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Product of repdigits with consecutive lengths in the Fibonacci sequence.

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA 2021年第2期27卷 1-9页

作者： Gomez, Jhonny C. Luca, Florian Univ Valle Dept Matemat Calle 13 100-00 Cali 25360 Colombia Univ Witwatersrand Sch Math Johannesburg South Africa King Abdulaziz Univ Res Grp Algebra Struct & Applicat Jeddah Saudi Arabia UNAM Ctr Ciencias Matemat Morelia Michoacan Mexico

From the well-known Fibonacci sequence, the number F-10=55=5 center dot 11 is an example not only as a repdigit (a number with only one distinct digit) but also as a product of two repdigits with consecutive lengths, 5 and 11. Here we find all the Fibonacci numbers that can be written as the product of k repdigits with consecutive lengths.

关键词： Fibonacci numbers Repdigits Applications of lower bounds for nonzero linear forms in logarithms of algebraic numbers lll algorithm

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Cryptanalysis of NTRU with n Public Keys

Cryptanalysis of NTRU with <i>n</i> Public Keys

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Conference on ISEA Asia Security and Privacy (ISEASP)

作者： Singh, Sonika Padhye, Sahadeo Motilal Nehru Natl Inst Technol Dept Math Allahabad 211004 Uttar Pradesh India

ISBN: (纸本)9781509059423

The NTRU public key cryptosystem was proposed by Hoffstein, Pipher and Silverman in 1996. NTRU is one of the most widely used public key cryptosystems and its security has been an active research topic. In 1977, coppersmith and Shamir applied new lattice basis reduction techniques to cryptanalyze the scheme, to discover either the original secret key, or an alternative secret key which is equally useful in decoding the ciphertexts. In 2014, A. Nitaj gave cryptanalysis of NTRU with two public keys and compared with lattice attack given by Coppersmith and Shamir. In this paper, we are generalizing the idea of A. Nitaj and presenting cryptanalysis of NTRU with n public keys.

关键词： NTRU Cryptosystem Lattices Shortest Vector Problem Closest Vector Problem lll algorithm

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Combined Forward and Backward Lattice Reduction Aided MMSE Detection in MIMO Systems

Combined Forward and Backward Lattice Reduction Aided MMSE D...

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68th IEEE Vehicular Technology Conference

作者： Fujino, Tadashi Shimokawa, Tetsuyoshi Univ Electrocommun Chofu Tokyo 1828585 Japan

ISBN: (纸本)9781424417223;9781424417216

This paper proposes a combined forward and backward lattice reduction scheme to improve estimation of transmitted signals in lattice-reduction aided (LRA) MMSE MIMO systems. The cross-correlation between the forward and the backward transform matrices is also analyzed to make sure that the proposed detector achieves more reliable estimates. The proposed detector achieves better BER performance than the conventional LRA detector. The achieved BER curve is improved by 3.5dB at BER=10(-5) over the curve of the conventional LRA MMSE detector in the 8x8 MIMO.

关键词： correlation of channels lattice reduction lll algorithm MIMO MMSE signal estimation

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Lattice Reduction Aided Precoding for Multiuser MIMO using Seysen's algorithm

Lattice Reduction Aided Precoding for Multiuser MIMO using S...

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20th IEEE Symposium on Personal, Indoor and Mobile Radio Communications

作者： An, HongSun Mohaisen, Manar Chang, KyungHi Inha Univ Grad Sch IT & T Inchon South Korea

ISBN: (纸本)9781424451234

Lenstra-Lenstra-Lovasz (lll) algorithm, which is one of the lattice reduction (LR) techniques, has been extensively used to obtain better basis of the channel matrix. In this paper, we jointly apply Seysen's lattice reduction algorithm (SA), instead of lll, with the conventional linear precoding algorithms. Since SA obtains more orthogonal lattice basis compared to that obtained by lll, lattice reduction aided (LRA) precoding based on SA algorithm outperforms the LRA precoding with lll. Simulation results demonstrate that a gain of 0.5dB at target BER of 10(-5) is achieved when SA is used instead of lll for the LR stage.

