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Area-Time-Efficient code-based Postquantum Key Encapsulation Mechanism on FPGA

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 2020年第12期28卷 2672-2684页

作者： Phoon, Jun-Hoe Lee, Wai-Kong Wong, Denis Chee-Keong Yap, Wun-She Goi, Bok-Min Univ Tunku Abdul Rahman Lee Kong Chian Fac Engn & Sci Petaling Jaya 43000 Malaysia Gachon Univ Dept Comp Engn Seongnam 13120 South Korea

Postquantum cryptography attracts a lot of attention from the research community recently due to the emergence threat from quantum computer toward the conventional cryptographic schemes. In view of that, NIST had initiated the standardization process in 2017. Bit flipping key encapsulation (BIKE) designed by Aragon et al. is one of the promising code-based schemes among the round-3 candidates. BIKE utilizes a quasi-cyclic medium density parity check (QC-MDPC) code and incorporates a few variants derived from the McEliece, Niederreiter, and Ouroboros schemes. In this article, we present efficient and constant time implementation of BIKEI and BIKE-III in field-programmable gate array (FPGA), which has the best area-time efficiency so far. We proposed modification to the original one-round bit flipping algorithm to achieve more area-time-efficient decoding in hardware, which achieved latency of 464.73 and 556.52 mu s for BIKE-I and BIKE-III, respectively, in Virtex-7. A pipelined key encapsulation architecture is proposed to speedup the key encapsulation of BIKE-I and BIKE-III, achieving the latency of 146.47 and 153.25 mu s on the same FPGA platform. Considering the Artix-7 FPGA platform, our combined key generation and encapsulation module for BIKE-I is also three more area-time efficient compared with the state-of-the-art BIKE-I implementation by Aragon et al.

关键词： Field programmable gate arrays Encapsulation Decoding NIST Public key code-based cryptography FPGA postquantum cryptography public key cryptography quasi-cyclic medium density parity check (QC-MDPC) McEliece

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Efficient error-correcting codes for the HQC post-quantum cryptosystem

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DESIGNS codeS AND cryptography 2024年第12期92卷 4511-4530页

作者： Aguilar-Melchor, Carlos Aragon, Nicolas Deneuville, Jean-Christophe Gaborit, Philippe Lacan, Jerome Zemor, Gilles SandboxAQ Palo Alto CA USA Univ Limoges Limoges France Univ Toulouse Federat ENAC ISAE SUPAERO ONERA Toulouse France Univ Toulouse ISAE SUPAERO Toulouse France Univ Bordeaux IMB Bordeaux France

The HQC post-quantum cryptosystem enables two parties to share noisy versions of a common secret binary string, and an error-correcting code is required to deal with the mismatch between both versions. This code is required to deal with binary symmetric channels with as large a transition parameter as possible, while guaranteeing, for cryptographic reasons, a decoding error probability of provably not more than 2-128. This requirement is non-standard for digital communications, and modern coding techniques are not amenable to this setting. This paper explains how this issue is addressed in the last version of HQC: precisely, we introduce a coding scheme that consists of concatenating a Reed-Solomon code with the tensor product of a Reed-Muller code and a repetition code. We analyze its behavior in detail and show that it significantly improves upon the previous proposition for HQC, which consisted of tensoring a BCH and a repetition code. As additional results, we also provide a better approximation of the weight distribution for HQC error vectors, and we remark that the size of the exchanged secret in HQC can be reduced to match the protocol security which also significantly improves performance.

关键词： Post-quantum cryptography code-based cryptography Public-key encryption HQC NIST

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An efficient code-based threshold ring signature scheme

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JOURNAL OF INFORMATION SECURITY AND APPLICATIONS 2019年第Apr.期45卷 52-60页

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

code based cryptography is a powerful and a promising alternative to the number theoretic cryptography as it is supposed to resist to the quantum computer. The migration to the post quantum hypothetical world requires the design of all the most important cryptographic primitives such as signature schemes. For this reason, we propose in this paper a ring signature and a threshold ring signature schemes that are based on coding theory assumptions. In the case of threshold ring signature scheme, we have a subset of users belonging to a group of users called a ring who collaborate in order to produce a signature on behalf of ring members while maintaining the anonymity of the identity of the real signers. In this paper, we use the AGS identification scheme, which is a coding theory zero-knowledge authentication protocol, to produce a ring signature and a threshold ring signature. By comparing our schemes with the best one in performance so far on 80 bits security level, we find an average 86% reduction of the signature size and also a reduction on the public key length at equivalent security level. The reduction is achieved for different values of the number of signers and ring's size. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Ring signature Threshold ring signature code-based cryptography AGS identification scheme Post-quantum Zero-knowledge

