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DESIGNS CODES AND CRYPTOGRAPHY 2017年第1-2期84卷 237-259页

作者： Neumaier, Arnold Univ Vienna Fak Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria

The paper describes improved analysis techniques for basis reduction that allow one to prove strong complexity bounds and reduced basis guarantees for traditional reduction algorithms and some of their variants. This is achieved by a careful exploitation of the linear equations and inequalities relating various bit sizes before and after one or more reduction steps.

关键词： Basis reduction Lattices BKZ algorithm lll algorithm

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Generalized Framework to Attack RSA with Special Exposed Bits of the Private Key

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2017年第10期E100A卷 2113-2122页

作者： Wang, Shixiong Qu, Longjiang Li, Chao Fu, Shaojing Natl Univ Def Technol Coll Comp Changsha Hunan Peoples R China Natl Univ Def Technol Coll Sci Changsha Hunan Peoples R China State Key Lab Cryptol Beijing Peoples R China

In this paper, we study partial key exposure attacks on RSA where the number of unexposed blocks of the private key is greater than or equal to one. This situation, called generalized framework of partial key exposure attack, was first shown by Sarkar [22] in 2011. Under a certain condition for the values of exposed bits, we present a new attack which needs fewer exposed bits and thus improves the result in [22]. Our work is a generalization of [28], and the approach is based on Coppersmith's method and the technique of unravelled linearization.

关键词： RSA partial key exposure attack lattice lll algorithm Coppersmith's method unravelled linearization

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A Lattice Basis Reduction Approach for the Design of Finite Wordlength FIR Filters

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第10期66卷 2673-2684页

作者： Brisebarre, Nicolas Filip, Silviu-Ioan Hanrot, Guillaume Univ Claude Bernard Lyon 1 INRIA ENS Lyon CNRSLab LIPUMR 5668 F-69007 Lyon France Univ Oxford Math Inst Oxford OX1 2JD England

Many applications of finite impulse response (FIR) digital filters impose strict format constraints on the filter coefficients. Such requirements increase the complexity of determining optimal designs for the problem at hand. We introduce a fast and efficient method, based on the computation of good nodes for polynomial interpolation and Euclidean lattice basis reduction. Experiments show that it returns quasi-optimal finite wordlength FIR filters;compared to previous approaches it also scales remarkably well (length 125 filters are treated in < 9 s). It also proves useful for accelerating the determination of optimal finite wordlength FIR filters.

关键词： BKZ algorithm Euclidean Lattice finite wordlength FIR coefficient quantization FIR digital filters HKZ algorithm lattice basis reduction lll algorithm minimax approximation

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Augmented Lattice Reduction for MIMO Decoding

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2010年第9期9卷 2853-2859页

作者： Luzzi, Laura Rekaya-Ben Othman, Ghaya Belfiore, Jean-Claude Telecom ParisTech Dept Commun & Elect F-75013 Paris France

Lattice reduction algorithms, such as the Lenstra-Lenstra-Lovasz (lll) algorithm, have been proposed as preprocessing tools in order to enhance the performance of suboptimal receivers in multiple-input multiple-output (MIMO) communications. A different approach, introduced by Kim and Park, allows to combine right preprocessing and detection in a single step by performing lattice reduction on an "augmented channel matrix". In this paper we propose an improvement of the augmented matrix approach which guarantees a better performance. We prove that our method attains the maximum receive diversity order of the channel. Simulation results evidence that it significantly outperforms lll reduction followed by successive interference cancellation (SIC) while requiring a moderate increase in complexity. A theoretical bound on the complexity is also derived.

