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On the Complexity of the LWR-Solving BKW Algorithm

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2020年第1期E103A卷 173-182页

作者： Okada, Hiroki Takayasu, Atsushi Fukushima, Kazuhide Kiyomoto, Shinsaku Takagi, Tsuyoshi KDDI Res Inc Informat Secur Lab Fujimino Shi 3568502 Japan Univ Tokyo Grad Sch Informat Sci & Technol Tokyo 1138654 Japan

The Blum-Kalai-Wasserman algorithm (BKW) is an algorithm for solving the learning parity with noise problem, which was then adapted for solving the learning with errors problem (LWE) by Albrecht et al. Duc et al. applied BKW also to the learning with rounding problem (LWR). The number of blocks is a parameter of BKW. By optimizing the number of blocks, we can minimize the time complexity of BKW. However, Duc et al. did not derive the optimal number of blocks theoretically, but they searched for it numerically. Duc et al. also showed that the required number of samples for BKW for solving LWE can be dramatically decreased using Lyubashevsky's idea. However, it is not shown that his idea is also applicable to LWR. In this paper, we theoretically derive the asymptotically optimal number of blocks, and then analyze the minimum asymptotic time complexity of the algorithm. We also show that Lyubashevsky's idea can be applied to LWR-solving BKW, under a heuristic assumption that is regularly used in the analysis of LPN-solving BKW. Furthermore, we derive an equation that relates the Gaussian parameter sigma of LWE and the modulus p of LWR. When sigma and p satisfy the equation, the asymptotic time complexity of BKW to solve LWE and LWR are the same.

关键词： lattice learning with errors learning with rounding Blum-Kalai-Wasserman algorithm

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Accelerating subset sum and lattice based public-key cryptosystems with multi-core CPUs and GPUs

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2018年 119卷 179-190页

作者： Al Badawi, Ahmad Veeravalli, Bharadwaj Aung, Khin Mi Mi Hamadicharef, Brahim Natl Univ Singapore Dept Elect & Comp Engn 4 Engn Dr 3 Singapore 117576 Singapore ASTAR DSI Connexis North Lobby 1 Fusionopolis Way Singapore 138632 Singapore

Post-quantum cryptosystems based on subset sum and lattice problems have gained much attention from researchers due to their simple construction, their resistance to quantum attacks, the new potential applications they provide, and above all, the mathematical security proofs that rigorously relate them to computational hard problems. However, the computational complexity of these cryptosystems is still high compared to classic number-theoretical ones, which may impede their adoption on a large scale. We studied the performance of three public-key cryptosystems based on subset sum, learning with errors and ring learning with errors problems. We provide a systematic study for choosing their parameters to guarantee sufficient security levels and detail an asymptotic comparison between them in terms of storage and running time complexities. We accelerate the running time of these cryptosystems by exploiting the inherent parallelism in computations through a GPGPU-based parallel implementation. The cryptosystems are implemented using C++ on Intel(R) Xeon(R) multi-core 64-bit processors machine with CUDA-enabled Tesla K80 GPUs. The parallel implementation is based on OpenCL framework and can run on arbitrary hardware platform accelerators with minor changes. Several optimizations and efficient algorithms were used to compute the core operations in each cryptosystem to achieve optimum performance. The ring learning with errors based cryptosystem showed the best performance while the Subset Sum cryptosystem showed the highest speedup gain for the encryption primitive. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Lattice cryptography Post-quantum cryptography Public-key cryptosystem Subset sum learning with errors GPGPU programming Parallel polynomial multiplier

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Lattice-based public-key encryption with equality test supporting flexible authorization in standard model

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THEORETICAL COMPUTER SCIENCE 2022年 929卷 124-139页

作者： Roy, Partha Sarathi Dung Hoang Duong Susilo, Willy Sipasseuth, Arnaud Fukushima, Kazuhide Kiyomoto, Shinsaku Univ Wollongong Sch Comp & Informat Technol Inst Cybersecur & Cryptol Northfields Ave Wollongong NSW 2522 Australia KDDI Res Inc Informat Secur Lab 2-1-15 Ohara Fujimino Saitama 3568502 Japan

