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37th IEEE International Conference on Computer Design (ICCD)

作者： Bellini, Emanuele Caullery, Florian Makarim, Rusydi Manzano, Marc Marcolla, Chiara Mateu, Victor Technol Innovat Inst Crypto Ctr Abu Dhabi U Arab Emirates

ISBN: (纸本)9781538666487

Recent works on reducing the size of Error Correcting codes have investigated the usage of rank metric instead of Hamming metric. Numerous proposals for the NIST Post-Quantum cryptography competition, including four second round candidates, rely on these codes. In this paper, we discuss several non-trivial issues when porting these schemes into real-world systems on different platforms, such as Intel x86, Armv6 and Armv8. We provide insights on how to implement the underlying finite field and polynomial arithmetic, or the generation of errors of a given rank in constant-time, and report execution time of several rank-based cryptosystems, showing that the achieved performance is similar to those of some of the most popular lattice-based cryptosystems.

关键词： Post-Quantum cryptography Rank Metric code-based cryptography

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The Rank-based cryptography Library 1

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9th International Workshop on code-based cryptography (CBCrypto)

作者： Aragon, Nicolas Bettaieb, Slim Bidoux, Loic Connan, Yann Coulaud, Jeremie Gaborit, Philippe Kominiarz, Anais Univ Limoges Limoges France Worldline Seclin France Technol Innovat Inst Abu Dhabi U Arab Emirates

ISBN: (数字)9783030983659

ISBN: (纸本)9783030983659;9783030983642

Rank-based cryptography provides cryptosystems that aim to be secure against both classical and quantum computers. In the past few years, the interest for code-based cryptography in the rank metric setting has tremendously increased notably since the beginning of the NIST post-quantum cryptography standardization process. This paper introduces RBC a library dedicated to Rank-based cryptography and details its design and architecture. The performances of RBC are illustrated against comparable state of the art librairies. RBC greatly outperforms those libraries as it is 2 to 5 times faster than NTL and 40 to 138 times faster than mpF(q) on the multiplication and inversion over F-qm(n) which are the most critical operations when it comes to rank-based cryptography performances. In addition, the performances of ROLLO and RQC two rank-based cryptosystems provided by the library are reported for two platforms: a desktop computer equipped with an Intel Skylake-X CPU and an ARM Cortex-M4 microcontroller.

关键词： RBC Rank metric Library code-based cryptography

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An improved Durandal signature scheme

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Science China(Information Sciences) 2020年第3期63卷 140-155页

作者： Yongcheng SONG Xinyi HUANG Yi MU Wei WU Fujian Provincial Key Laboratory of Network Security and Cryptology College of Mathematics and InformaticsFujian Normal University

Constructing secure and effective code-based signature schemes has been an open problem. In this paper, we efficiently reduce the key size of the Durandal signature scheme introduced by Aragon et al.(EUROCRYPT 2019). We prove that the improved scheme is EUF-CMA secure by reducing its security to the advanced product spaces subspaces indistinguishability(PSSI+) problem, the decisional rank syndrome decoding(DRSD) problem, and the affine rank syndrome decoding(ARSD) problem under the random oracle model. Furthermore, our signature scheme is more secure than the Durandal scheme because recovering key attacks are equivalent to solving the rank syndrome decoding(RSD) problem, instead of the rank support learning(RSL) problem in the original Durandal scheme. Our signature scheme takes less time to generate a signature owing to the fact that our signature scheme enjoys smaller security parameters in comparison to the Duradual scheme. We compare the new scheme with existing code-based signature schemes and find that our signature scheme has advantages in terms of the public key size.

关键词： post-quantum cryptography code-based cryptography rank metric digital signatures provable security

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Compact code-based Signature for Reconfigurable Devices With Side Channel Resilience

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2020年第7期67卷 2305-2316页

作者： Hu, Jingwei Liu, Yao Cheung, Ray C. C. Bhasin, Shivam Ling, San Wang, Huaxiong Nanyang Technol Univ Sch Phys & Math Sci Singapore 639798 Singapore City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China Nanyang Technol Univ Temasek Labs Singapore 639798 Singapore

In this paper, we present a compact design for the code based signature called LEDAsig with side channel resistance. Existing implementations concentrate on the high-speed feature while few of them have considerations on area or power efficiency which are particularly decisive for low-cost or power constrained IoT applications. We propose an area-efficient FPGA architecture for systematically rotating the QC-LDGM codes amongst the block RAMs with read-first mode. Additionally, the side channel vulnerability of LEDAsig is carefully examined, and protective masking schemes are introduced accordingly to safeguard our design from power analysis attacks. Effectiveness of these schemes is verified on SAKURA-G FPGA board. Up till now, the design presented in this work is the most compact one and also the first side-channel secure one addressing first-order and (univariate) second-order differential power analysis for the code based signature schemes in the open literature. We show for instance that our first-order (second-order) protected implementation can sign a signature in 117 (203) ms on a Xilinx Spartan-6 FPGA, occupying only 622 (1142) slices, and therefore is a prospective candidate for post-quantum signature schemes in low-resource settings.