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Toward Practical code-based Signature: Implementing Fast and Compact QC-LDGM Signature Scheme on Embedded Hardware

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2017年第8期64卷 2086-2097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, fast and compact implementations for code-based signature are presented. Existing designs are either using enormous memory storage or suffering from slow issuing speed of signatures. A vastly optimized new design solving these problems is proposed by exploiting quasi-cyclic low-density generator matrix codes at different levels. In particular, this paper provides a new algorithmic enhancement of signature generation and gives detailed and optimized solutions for critical steps of this algorithm. The design presented in this paper is the fastest implementation of code-based signatures in open literature. It is shown, for instance, that our implementation of signature generation engine can generate approximately 60 000 signatures per second on a Xilinx Virtex-6 FPGA, requiring only 5992 slices and 60 memory blocks. In addition, a very compact implementation is also provided, producing 5438 signatures per second with only 18 memory blocks.

关键词： code-based cryptography CFS signature scheme QC-LDGM code FPGA

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Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes

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DESIGNS codeS AND cryptography 2014年第2期73卷 641-666页

作者： Couvreur, Alain Gaborit, Philippe Gauthier-Umana, Valerie Otmani, Ayoub Tillich, Jean-Pierre INRIA Saclay GRACE Project F-91120 Palaiseau France Ecole Polytech CNRS UMR 7161 LIX F-91120 Palaiseau France Univ Limoges CNRS UMR 7252 XLIM F-87060 Limoges France Univ Rosario Fac Nat Sci & Math Dept Math Bogota Colombia Normandie Univ LITIS UR F-76821 Mont St Aignan France INRIA Rocquencourt SECRET Project F-78153 Le Chesnay France

Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink proposed a variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed-Solomon code. More recently, new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee, and a variation of the McEliece cryptosystem proposed by Baldi et al. which hides the generalized Reed-Solomon code by means of matrices of very low rank. In this work, we show how to mount key-recovery attacks against these public-key encryption schemes. We use the concept of distinguisher which aims at detecting a behavior different from the one that one would expect from a random code. All the distinguishers we have built are based on the notion of component-wise product of codes. It results in a powerful tool that is able to recover the secret structure of codes when they are derived from generalized Reed-Solomon codes. Lastly, we give an alternative to Sidelnikov and Shestakov attack by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed-Solomon code.

关键词： code-based cryptography Generalized Reed-Solomon codes Key-recovery Distinguisher Homomorphic encryption

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A privacy-preserving code-based authentication protocol for Internet of Things

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JOURNAL OF SUPERCOMPUTING 2019年第12期75卷 8231-8261页

作者： Chikouche, Noureddine Cayrel, Pierre-Louis Mboup, El Hadji Modou Boidje, Brice Odilon Univ Msila Comp Sci Dept BP 166 Ichebilia 28000 Msila Algeria CNRS UMR 5516 Lab Hubert Curien Batiment F18 Rue Prof Benoit Lauras F-42000 St Etienne France Univ Cheikh Anta Diop Dakar Lab Algebre Cryptog Geometrie Algebr & Applicat Dakar Senegal

The Internet of Things (IoT) is an upcoming technology that permits to interconnect different devices and machines using heterogeneous networks. One of the most critical issues in IoT is to secure communication between IoT components. The communication between the different IoT components is insecure, which requires the design of a secure authentication protocol and uses hardness cryptographic primitives. In 2017, Wang et al. proposed an improved authentication protocol based on elliptic curve cryptography for IoT. In this paper, we demonstrate that Wang et al.'s protocol is not secure. Additionally, we propose a privacy-preserving authentication protocol using code-based cryptosystem for IoT environments. The code-based cryptography is an important post-quantum cryptography that can resist quantum attacks. It is agreed in design several cryptographic schemes. To assess the proposed protocol, we carry out a security and performance analysis. Informal security analysis and formal security validation show that our protocol achieves different security and privacy requirements and can resist several common attacks, such as desynchronization attacks, quantum attacks, and replay attacks. Moreover, the performance evaluation indicates that our protocol is compatible with capabilities of IoT devices.

