• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.1-20
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• 2016

The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial selection (being used in factoring RSA challenge numbers) is to select a nonlinear polynomial for algebraic sieving and a linear polynomial for rational sieving. There is another method called a nonlinear method which selects two polynomials of the same degree greater than one. In this paper, we generalize Montgomery's method [12] using geometric progression (GP) (mod N) to construct a pair of nonlinear polynomials. We also introduce GP of length d + k with $1{\leq}k{\leq}d-1$ and show that we can construct polynomials of degree d having common root (mod N), where the number of such polynomials and the size of the coefficients can be precisely determined.

• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.3
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• pp.55-61
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• 2011

This paper presents an implementation of Lattice Reduction (LR)-aided detector for Multiple-Input Multiple-Output (MIMO) system using Graphics Processing Unit (GPU). GPU is a parallel processor which has a number of Arithmetic Logic Units (ALUs), thus, it can minimize the operation time of LR algorithm through the parallelization using multiple threads in the GPU. Through the implemented LR-aided detector, we verify that the LR-aided detector operates a lot faster than Maximum Likelihood (ML) detector. The implemented LR-aided detector has been applied to WiMAX system to show the feasibility of its real-time processing. In addition, we demonstrate that the processing time can be reduced at the cost of 3dB SNR loss by limiting the repeating loop in Lenstra-Lenstra-Lovasz (LLL) algorithm which is frequently used in LR-aided detector.

• Journal of the Korean Society for Nondestructive Testing
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• v.37 no.1
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• pp.13-20
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• 2017

A conventional phased array ultrasonic system offers the ability to steer an ultrasonic beam by applying independent time delays of individual elements in the array and produce an ultrasonic image. In contrast, full matrix capture (FMC) is a data acquisition process that collects a complete matrix of A-scans from every possible independent transmit-receive combination in a phased array transducer and makes it possible to reconstruct various images that cannot be produced by conventional phased array with the post processing as well as images equivalent to a conventional phased array image. In this paper, a basic algorithm based on the LLL mode total focusing method (TFM) that can image crack type flaws is described. And this technique was applied to reconstruct flaw images from the FMC dataset obtained from the experiments and ultrasonic simulation.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.4 no.3
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• pp.189-196
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• 2011

In this paper, we analyze the error performance of SIC-based signal detection methods in MIMO systems. Considered detection methods are SIC signal detection and LR-SIC signal detection. We derive BLER performance of the methods and the performance is confirmed by computer simulations.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.721-741
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• 2009

Consider RSA with N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. We first study cryptanalysis of RSA when certain amount of the Most Significant Bits (MSBs) or Least Significant Bits (LSBs) of d is known. The basic lattice based technique is similar to that of Ernst et al. in Eurocrypt 2005. However, our idea of guessing a few MSBs of the secret prime p substantially reduces the requirement of MSBs or LSBs of d for the key exposure attack. Further, we consider the RSA variant proposed by Sun and Yang in PKC 2005 and show that the partial key exposure attack works significantly on this variant.

• International journal of advanced smart convergence
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• v.7 no.3
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• pp.37-43
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• 2018

Lattice-reduction (LR) techniques have been developed for signal detection in spatial multiplexing multiple input multiple output (MIMO) systems to obtain the largest diversity gain. Thus, an LR-assisted zero-forcing (ZF) receiver can achieve the maximum diversity gain in spatial multiplexing MIMO systems. In this paper, a simplified analysis of the achievable diversity gain is presented by fitting the channel coefficients lattice-reduced by a complex Lenstra-Lenstra-$Lov{\acute{a}}z$ (LLL) algorithm into approximated Gaussian random variables. It will be shown that the maximum diversity gain corresponding to two times the number of receive antennas can be achieved by the LR-based ZF detector. In addition, the approximated bit error rate (BER) expression is also derived. Finally, the analytical BER performance is comparatively studied with the simulated results.

• Journal of Advanced Information Technology and Convergence
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• v.10 no.1
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• pp.1-14
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• 2020

Antenna selection is a method to enhance the performance of spatial multiplexing multiple-input multiple-output (MIMO) systems, which can achieve the diversity order of the full MIMO systems. Although various selection criteria have been studied in the literature, they should be adjusted to the detection operation implemented at the receiver. In this paper, antenna selection methods that optimize the post-processing signal-to-noise ratio (SNR) and eigenvalue are considered for the lattice reduction (LR)-based receiver. To develop a complexity-efficient antenna selection algorithm, the incremental selection strategy is adopted. Moreover, for improvement of performance, an additional iterative selection method is presented in combination with an incremental strategy.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.7
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• pp.3010-3025
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• 2016

Lattice reduction (LR) has been used widely in conventional multiple-input multiple-output (MIMO) systems to enhance the performance. However, LR is hard to be applied to the relay systems which are important but more complicated in the wireless communication theory. This paper introduces a new viewpoint for utilizing LR in multiuser MIMO relay systems. The vector precoding (VP) is designed along with zero force (ZF) criterion and minimum mean square error (MMSE) criterion and enhanced by LR algorithm. This implementable precoder design combines nonlinear processing at the base station (BS) and linear processing at the relay. This precoder is capable of avoiding multiuser interference (MUI) at the mobile stations (MSs) and achieving excellent performance. Moreover, it is shown that the amount of feedback information is much less than that of the singular value decomposition (SVD) design. Simulation results show that the proposed scheme using the complex version of the Lenstra--Lenstra--Lovász (LLL) algorithm significantly improves system performance.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.10C
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• pp.614-620
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• 2011

RSA, the most commonly used public-key cryptosystem, is based on the difficulty of factoring very large integers. The fastest known factoring algorithm is the Number Field Sieve(NFS). NFS first chooses two polynomials having common root modulo N and consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root, of which the most time consuming step is the Sieving step. However, in recent years, the importance of the Polynomial Selection step has been studied widely, because one can save a lot of time and memory in sieving and matrix step if one chooses optimal polynomial for NFS. One of the ideal ways of choosing sieving polynomial is to choose two polynomials with same degree. Montgomery proposed the method of selecting two (nonlinear) quadratic sieving polynomials. We proposed two cubic polynomials using 5-term geometric progression.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.6C
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• pp.523-529
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• 2010

We propose a very low complexity lattice reduction (LR) algorithm for MIMO detection in time varying channels. The proposed scheme reduces the complexity by performing LR in a block-wise manner. The proposed scheme takes advantage of the temporal correlation of the channel matrices in a block and its impact on the unimodular matrices during LR process. From this, the proposed scheme can skip a number of redundant LR processes for consecutive channel matrices and performs a single LR in a block. The simulation results investigated in this letter reveal that the proposed detection scheme requires only 43.4% multiplications and 17.3% divisions of LLL-LR and only 50.2% multiplications and 68.2% divisions of the conventional adaptive LR with almost no performance degradation.