关键词： Lattice reduction-aided decoding lll algorithm right preprocessing

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An efficient lattice reduction using reuse technique blockwisely on NTRU

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DISCRETE APPLIED MATHEMATICS 2016年第0期214卷 88-98页

作者： Chung, Kyungmi Lee, Hyang-Sook Lim, Seongan Ewha Womans Univ Dept Math Seoul South Korea Ewha Womans Univ Inst Math Sci Seoul South Korea

In this paper, we propose a lattice reduction algorithm for use with NTRU lattices. Given an NTRU lattice as its input, the algorithm computes an lll-reduced basis. The proposed lattice reduction algorithm is more efficient than the classical lll algorithm. Recently, a lattice reduction algorithm for ideal lattices, named illl, was proposed by Plantard, Susilo, and Zhang. This algorithm is identical to that of the lll except for the fact that it contains an additional subroutine, named Reuse. The subroutine serves to further reduce a set of short vectors that has already been computed by the algorithm prior to its initiation. As a result, the illl is able to output an lll-reduced basis more efficiently than the lll is able to do so. However, the illl cannot be directly applied to an NTRU lattice, because it is not an ideal lattice. Yet, from the fact that an NTRU lattice is also a module lattice (a generalization of an ideal lattice), we can adapt the main idea behind the illl blockwisely in our approach to NTRU lattices. We demonstrate that the proposed algorithm (containing a modified version of the aforementioned subroutine Reuse) is asymptotically 5 times faster at outputting an lll-reduced basis than the lll when applied to NTRU lattices of dimension n. In the case of small n, our experiments show that the proposed algorithm is slightly faster at outputting an lll-reduced basis than the lll. In addition, we present an example of how to recover a private key of an NTRU encryption scheme by using the proposed algorithm in the case of n = 22. (C) 2016 Elsevier B.V. All rights reserved.

关键词： NTRU lattice lll algorithm illl algorithm Reuse technique

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Structure of the rational monoid algebra for Boolean matrices of order 3

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LINEAR ALGEBRA AND ITS APPLICATIONS 2014年 449卷 381-401页

作者： Bremner, Murray R. Univ Saskatchewan Dept Math & Stat Saskatoon SK S7N 0W0 Canada

We use the computer algebra system Maple to study the 512-dimensional associative algebra QB(3), the rational monoid algebra of 3 x 3 Boolean matrices. Using the lll algorithm for lattice basis reduction, we obtain a basis for the radical in bijection with the 42 non-regular elements of B-3. The center of the 470-dimensional semisimple quotient has dimension 14;we use a splitting algorithm to find a basis of orthogonal primitive idempotents. We show that the semisimple quotient is the direct sum of simple two-sided ideals isomorphic to matrix algebras M-d(Q) for d = 1, 1, 1, 2, 3, 3, 3, 3, 6, 6, 7, 9, 9, 12. We construct the irreducible representations of 133 over Q by calculating the representation matrices for a minimal set of generators. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Boolean matrices Associative algebras Radical lll algorithm Semisimple quotient Wedderburn decomposition Simple two-sided ideals Rational representations

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Dual RSA and its security analysis

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IEEE TRANSACTIONS ON INFORMATION THEORY 2007年第8期53卷 2922-2933页

作者： Sun, Hung-Min Wu, Mu-En Ting, Wei-Chi Hinek, M. Jason Natl Tsing Hua Univ Dept Comp Sci Hsinchu 300 Taiwan Univ Waterloo David R Cheriton Sch Comp Sci Waterloo ON N2L 3G1 Canada

We present new variants of an RSA whose key generation algorithms output two distinct RSA key pairs having the same public and private exponents. This family of variants, called Dual RSA, can be used in scenarios that require two instances of RSA with the advantage of reducing the storage requirements for the keys. Two applications for Dual RSA, blind signatures and authentication/secrecy, are proposed. In addition, we also provide the security analysis of Dual RSA. Compared to normal RSA, the security boundary should be raised when applying Dual RSA to the types of Small-d, Small-e, and Rebaianced-RSA.