关键词： Authentication protocol Internet of Things code-based cryptography Security Privacy

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Extending Coggia-Couvreur attack on Loidreau's rank-metric cryptosystem

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DESIGNS codeS AND cryptography 2022年第1期90卷 215-238页

作者： Ghatak, Anirban RC Bose Ctr Secur & Cryptol ISI Kolkata India

A recent paper by Coggia and Couvreur presents a polynomial time key-recovery attack on Loidreau's encryption scheme, based on rank-metric codes, for some parameters. Their attack was formulated for the particular case when the secret matrix in Loidreau's scheme is restricted to a 2-dimensional subspace. We present an extension of the Coggia-Couvreur attack to deal with secret matrices chosen over subspaces of dimension greater than 2.

关键词： Rank-metric codes code-based cryptography Cryptanalysis

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On the dimension and structure of the square of the dual of a Goppa code

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DESIGNS codeS AND cryptography 2022年第4期91卷 1351-1372页

作者： Mora, Rocco Tillich, Jean-Pierre INRIA Team COSMIQ 2 Rue Simone Iff F-75012 Paris France UPMC Univ Paris 06 Sorbonne Univ 4 Pl Jussieu F-75005 Paris France

The Goppa code distinguishing (GD) problem asks to distinguish efficiently a generator matrix of a Goppa code from a randomly drawn one. We revisit a distinguisher for alternant and Goppa codes through a new approach, namely by studying the dimension of square codes. We provide here a rigorous upper bound for the dimension of the square of the dual of an alternant or Goppa code, while the previous approach only provided algebraic explanations based on heuristics. Moreover, for Goppa codes, our proof extends to the non-binary case as well, thus providing an algebraic explanation for the distinguisher which was missing up to now. All the upper bounds are tight and match experimental evidence. Our work also introduces new algebraic results about products of trace codes in general and of dual of alternant and Goppa codes in particular, clarifying their square code structure. This might be of interest for cryptanalysis purposes.

关键词： Algebraic codes Goppa codes Alternant codes Square codes Distinguisher of Goppa codes code-based cryptography

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A code-based group signature scheme

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DESIGNS codeS AND cryptography 2017年第1-2期82卷 469-493页

作者： Alamelou, Quentin Blazy, Olivier Cauchie, Stephane Gaborit, Philippe Univ Limoges XLIM DMI Limoges France Worldline R&D Dept Seclin France

This work is the extended version of Alam,lou et al. (in: Tillich et al. (eds.) The 9th International workshop on coding and cryptography 2015 (WCC2015), 2015) which proposed the first code-based group signature. The new group signature scheme we present here has numerous advantages over all existing post-quantum constructions and even competes (in terms of properties) with pairing based constructions: it allows to add new members during the lifetime of the group (dynamic). Plus, it appears that our scheme might be extended into a traceable signature according to the definition of Kiayias et al. (in: Cachin and Camenisch (eds.) Advances in cryptology-EUROCRYPT 2004, 2004) (KTY model) while handling membership revocation. Our security is based on a relaxation of the model of Bellare et al. (in: Topics in cryptology-CT-RSA 2005, 2005) (BSZ model) verifying the properties of anonymity, traceability and non-frameability. The main idea of our scheme consists in building an offset collision of two syndromes associated to two different matrices: a random one which enables to build a random syndrome from a chosen small weight vector;and a trapdoor matrix for the syndrome decoding problem, which permits to find a small weight preimage of the previous random syndrome to which a fixed syndrome is added. These two small weight vectors will constitute the group member's secret signing key whose knowledge will be proved thanks to a variation of Stern's authentication protocol. For applications, we consider the case of the code-based CFS signature scheme (Nicolas in Advances in cryptology-ASIACRYPT 2001, 2001) of Courtois, Finiasz and Sendrier. If one denotes by N the number of group members, CFS leads to signatures and public keys sizes in . Along with this work, we also introduce a new kind of proof of knowledge, Testable weak Zero Knowledge (TwZK), implicitly covered in the short version of this paper (Alam,lou et al. in: Tillich et al. (eds.) The 9th international workshop on

关键词： code-based cryptography Group signature Proof of knowledge Random oracle model

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Information Theoretical Cryptogenography

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JOURNAL OF CRYPTOLOGY 2017年第4期30卷 1067-1115页

作者： Jakobsen, Sune K. UCL Dept Comp Sci London England

We consider problems where n people are communicating and a random subset of them is trying to leak information, without making it clear who are leaking the information. We introduce a measure of suspicion and show that the amount of leaked information will always be bounded by the expected increase in suspicion, and that this bound is tight. Suppose a large number of people have some information they want to leak, but they want to ensure that after the communication, an observer will assign probability at most c to the events that each of them is trying to leak the information. How much information can they reliably leak, per person who is leaking? We show that the answer is (-log(1-c)/c - log(e)) bits.

关键词： Anonymity code-based cryptography cryptography Information theory Steganography

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