• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.613-626
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• 1996

This paper is a contribution to the study of the properties of the lattice of all lattice varieties. Among the properties, that of finite base is investigated here. The question whether the join of two finitely based modular lattice varieties is finitely based is investigated under certain conditions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.1
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• pp.287-304
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• 2022

With the development of quantum computers, ring signature schemes based on large integer prime factorization, discrete logarithm problem, and bilinear pairing are under threat. For this reason, we design a ring signature scheme based on lattice with a fixed verification key. Compared with the previous ring signature scheme based on lattice, our design has a fixed verification key and does not disclose the signer's identity. Meanwhile, we propose an anonymous electronic voting scheme by using our ring signature scheme based on lattice and (t, n) threshold scheme, which makes up for the lack of current anonymous electronic voting that cannot resist attacks of the quantum computer. Finally, under standard model (SM), we prove that our ring signature scheme based on lattice is anonymous against the full-key exposure, and existentially non-forgeable against insider corruption. Furthermore, we also briefly analyze the security of our anonymous electronic voting scheme.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.195-211
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• 2024

In this paper, we introduce the concept of a fuzzy lattice ordered group, which is based on a fuzzy lattice that Chon developed in his paper "Fuzzy Partial Order Relations and Fuzzy Lattice". We will also discuss fuzzy lattice-ordered groups in detail, provide several results that are analogous to the classical theory of lattice-ordered groups, and characterize the relationship between a fuzzy lattice-ordered group using its level set and support. Moreover, we define the concepts of fl-subgroups, quotients, and cosets of fl-groups and obtain some fundamental results for these fuzzy algebraic structures.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.1
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• pp.47-57
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• 2004

The Goldreich-Goldwasser-Halevi(GGH)'s signature scheme from Crypto '97 is cryptanalyzed, which is based on the well-blown lattice problem. We mount a chosen message attack on the signature scheme, and show the signature scheme is vulnerable to the attack. We collects n lattice points that are linearly independent each other, and constructs a new basis that generates a sub-lattice of the original lattice. The sub-lattice is shown to be sufficient to generate a valid signature. Empirical results are presented to show the effectiveness of the attack Finally, we show that the cube-like parameter used for the private-key generation is harmful to the security of the scheme.

• Geomechanics and Engineering
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• v.31 no.5
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• pp.529-543
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• 2022

The lattice-spring-based synthetic rock mass model (LS-SRM) technique has been extensively employed in large open-pit mining and underground projects in the last decade. Since the LS-SRM requires a complex and time-consuming calibration process, a robust approach was developed using the Response Surface Methodology (RSM) to optimize the calibration procedure. For this purpose, numerical models were designed using the Box-Behnken Design technique, and numerical simulations were performed under uniaxial and triaxial stress states. The model input parameters represented the models' micro-mechanical (lattice) properties and the macro-scale properties, including uniaxial compressive strength (UCS), elastic modulus, cohesion, and friction angle constitute the output parameters of the model. The results from RSM models indicate that the lattice UCS and lattice friction angle are the most influential parameters on the macro-scale UCS of the specimen. Moreover, lattice UCS and elastic modulus mainly control macro-scale cohesion. Lattice friction angle (flat joint fiction angle) and lattice elastic modulus affect the macro-scale friction angle. Model validation was performed using physical laboratory experiment results, ranging from weak to hard rock. The results indicated that the RSM model could be employed to calibrate LS-SRM numerical models without a trial-and-error process.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.439-453
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• 1996

In R. McKenzie[12], it is shown that the cardinality of the lattice variety is $2^\aleph_0$ and K. Baker[1] contains the stronger result that M, the variety of all modular lattices, has $2^\aleph_0$ subvarieties. It follows that there exists a variety of modular lattices that is not finitely based. In fact, K. Baker[2] gave an example of such a variety. And it was proved by K. Baker [2] and B. Jonsson [8] that join of two finitely based lattice varieties is not always finitely based. K. Baker[2] gave an explicit example of case of nonmodular lattice variety. Then it is proposed whether the join of two finitely based varieties if finitely based under certain conditions. The answer to the question is not affirmative.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.575-589
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• 2011

In order to examine the possibility of some topological structures into the fields of network science, telecommunications related to the future internet and a digitization, the paper studies the Marcus Wyse topological structure. Further, this paper develops the notions of lattice based Marcus Wyse continuity and lattice based Marcus Wyse homeomorphism which can be used for studying spaces $X{\subset}R^2$ in the Marcus Wyse topological approach. By using these two notions, we can study and classify lattice based simple closed Marcus Wyse curves.

• Proceedings of the Korean Nuclear Society Conference
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• 1997.05a
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• pp.57-61
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• 1997

A Canadian Deuterium Uranium (CANDU) reactor core calculation was performed using lattice parameters generated by HELIOS. The HELIOS-based lattice parameters were processed by TABGEN in a form suitable for the core analysis code RFSP. The core calculation was performed and the results were compared to those of the reference calculation which uses POWDERPUFS-V (PPV) for the lattice parameter generation. The characteristics of the core calculated based on the PPV and HELIOS lattice parameters match within 0.4%$\Delta$k and 7% for the excess reactivity and the channel power distribution, respectively.

• Journal of Communications and Networks
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• v.15 no.1
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• pp.1-7
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• 2013

Most of the provably-secure proxy signature schemes rely on the average-case hardness problems such as the integer factorization problems and the discrete logarithm problems. Therefore, those schemes are insecure to quantum analysis algorithms, since there exist quantum algorithms efficiently solving the factorization and logarithm problems. To make secure proxy signature schemes against quantum analysis, some lattice-based proxy signature schemes are suggested. However, none of the suggested lattice-based proxy signature schemes is proxy-protected in the adaptive security model. In the paper, we propose a provably-secure ID-based proxy signature scheme based on the lattice problems. Our scheme is proxy-protected in the adaptive security model.

• ETRI Journal
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• v.45 no.6
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• pp.1090-1102
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• 2023

Authenticated multiple key agreement (AMKA) protocols provide participants with multiple session keys after one round of authentication. Many schemes use Diffie-Hellman or authenticated key agreement schemes that rely on hard integer factorizations that are vulnerable to quantum algorithms. Lattice cryptography provides quantum resistance to authenticated key agreement protocols, but the certificate always incurs excessive public key infrastructure management overhead. Thus, a lightweight lattice-based secure system is needed that removes this overhead. To answer this need, we provide a two-party lattice- and identity-based AMKA scheme based on bilateral short integer or computational bilateral inhomogeneous small integer solutions, and we provide a security proof based on the random oracle model. Compared with existing AMKA protocols, our new protocol has higher efficiency and stronger security.