关键词： Sparse matrices Field programmable gate arrays Generators Random access memory Elliptic curve cryptography code-based cryptography CFS signature scheme QC-LDGM code hardware security compact implementation

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ECC²: Error correcting code and elliptic curve based cryptosystem

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INFORMATION SCIENCES 2020年 526卷 301-320页

作者： Zhang, Fangguo Zhang, Zhuoran Guan, Peidong Sun Yat Sen Univ Sch Data & Comp Sci Guangzhou 510006 Peoples R China Guangdong Key Lab Informat Secur Guangzhou 510006 Peoples R China

code-based cryptography has aroused wide public concern as one of the main candidates for post quantum cryptography to resist attacks against cryptosystems from quantum computation. However, the large key size becomes a drawback that prevents it from wide practical applications although it performs pretty well on the speed of both encryption and decryption. The use of algebraic geometry codes is considered to be a good solution to reduce the key size, but the special structures of algebraic geometry codes results in lots of attacks including Minder's attack. To cope with the barriers of large key size as well as attacks from the special structures of algebraic codes, we propose a code-based encryption system using elliptic codes. The special structure of elliptic codes helps us to effectively reduce the size of secret key. By choosing the rational points carefully, we build elliptic codes whose minimum weight codeword is hard to sample. Such codes are used in constructing encryption systems such that Minder's attacks can be resisted. More importantly, we apply the list decoding algorithm in the decryption process thus more errors beyond half of the minimum distance of the code could be corrected, which is the key point to resist other known attacks for algebraic geometry codes based cryptosystems. Our implementation shows that the proposed encryption system performs well on the key size and ciphertext expansion rate. (C) 2020 Elsevier Inc. All rights reserved.

关键词： code-based cryptography Post quantum cryptography Elliptic codes List decoding

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Generalized Low-Rank Parity-Check codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第8期70卷 5589-5605页

作者： Franch, Ermes Gaborit, Philippe Li, Chunlei Univ Bergen Dept Informat N-5008 Bergen Norway Univ Limoges XLIM F-87032 Limoges France

Let F(q )be the finite field with q elements and m be a positive integer. The Fqm -linear low-rank parity-check (LRPC) codes have been used in many cryptographic schemes. Motivated by recent attacks on those schemes, this paper generalizes LRPC codes based on 3-tensors in Fmxmxmq . The generalized LRPC codes are mostly F-q -linear matrix codes, while a particular choice of the 3-tensor is isomorphic to the original F-q(m) -linear LRPC codes. We first introduce a bilinear T-product over F-q(m) associated with a 3-tensor T is an element of F-q (mxmxm). based on the T-product, we propose a generic method to expand Fq -linear matrix code from dimension k to dimension km and then use the method to generalize LRPC codes. Finally, we propose two probabilistic polynomial-time decoding algorithms for the generalized LRPC codes under different circumstances. We provide estimates of their decoding failure rates, which, confirmed by experimental results, are almost the same as that of decoding F(q)m -linear LRPC codes.

关键词： Error correction codes rank metric low-rank parity-check (LRPC) codes decoding NP complete code-based cryptography Error correction codes rank metric low-rank parity-check (LRPC) codes decoding NP complete code-based cryptography

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New code-based cryptographic accumulator and fully dynamic group signature

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DESIGNS codeS AND cryptography 2022年第12期90卷 2861-2891页

作者： Ayebie, Edoukou Berenger Souidi, El Mamoun Mohammed V Univ Rabat Fac Sci Lab Math Comp Sci Applicat & Informat Secur BP 1014 RP Rabat Morocco

A cryptographic accumulator is a cryptographic primitive which produces a succinct aggregate of a set of elements. This type of scheme allows to produce a membership proof for each element of the set. In this paper, we propose a code-based cryptographic accumulator that is quantum computer resistant. Specifically, our scheme is based on the hardness of the Syndrome Decoding problem and satisfies the collision freeness and indistinguishability requirements. We also use double circulant codes which allow us to get a small key size, especially we get for an 80 bits security a small public key of 347 bits. Furthermore, we use the proposed cryptographic accumulator to create a fully dynamic code-based group signature. Moreover, we give an implementation of our scheme which is, to the best of our knowledge, the first direct implementation of a post-quantum cryptographic accumulator.