关键词： cryptography encryption lattice basis reduction lll algorithm rebalanced RSA RSA twin RSA

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An Improved Quantization Scheme for Lattice-Reduction Aided MIMO Detection Based on Gram-Schmidt Orthogonalization

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2013年第12期E96A卷 2405-2414页

作者： Hou, Wei Fujino, Tadashi Kojima, Toshiharu Univ Electrocommun Dept Informat & Commun Chofu Tokyo 1828585 Japan

Lattice-reduction (LR) technique has been adopted to improve the performance and reduce the complexity in MIMO data detection. This paper presents an improved quantization scheme for LR aided MIMO detection based on Gram-Schmidt orthogonalization. For the LR aided detection, the quantization step applies the simple rounding operation, which often leads to the quantization errors. Meanwhile, these errors may result in the detection errors. Hence the purpose of the proposed detection is to further solve the problem of degrading the performance due to the quantization errors in the signal estimation. In this paper, the proposed quantization scheme decreases the quantization errors using a simple tree search with a threshold function. Through the analysis and the simulation results, we observe that the proposed detection can achieve the nearly optimal performance with very low complexity, and require a little additional complexity compared to the conventional LR-MMSE detection in the high E-b/N-0 region. Furthermore, this quantization error reduction scheme is also efficient even for the high modulation order.

关键词： Gram-Schmidt orthogonalization lll algorithm lattice-reduction MIMO quantization error

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Security Analysis of Hybrid Attack for NTRU-Class Encryption Schemes

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IEEE ACCESS 2023年 11卷 109939-109952页

作者： Levina, Alla Kadykov, Victor Valluri, Maheswara Rao St Petersburg Electrotech Univ LETI Lab Fundamentals Intelligent Syst LETI St Petersburg 197376 Russia Quinfosystems Pvt Ltd Telangana 500072 India

One of the significant post-quantum cryptographic candidates is the NTRU public key cryptosystem. It operates on polynomial rings, where the parameter largely determines the security of the system. Although NTRU is being studied currently, it has a long and well-established history. There are several lattice-based attacks on NTRU-like systems that exploit the special structures of the rings used in these systems. The aim of this paper is to analyze the original NTRU, NTRU Encrypt, and NTRU Primes encryption schemes by structuring their common elements and showing the strongest hybrid attack using both lattice reduction and meet-in-the-middle (MITM) search on them. Furthermore, it is noted that, ignoring a polynomial factor of the not-well-studied cost of Block Korkin-Zolotarev (BKZ) algorithm, we estimate the security of the construction of encryption keys and show that by balancing lattice reduction costs and a MITM search cost, one can achieve better performance than using any of these methods on their own. Unlike previous studies, we found the way to ignore polynomial impact 2(2)-2(4) from BKZ loops with multiple shortest vector problem (SVP) and the factor of 2(7) was omitted from the cost of one step in guessing the SVP.

关键词： BKZ algorithm cryptography ideals lattices lll algorithm NTRU public key polynomial ring security proof

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Solving a class of modular polynomial equations and its relation to modular inversion hidden number problem and inversive congruential generator

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DESIGNS CODES AND CRYPTOGRAPHY 2018年第9期86卷 1997-2033页

作者： Xu, Jun Sarkar, Santanu Hu, Lei Huang, Zhangjie Peng, Liqiang Chinese Acad Sci Inst Informat Engn State Key State Lab Informat Secur Beijing 100093 Peoples R China Chinese Acad Sci Data Assurance & Commun Secur Res Ctr Beijing 100093 Peoples R China Indian Inst Technol Madras Dept Math Chennai 600036 Tamil Nadu India

In this paper we revisit the modular inversion hidden number problem (MIHNP) and the inversive congruential generator (ICG) and consider how to attack them more efficiently. We consider systems of modular polynomial equations of the form and show the relation between solving such equations and attacking MIHNP and ICG. We present three heuristic strategies using Coppersmith's lattice-based root-finding technique for solving the above modular equations. In the first strategy, we use the polynomial number of samples and get the same asymptotic bound on attacking ICG proposed in PKC 2012, which is the best result so far. However, exponential number of samples is required in the work of PKC 2012. In the second strategy, a part of polynomials chosen for the involved lattice are linear combinations of some polynomials and this enables us to achieve a larger upper bound for the desired root. Corresponding to the analysis of MIHNP we give an explicit lattice construction of the second attack method proposed by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001. We provide better bound than that in the work of PKC 2012 for attacking ICG. Moreover, we propose the third strategy in order to give a further improvement in the involved lattice construction in the sense of requiring fewer samples.

关键词： Modular inversion hidden number problem Inversive congruential generator Lattice lll algorithm Coppersmith's technique

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