关键词： Seysen's algorithm lattice reduction multiuser-MIMO precoding lll algorithm

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Secure Outsourcing of Lattice Basis Reduction 26th

Secure Outsourcing of Lattice Basis Reduction

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26th International Conference on Neural Information Processing (ICONIP) of the Asia-Pacific-Neural-Network-Society (APNNS)

作者： Liu, Jiayang Bi, Jingguo Tsinghua Univ Beijing 100084 Peoples R China Beijing Res Inst Telemetry Beijing 100094 Peoples R China

ISBN: (纸本)9783030367114;9783030367107

In the recent twenty years, lattice basis reduction algorithm, such as the celebrated lll (A.K. Lenstra-H.W. Lenstra Jr.-L. Lovasz) algorithm plays an important role in the public-key schemes design and cryptanalysis. To assess the security of the public-key cryptosystems by lattice reduction algorithms, the most time-consuming part is running the lattice reduction algorithm on the corresponding lattice with high dimension or big coefficients. In this paper, we investigate secure out-sourcing for lattice basis reduction for the first time. We propose a lattice basis reduction scheme such that the clients can outsource their main computation workloads to the untrusted cloud servers. We employ rounding technique and unimodular transformation matrix for privacy protection before sending the target lattice basis to the cloud. The results returned from the cloud need to be decrypted and verified to satisfy reduction conditions. The experimental results indicate that our scheme is correct, efficient and feasible.

关键词： Cloud computing Outsource-secure Lattice basis reduction lll algorithm QR-factorization

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Efficient polynomial L∞-approximations

Efficient polynomial L∞-approximations

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18th IEEE Symposium on Computer Arithmetic

作者： Brisebarre, Nicolas Chevillard, Sylvain Univ St Etienne LaMUSE 23 Rue Dr P Michelon F-42023 St Etienne 02 France Univ Lyon 1 INRIA CNRS ENS Lyon LIP F-69364 Lyon France

ISBN: (纸本)9780769528540

We address the problem of computing a good floating-point-coefficient polynomial approximation to a function, with respect to the supremum norm. This is a key step in most processes of evaluation of a function. We present a fast and efficient method, based on lattice basis reduction, that often gives the best polynomial possible and most of the time returns a very good approximation.

关键词： efficient polynomial approximation floating-point arithmetic absolute error L infinity norm lattice basis reduction closest vector problem lll algorithm

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Efficient Texture Regularity Estimation for Second Order Statistical Descriptors 10

Efficient Texture Regularity Estimation for Second Order Sta...

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Proceedings of the 10th International Symposium on Image and Signal Processing and Analysis

作者： Tiba, Attila Harangi, Balazs Hajdu, Andras Univ Debrecen Fac Informat POB 400 H-4002 Debrecen Hungary

ISBN: (纸本)9781509040117

Co-occurrence matrices as sources of second order statistical descriptors are commonly used in texture classification tasks. To generate such a matrix, we need a position vector to check possible intensity frequencies in its endpoints. In this paper, we propose an efficient algorithm to locate such position vectors according which the pattern of the texture repeats and thus, the descriptors (Haralick features) derived from the co-occurrence matrix are capable to characterize the regularity of the pattern. The essence of our approach is to look for vectors that span well-approximating grids defined by reference points obtained by quantizing the input image. To extract such grids we use the lll algorithm, which has a polynomial running time. Thus, we have a much more efficient solution than e.g. a brute force based search. Our results show that the proposed approach is capable to suggest position vectors for an efficient co-occurrence matrix based texture analysis.

关键词： co-occurrence matrix texture analyses regular texture descriptors lll algorithm

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A Low Complexity ZF-Based Lattice Reduction Detection Using Curtailment Parameter in MIMO Systems 15

A Low Complexity ZF-Based Lattice Reduction Detection Using ...