As cloud computing has developed rapidly, outsourcing data to cloud servers for remote storage has become an attractive trend. However, when cloud clients store their data in the cloud, the security and privacy of cloud data would be threatened due to accidental corruptions or purposive attacks caused by a semi-trusted cloud server. The widely used method of addressing the security and privacy of cloud data is to store encrypted data instead of plain data. As the resulting system is unusable, since the cloud can no longer search throughout the data, new cryptographic primitive such as public-key encryption with equality test (PKEET) has been introduced. PKEET has many interesting applications such as keyword search on encrypted data, encrypted data partitioning for efficient encrypted data management, personal health record systems, spam filtering in encrypted email systems and so forth. PKEET allows checking whether two ciphertexts encrypted under different public keys contain the same message or not. However, unrestricted access to equality tests can reveal information about the underlying data. This is not acceptable in respect of users' privacy. In 2015, Ma et al. introduce the notion of PKEET with flexible authorization (PKEET-FA) which strengthens privacy protection. Since 2015, there are several follow-up works on PKEET-FA. However, all are secure in the random oracle model and vulnerable to quantum attacks. In this paper, we provide two constructions of quantum-safe PKEET-FA secure in the standard model based on the hardness assumptions of integer lattices and ideal lattices. Finally, we implement the PKEET-FA scheme over ideal lattices. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Post-quantum cryptography Equality test Cloud computing learning with errors

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Identity-based signcryption from lattices

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SECURITY AND COMMUNICATION NETWORKS 2015年第18期8卷 3751-3770页

作者： Yan, Jianhua Wang, Licheng Dong, Mianxiong Yang, Yixian Yao, Wenbin Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China Ludong Univ Sch Informat & Elect Engn Yantai 264025 Peoples R China Natl Inst Informat & Commun Technol Kyoto 6190289 Japan

Signcryption as a cryptographic primitive can carry out signature and encryption simultaneously at a remarkably reduced cost. Identity-based cryptography is more convenient than public key infrastructure-based cryptography in certificate management. As a result, identity-based signcryption has been studied extensively, and many efficient and provably secure constructions have been proposed. However, most of these schemes are based on intractability assumptions from number theory, and these assumptions have been threatened by the booming quantum computation. Therefore, a recent trend in cryptography is to construct cryptosystems that are based on lattice-based intractability assumptions because of their plausible features of quantum attack resistance. In this paper, several identity-based signcryption schemes from lattice hardness assumptions are proposed. In the standard model, these schemes are indistinguishable against inner adaptively chosen ciphertext attacks (IND-CCA2) and strongly unforgeable against inner chosen message attacks. In our construction, it does not matter whether the original encryption scheme used to construct signcryption is deterministic or probabilistic;the resulted signcryption schemes can reach IND-CCA2 security. To achieve this, we carefully combine three techniques-the identity-based encryption from lattice due to Agrawal-Boneh-Boyen (EUROCRYPT 2010), the framework of lattice-based short signature due to Boyen (Public Key Cryptography 2010), and the Canetti-Halevi-Katz (abbr. CHK) technique, with necessary and tailored optimization-for transforming an (l + 1)-level indistinguishable under chosen plaintext attack secure hierarchical identity-based encryption (HIBE) into an l level IND-CCA2 secure HIBE scheme. In addition, our security proof also contains a more efficient simulation tool that might have separate interest in cryptographic applications. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： signcryption lattice standard model learning with errors learning with rounding short integer solution

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Maliciously circuit-private multi-key FHE and MPC based on LWE

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DESIGNS CODES AND CRYPTOGRAPHY 2023年第5期91卷 1645-1684页

作者： Attrapadung, Nuttapong Hanaoka, Goichiro Hiromasa, Ryo Matsuda, Takahiro Schuldt, Jacob C. N. Natl Inst Adv Ind Sci & Technol 2-3-26 Aomi Koto ku Tokyo 1350064 Japan Mitsubishi Elect 5-1-1 Ofuna Kamakura Kanagawa 2470056 Japan