关键词： Cryptographic accumulator code-based cryptography Merkle-Tree Double circulant codes Post-quantum cryptography Fully dynamic group signature

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Smooth Projective Hash Function From codes and its Applications

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IEEE TRANSACTIONS ON SERVICES COMPUTING 2022年第6期15卷 3541-3553页

作者： Shooshtari, Masoumeh Koochak Aref, Mohammad Reza Sharif Univ Technol Dept Elect Engn Informat Syst & Secur Lab ISSL Tehran *** Iran

Nowadays, Smooth Projective Hash Functions (SPHFs) play an important role in constructing cryptographic tools such as secure Password-based Authenticated Key Exchange (PAKE) protocol in the standard model, oblivious transfer, and zero-knowledge proofs. Specifically, in this article, we focus on constructing PAKE protocol;that is, a kind of key exchange protocol which needs only a low entropy password to produce a cryptographically strong shared session key. In spite of relatively good progress of SPHFs in applications, it seems there has been little effort to build them upon quantum-resistant assumptions such as lattice-based cryptography and code-based cryptography to make them secure against quantum computer attacks. More precisely, there are two proposals based on lattice assumptions that utilize the SPHFs to construct PAKE secured in standard model. Considering quantum-resistant assumptions is less than straightforward and needs some relaxations. In this article, we introduce two new Approximate SPHF (ASPHFs) from error-correcting codes. Upon designing ASPHF, we can construct two efficient PAKE protocols. The security of our protocols could be proved based on the hardness of bounded decoding (BD) problem and learning with parity (LPN) problem in the standard model.

关键词： Password-based authenticated key exchange protocol smooth projective hash function code-based cryptography standard model provable security

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LIGA: a cryptosystem based on the hardness of rank-metric list and interleaved decoding

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DESIGNS codeS AND cryptography 2021年第6期89卷 1279-1319页

作者： Renner, Julian Puchinger, Sven Wachter-Zeh, Antonia Tech Univ Munich TUM Inst Commun Engn Munich Germany Tech Univ Denmark DTU Dept Appl Math & Comp Sci Lyngby Denmark

We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. LIGA is an improved variant of the Faure-Loidreau (FL) system, which was broken in a structural attack by Gaborit, Otmani, and Tale Kalachi (GOT, 2018). We keep the FL encryption and decryption algorithms, but modify the insecure key generation algorithm. Our crucial observation is that the GOT attack is equivalent to decoding an interleaved Gabidulin code. The new key generation algorithm constructs public keys for which all polynomial-time interleaved decoders fail-hence LIGA resists the GOT attack. We also prove that the public-key encryption version of LIGA is IND-CPA secure in the standard model and the key encapsulation mechanisms version is IND-CCA2 secure in the random oracle model, both under hardness assumptions of formally defined problems related to list decoding and interleaved decoding of Gabidulin codes. We propose and analyze various exponential-time attacks on these problems, calculate their work factors, and compare the resulting parameters to NIST proposals. The strengths of LIGA are short ciphertext sizes and (relatively) small key sizes. Further, LIGA guarantees correct decryption and has no decryption failure rate. It is not based on hiding the structure of a code. Since there are efficient and constant-time algorithms for encoding and decoding Gabidulin codes, timing attacks on the encryption and decryption algorithms can be easily prevented.

关键词： code-based cryptography Gabidulin codes Interleaved decoding List decoding Rank-metric codes

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On Design of Single-Layer and Multilayer code-based Linkable Ring Signatures

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IEEE ACCESS 2020年 8卷 17854-17862页

作者： Ren, Yan Zhao, Qiuxia Guan, Haipeng Lin, Zhiqiang Yuncheng Univ Sch Math & Informat Technol Yuncheng 044000 Peoples R China Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Guangdong Peoples R China

In this paper, we present an effective code-based linkable ring signature scheme based on Borromean ring signature. The security of the scheme is based on the hardness of Syndrome Decoding problem, General Syndrome Decoding problem and codeword Finding problem. We prove that our scheme has all the properties that a linkable ring signature scheme should have: unforgeability, anonymity, linkability and non-slanderability. Efficiency analysis shows that our scheme has a smaller signature size than the existing scheme under the same security conditions. Furthermore, this signature scheme can be easily extended to multiple layers. That is, code-based multilayer linkable ring signature scheme can be obtained and used for transactions with multiple inputs.

关键词： Post-quantum ring signature linkable ring signature code-based cryptography

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