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15th IEEE/ACIS International Conference on Computer and Information Science (ICIS)

作者： Mitsunaga, Daisuke Khine, Thae Thae Yu Zhao, Hua-An Kumamoto Univ Dept Comp Sci & Elect Engn Kumamoto 860 Japan

ISBN: (纸本)9781509008056

As the large-scale multiple-input multiple-output (MIMO) systems have been advanced in wireless communication, the low complexity and high performance receiver technique have been required. Recently, lattice reduction technique have attracted attention in MIMO detection. Especially, lattice reduction aided linear detection like zero-forcing (ZF) can largely improve the performance with low complexity. Among all the lattice reduction algorithms, the Lenstra-Lenstra-Lovasz (lll) algorithm is well-known and widely used algorithm. lll algorithm reduces the basis of channel matrix by using two conditions and it adopts a parameter in order to get nearly orthogonal basis. Although the parameter is defined range, a constant value is commonly used. However it can't be said that the constant value is the best value for all MIMO system. In this paper, we propose an appropriate parameter to reduce computational complexity in lll algorithm for ZF detection and we also propose an architecture to adapt our proposed parameter in MIMO detection. The proposed parameter is showed simply and corresponds to the number of antennas. Simulation results show that the proposed parameter provides lll lattice reduction aided ZF detection achieving the same performance as the widely used constant value with lower complexity and also correspond to every MIMO system including large-scale MIMO system.

关键词： multiple-input multiple-output (MIMO) lattice reduction complexity reduction lll algorithm parameter delta

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LATENCY-CONSTRAINED LOW-COMPLEXITY LATTICE REDUCTION FOR MIMO-OFDM SYSTEMS

LATENCY-CONSTRAINED LOW-COMPLEXITY LATTICE REDUCTION FOR MIM...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Liao, Chun-Fu Lan, Fang-Chun Huang, Yuan-Hao Chiu, Po-Lin Natl Tsing Hua Univ Inst Commun Engn Hsinchu Taiwan

ISBN: (纸本)9781457705397

Recent studies have investigated lattice-reduction (LR) preprocessing technique for multiple-input multiple-output (MIMO) detection. However, if LR is applied to the orthogonal-frequency-division-multiplexing (OFDM) system, its complexity and latency increase greatly because of the large number of sub-carriers. This paper proposes a new processing architecture for LR-aided MIMO-OFDM system. This LR processing architecture reduces the number of iteration loops by using preprocessing matrix of adjacent sub-carrier. Beside, the grouping of sub-carriers can break the long critical computational path so as to comprise the computational complexity and latency. We simulate the proposed LR-aided MIMO-OFDM processing in the 3GPP-LTE system. The proposed method not only reduces the computational complexity but also shortens the latency for the lattice reduction.

关键词： MIMO OFDM Lattice Reduction lll algorithm

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Attacking RSA with a Composed Decryption Exponent Using Unravelled Linearization 10

Attacking RSA with a Composed Decryption Exponent Using Unra...

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10th China International Conference on Information Security and Cryptology (Inscrypt)

作者： Huang, Zhangjie Hu, Lei Xu, Jun Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China Chinese Acad Sci Data Assurance & Commun Secur Res Ctr Beijing 100093 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

ISBN: (纸本)9783319167459;9783319167442

Recently, Nitaj and Douh presented a new attack on RSA with a composed decryption exponent. To be specific, they assumed that the decryption exponent in RSA is of the form d = Md-1+d(0) where M is a known positive integer and d(0) and d(1) are two suitably small unknown integers. They gave a lattice-based decryption exponent recovery attack on this kind of RSA when the exponent d is under a larger bound than the well-known one N-0.292 given by Boneh and Durfee. In this paper, we reconsider the same problem and present a new attack by using the unravelled linearization technique proposed by Herrmann and May at Asiacrypt 2009. Our result is theoretically better than that of Nitaj and Douh and more importantly, is more efficient in terms of the dimension of lattice involved in the attack.

关键词： RSA Unravelled linearization Coppersmith's method Lattice basis reduction lll algorithm

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