In this paper, we construct multi-key homomorphic and fully homomorphic encryption (resp. MKHE and MKFHE) schemes with malicious circuit privacy. Our schemes are based on learning with errors (LWE) besides appropriate circular security assumptions. In contrast, the previous maliciously circuit-private MKFHE scheme by Chongchitmate and Ostrovsky (PKC, 2017) is based on the non-standard decisional small polynomial ratio (DSPR) assumption with a super-polynomial modulus, besides ring learning with errors and circular security assumptions. We note that it was shown by Albrecht et al. (CRYPTO, 2016) that there exists a sub-exponential time attack against this type of DSPR assumption. The main building block of our maliciously circuit-private MKFHE scheme is a (plain) MKFHE scheme by Brakerski et al. (TCC, 2017), and the security of our schemes is proven under the hardness of LWE with sub-exponential modulus-to-noise ratio and circular security assumptions related to the Brakerski et al. scheme. Furthermore, based on our MKFHE schemes, we construct four-round multi-party computation (MPC) protocols with circuit privacy against a semi-honest server and malicious clients in the plain model. The protocols are obtained by combining our schemes with a maliciously sender-private oblivious transfer protocol and a circuit garbling scheme, all of which can be instantiated only assuming LWE.

关键词： Multi-key fully homomorphic encryption Circuit privacy learning with errors Multi-party computation

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Lattice-based public key searchable encryption with fine-grained access control for edge computing

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FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2022年 127卷 373-383页

作者： Wang, Peng Chen, Biwen Xiang, Tao Wang, Zhongming Chongqing Univ Sci & Technol Sch Intelligent Technol & Engn Chongqing 401331 Peoples R China Chongqing Univ Coll Comp Sci Chongqing 400044 Peoples R China

As a bridge between cloud computing platforms and the Internet of Things (IoT) devices, edge computing provides various on-demand data services to reduce latency and network congestion. To ensure data security in edge computing, sensitive data should be encrypted before being outsourced to edge servers. Public key encryption with keyword search (PEKS) can provide search service for encrypted data. Nevertheless, most existing PEKS schemes are susceptible to quantum attacks because their security assumptions are based on traditional hardness assumptions. Moreover, many lattice based PEKS schemes only apply to the single-user scenario, limiting the range of applications. In this paper, we present an efficient lattice-based public key searchable encryption with fine-grained access control for edge computing. Our scheme achieves post-quantum security and highly flexible access control policies for multi-user applications, by utilizing the learning with errors (LWE) assumption and subset predicate encryption. The security proof illustrates that our proposed scheme is secure under chosen plaintext attacks and chosen keyword attacks. Finally, extensive experiments on real-world datasets illustrate that our encryption algorithm is faster than existing approaches. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Edge computing Searchable encryption Post-quantum security learning with errors

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CP-ABSEL: Ciphertext-policy attribute-based searchable encryption from lattice in cloud storage

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PEER-TO-PEER NETWORKING AND APPLICATIONS 2021年第3期14卷 1290-1302页

作者： Varri, Uma Sankararao Pasupuleti, Syam Kumar Kadambari, K. V. Natl Inst Technol Warangal Andhra Pradesh India Inst Dev & Res Banking Technol Hyderabad Telangana India

Ciphertext-policy attribute-based searchable encryption (CP-ABSE) is widely used in the cloud environment to provide data privacy and fine-grained access control over encrypted data. The existing CP-ABSE schemes are designed based on bilinear pairing hardness assumptions to prove their security. However, these schemes are vulnerable to quantum attacks, i.e., adversaries can break the security of these schemes with the use of quantum computers. To address this issue, in this paper, we propose a novel ciphertext-policy attribute-based searchable encryption from lattice (CP-ABSEL) in cloud storage, since lattice-based cryptography is quantum attacks free. In CP-ABSEL, we adopted learning with errors (LWE) hardness assumption to resist from quantum attacks. Further, CP-ABSEL is indistinguishable against the chosen keyword attack and indistinguishable against chosen plaintext attack. Moreover, CP-ABSEL allows only legitimate users to perform a keyword search over an encrypted index, and unauthorized users cannot get even the ciphertext form of documents. The performance analysis proves that CP-ABSEL is efficient and practical.

