and repeating this process iteratively, we find the final solution(s). We show that our novel algorithm performs better than other ISDs in the memory-restricted scenario when applied to McEliece. Notably, in the case of problem instances with very low relative weight, the sieving approach uses significantly less memory compared to other ISD algorithms while being competitive in terms of performance.

关键词： code-based cryptography NIST post-quantum standardization information-set decoding classic-McEliece BIKE HQC code-based cryptography NIST post-quantum standardization information-set decoding classic-McEliece BIKE HQC

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MODRED: A code-based non-interactive key exchange protocol

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THEORETICAL COMPUTER SCIENCE 2024年 1021卷

作者： Pei, Junling Fu, Fang-Wei Nankai Univ Chern Inst Math Tianjin 300071 Peoples R China

How to construct a non-interactive key exchange (NIKE) protocol based on coding theory is an opening problem. In this paper, we propose the first code-based NIKE protocol MODRED, whose security relies on the hardness of the Restricted Syndrome Decoding (R-SD) problem and its variant. A non-interactive error reconciliation mechanism is presented and applied to MODRED, which enables the two sides of communication to "approximately agree" on the shared key. This is of great significance because it may lead to a more generic framework construction. Furthermore, our proposal is competitive and practical. We provide an initial choice of parameters for MODRED, tailored to 120-bit post-quantum security level, yielding the public keys of less than 1.2 MBs.

关键词： code-based cryptography Non-interactive key exchange protocol Restricted Syndrome Decoding problem Reconciliation mechanism

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Extended security arguments for signature schemes

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DESIGNS codeS AND cryptography 2016年第2期78卷 441-461页

作者： Dagdelen, Ozgur Galindo, David Veron, Pascal Alaoui, Sidi Mohamed El Yousfi Cayrel, Pierre-Louis Tech Univ Darmstadt Darmstadt Germany LORIA CNRS Nancy France Univ Sud Toulon Var IML IMATH La Garde France Univ St Etienne Lab Hubert Curien St Etienne France

It is known how to transform certain canonical three-pass identification schemes into signature schemes via the Fiat-Shamir transform. Pointcheval and Stern showed that those schemes are existentially unforgeable in the random-oracle model leveraging the, at that time, novel forking lemma. Recently, a number of 5-pass identification protocols have been proposed. Extending the above technique to capture 5-pass identification schemes would allow to obtain novel unforgeable signature schemes. In this paper, we provide an extension of the forking lemma (and the Fiat-Shamir transform) in order to assess the security of what we call n-generic signature schemes. These include signature schemes that are derived from certain (2n + 1)-pass identification schemes. In doing so, we put forward a generic methodology for proving the security of a number of signature schemes derived from (2n+ 1)-pass identification schemes for n >= 2. As an application of this methodology, we obtain two new code-based existentially-unforgeable signature schemes, along with a security reduction. In particular, we solve an open problem in multivariate cryptography posed by Sakumoto, Shirai and Hiwatari at CRYPTO 2011.

关键词： code-based cryptography Multivariate cryptography Signature schemes Forking lemma Identification schemes Fiat-Shamir

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code-based signatures from new proofs of knowledge for the syndrome decoding problem

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DESIGNS codeS AND cryptography 2023年第2期91卷 497-544页

作者： Bidoux, Loic Gaborit, Philippe Kulkarni, Mukul Mateu, Victor Technol Innovat Inst Abu Dhabi U Arab Emirates Univ Limoges Limoges France

In this paper, we study code-based signatures constructed from Proofs of Knowledge (PoK). This line of work can be traced back to Stern who introduced the first efficient PoK for the syndrome decoding problem in 1993 (Stern in A new identification scheme based on syndrome decoding. In: International cryptology conference (CRYPTO), 1993). Afterwards, different variations were proposed in order to reduce signature's size. In practice, obtaining a smaller signature size relies on the interaction of two main considerations: (i) the underlying protocol and its soundness error and (ii) the types of optimizations which are compatible with a given protocol. In particular, optimizations related to the possibility of using random seeds instead of long vectors have a great impact on the final signature length. Over the years, different variations were proposed to improve the Stern scheme such as the Veron scheme (with public key as a noisy codeword rather than a syndrome) (Veron in Appl Algebra Eng Commun Comput 8(1):57-69, 1997), the AGS scheme which is a 5-pass protocol with soundness error asymptotically equal to 1/2 (Aguilar et al. in A new zero-knowledge code based identification scheme with reduced communication. In: IEEE information theory workshop, 2011) and more recently the FJR approach which permits to decrease the soundness probability to 1/N but induces a performance overhead (Feneuil et al. in Shared permutation for syndrome decoding: new zero-knowledge protocol and code-based signature. Cryptology ePrint archive, report 2021/1576, 2021). Overall the length of the signature depends on a trade-off between: the scheme in itself, the possible optimizations and the cost of the implementation. For instance, depending on the application one may prefer a 30% shorter signature at the cost of a ten times slower implementation rather than a longer signature but a faster implementation. The recent approaches which increase the cost of the implementation open the door to man

关键词： code-based cryptography Signature Proof of knowledge

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