• Kyungpook Mathematical Journal
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• v.6 no.1
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• pp.3-5
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• 1964

• Journal of IKEEE
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• v.26 no.4
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• pp.736-741
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• 2022

Lattice-based cryptography is the most practical post-quantum cryptography because it enjoys strong worst-case security, relatively efficient implementation, and simplicity. Ring learning with errors (R-LWE) is a public key encryption (PKE) method of lattice-based encryption (LBC), and the most important operation of R-LWE is the modular polynomial multiplication of rings. This paper proposes a method for optimizing modular multipliers based on approximate computing (AC) technology, targeting the medium-security parameter set of the R-LWE cryptosystem. First, as a simple way to implement complex logic, LUT is used to omit some of the approximate multiplication operations, and the 2's complement method is used to calculate the number of bits whose value is 1 when converting the value of the input data to binary. We propose a total of two methods to reduce the number of required adders by minimizing them. The proposed LUT-based modular multiplier reduced both speed and area by 9% compared to the existing R-LWE modular multiplier, and the modular multiplier using the 2's complement method reduced the area by 40% and improved the speed by 2%. appear. Finally, the area of the optimized modular multiplier with both of these methods applied was reduced by up to 43% compared to the previous one, and the speed was reduced by up to 10%.

• Nuclear Engineering and Technology
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• v.56 no.3
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• pp.907-915
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• 2024

Various core designs with multi-batch fuel management (FM) are proposed and optimized for an innovative small modular reactor (iSMR), focusing on enhancing the inherent safety and neutronic performance. To achieve soluble-boron-free (SBF) operation, cylindrical centrally-shielded burnable absorbers (CSBAs) are utilized, reducing the burnup reactivity swing in both two- and three-batch FMs. All 69 fuel assemblies (FAs) are loaded with 2-cylindrical CSBA. Furthermore, the neutron economy is improved by deploying a truly-optimized PWR (TOP) lattice with a smaller fuel radius, optimized for neutron moderation under the SBF condition. The fuel shuffling and CSBA loading patterns are proposed for both 2- and 3-batch FM with the aim to lower the core leakage and achieve favorable power profiles. Numerical results show that both FM configurations achieve a small reactivity swing of about 1000 pcm and the power distributions are within the design criteria. The average discharge burnup in the two-batch core is comparable to three-batch commercial PWR like APR-1400. The proposed checker-board CR pattern with extended fingers effectively assures cold shutdown in the two-batch FM scenario, while in the three-batch FM, three N-1 scenarios are failed. The whole evaluation process is conducted using Monte Carlo Serpent 2 code in conjunction with ENDF/B-VII.1 nuclear library.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.237-242
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• 1994

One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.461-468
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• 2008

We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.496-499
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• 2005

In this paper, We discuss various types of sublattice of the lattice of intuitionistic fuzzy subgroups of a given group. We Prove that a special class of intuitionistic fuf normal subgroups constitutes a modular sublattice of the lattice of intuitionistic fuzzy subgroups. Moreover, we exhibit the relationship of the sublattices of the lattice of intuitionistic fuzzy subgroups.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.7-16
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• 2007

First, we investigate fuzzy equivalence relations on a set X in the sense of Youssef and Dib. Second, we discuss fuzzy congruences generated by a given fuzzy relation on a fuzzy groupoid. In particular, we obtain the characterizations of ${\rho}\;o\;{\sigma}{\in}$ FC(S) for any two fuzzy congruences ${\rho}\;and\;{\sigma}$ on a fuzzy groupoid ($S,{\odot}$). Finally, we study the lattice of fuzzy equivalence relations (congruences) on a fuzzy semigroup and give certain lattice theoretic properties.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.25 no.8
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• pp.122-131
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• 2011

In this paper, the design and analysis of a reconfigurable modular structure, which reforms itself according to the change of the environment and realize appropriate forms and motions, are dealt with. This modular is a free structure from the restrictions with constraints about fixed environment and has various forms and motions by combining units. The form of this unit has a shape of a square with 7 centimeters side each, and has a structure which can be combined in a chain-shape or a lattice-shape. Additionally, The structure has a mobility by being equipped with wheels so that it can be combined for itself. In this paper, all the wireless controllers, sensor system, and communicating method between modules according to module structures were suggested and transformation method to be transformed to shape of snakes, caterpillars were presented. Moreover, simulations for each method were performed to show the validity of the motions including motor torque analysis. All the motions suggested were realized and experimented, whereby the availability of the designed mechanism and algorithm was verified with the result of experiments.

• Journal of IKEEE
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• v.25 no.1
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• pp.88-94
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• 2021

Public-key cryptographic algorithms such as RSA and ECC, which are currently in use, have used mathematical problems that would take a long time to calculate with current computers for encryption. But those algorithms can be easily broken by the Shor algorithm using the quantum computer. Lattice-based cryptography is proposed as new public-key encryption for the post-quantum era. This cryptographic algorithm is performed in the Polynomial Ring, and polynomial multiplication requires the most processing time. Therefore, a hardware model module is needed to calculate polynomial multiplication faster. Number Theoretic Transform, which called NTT, is the FFT performed in the finite field. The logic verification was performed using HDL, and the proposed design at the transistor level using Hspice was compared and analyzed to see how much improvement in delay time and power consumption was achieved. In the proposed design, the average delay was improved by 30% and the power consumption was reduced by more than 8%.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.5
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• pp.398-406
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• 2003

In modular fixturing systems, a given part or a subassembly is fixed by placing fixture elements such as locators and clamps adequately on a plate with a lattice of holes. It is known that the minimal number of point contacts to restrict translational and rotational motions on a plane is four and the type of three locators and a clamp(3L/1C) is the minimal future. Brost and Goldberg developed the complete algorithm to automatically synthesize 3L/1C types of fixtures which satisfy the condition of form closure. Due to the nature of the fixture, the clearance between the fixture and the part is extremely small. It is hard to load the part repeatedly and accurately for human as well as for robot. However the condition of loadability has not been taken into account in the B&G algorithm. In this paper, a new method to decide a given fixture to be loadable by using configuration space is proposed. A method to plan for a part to be loaded by using compliance safely even in the presence of control and sensing uncertainty is proposed is well.