关键词： Ciphertext-policy attribute-based searchable encryption Lattice Cloud storage learning with errors

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A post quantum secure construction of an authentication protocol for satellite communication

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INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS AND NETWORKING 2022年第1期41卷 14-28页

作者： Dharminder, Dharminder Dadsena, Pradeep Kumar Gupta, Pratik Sankaran, Sathya Amrita Vishwa Vidyapeetham Dept Comp Sci & Engn Amrita Sch Engn Chennai Tamil Nadu India Govt Engn Coll Dept Math Jagdalpur India Mandsaur Univ Dept Math Mandsaur India

Satellite's communication system is used to communicate under significant distance and circumstances where the other communication systems are not comfortable. Since all the data are exchanged over a public channel, so the security of the data is an essential component for the communicating parties. Both key exchange and authentication are two cryptographic tools to establish a secure communication between two parties. Currently, various kinds of authentication protocols are available to establish a secure network, but all of them depend on number-theoretical (discrete logarithm problem/factorization assumption) hard assumptions. Due to Shor's and Grover's computing algorithm number theoretic assumptions are breakable by quantum computers. Although Kumar and Garg have proposed a quantum attack-resistant protocol for satellite communication, it cannot resist stolen smart card attack. We have analyzed that how Kumar and Garg is vulnerable to the stolen smart card attack using differential power analysis attack described in He et al and Chen and Chen. We have also analyzed the modified version of signal leakage attack and sometimes called improved signal leakage attack on Kumar and Garg's protocol. We have tried to construct a secure and efficient authentication protocol for satellites communication that is secure against quantum computing. This is more efficient as it requires only three messages of exchange. This paper includes security proof and performance of the proposed authentication and key agreement protocol.

关键词： authentication learning with errors post quantum key agreement satellite communication

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Trapdoor function based on the Ring-LWE and applications in communications

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JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2019年第5期10卷 1821-1827页

作者： Zhang, Chengli Ma, Wenping Zhao, Feifei Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Shaanxi Peoples R China

The strong trapdoor function for lattice has been constructed by Daniele Micciancio and Chris Peikert in EUROCRYPT 2012, which is simple, efficient, and easy to implement. In this paper, we present a new trapdoor function based on ring learning with errors problem (Ring-LWE) on lattice, and simultaneously the corresponding efficient inverse algorithm is given which involves two sub-algorithms: the trapdoor inverse algorithm and the iterative inverse algorithm. Our trapdoor function for lattice based on Ring-LWE is simultaneously more simple and efficient because of the ring structure. In addition to these advantages, our algorithm extends the parameters, and this can make our trapdoor function have a wider choice of applications.

关键词： Lattice Trapdoor function learning with errors Ring Cryptography

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A construction of post quantum secure authenticated key agreement design for mobile digital rights management system

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MULTIMEDIA TOOLS AND APPLICATIONS 2023年第17期82卷 26643-26660页

作者： Dadsena, Pradeep Kumar Jain, Jainendra Rana, Saurabh Dharminder, Dharminder Govt Engn Coll Dept Math Jagdalpur India Chandigarh Univ Dept Math Chandigarh India Amrita Vishwa Vidyapeetham Amrita Sch Comp Dept Comp Sci Engn Chennai India

The quantum computing being a threat motivates us to design a post quantum secure authentication protocol for mobile digital rights management system. In current, a post quantum secure protocol "learning with error based secure mobile digital rights management system" has been proposed. The protocol has been claimed to post quantum secure under the ring learning with errors assumption. We have analyzed that this protocol allows the server to keep a fixed private/public key that causes less communication and computation overheads. But, this leads to signal leakage/modified signal leakage attacks. In this paper, we have discussed signal leakage attacks during the authentication phase of the existing protocol. We have proposed a new post quantum authenticated key agreement protocol for the digital rights management system. In the proposed protocol, the server uses a random value instead of using fixed value chosen by the user, and it establishes a session key with the user. Moreover, this protocol needs to exchange just two messages that confirm the efficiency. The protocol has been proved secure in a random oracle model under ring learning with errors assumption. Moreover, the article contains an informal security discussion and a simulation using NS3 simulator.

关键词： Digital rights management system Privacy Security Authentication Ideal lattice learning with errors

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