• Journal of information and communication convergence engineering
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• v.15 no.4
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• pp.212-216
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• 2017

In this paper, we introduce novel techniques to improve the high performance of AE functions on modern high-end IoT platforms (ARM-NEON), which support SIMD and cryptography instruction sets. For the Sophie Germain Counter Mode of operation (SGCM), counter modes of encryption and prime field multiplication are required. We chose the Montgomery multiplication for modular multiplication. We perform Montgomery multiplication in a parallel way by exploiting both the ARM and NEON instruction sets. Specifically, the NEON instruction performed 128-bit integer multiplication and the ARM instruction performed Montgomery reduction, simultaneously. This approach hides the latency for ARM in the NEON instruction set. For a high-speed counter mode of encryptions for both AE functions, we introduced two-level computations. When the tasks were large volume, we switched to the NEON instruction to execute the encryption operations. Otherwise, we performed the encryptions on the ARM module.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.2
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• pp.738-756
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• 2020

The modular multiplication is the key module of public-key cryptosystems such as RSA (Rivest-Shamir-Adleman) and ECC (Elliptic Curve Cryptography). However, the efficiency of the modular multiplication, especially the modular square, is very low. In order to reduce their operation cycles and power consumption, and improve the efficiency of the public-key cryptosystems, a dual-field efficient FIPS (Finely Integrated Product Scanning) modular multiplication algorithm is proposed. The algorithm makes a full use of the correlation of the data in the case of equal operands so as to avoid some redundant operations. The experimental results show that the operation speed of the modular square is increased by 23.8% compared to the traditional algorithm after the multiplication and addition operations are reduced about (s² - s) / 2, and the read operations are reduced about s² - s, where s = n / 32 for n-bit operands. In addition, since the algorithm supports the length scalable and dual-field modular multiplication, distinct applications focused on performance or cost could be satisfied by adjusting the relevant parameters.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1031-1051
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• 2012

In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set $T(M)^*$ makes up the vertices of the corresponding torsion graph, ${\Gamma}(M)$, with any two distinct vertices forming an edge if $[x:M][y:M]M=0$. We prove that, if ${\Gamma}(M)$ contains a cycle, then $gr({\Gamma}(M)){\leq}4$ and ${\Gamma}(M)$ has a connected induced subgraph ${\overline{\Gamma}}(M)$ with vertex set $\{m{\in}T(M)^*{\mid}Ann(m)M{\neq}0\}$ and diam$({\overline{\Gamma}}(M)){\leq}3$. Moreover, if M is a multiplication R-module, then ${\overline{\Gamma}}(M)$ is a maximal connected subgraph of ${\Gamma}(M)$. Also ${\overline{\Gamma}}(M)$ and ${\overline{\Gamma}}(S^{-1}M)$ are isomorphic graphs, where $S=R{\backslash}Z(M)$. Furthermore, we show that, if ${\overline{\Gamma}}(M)$ is uniquely complemented, then $S^{-1}M$ is a von Neumann regular module or ${\overline{\Gamma}}(M)$ is a star graph.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.435-447
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• 2012

Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $I^nK{\subseteq}Q$, where $I{\subseteq}h(R)$, n is a positive integer, and $K{\subseteq}h(M)$, then $IK{\subseteq}Q$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad$(Q){\cap}h(M)=Q+{\cap}h(M)$. Furthermore if M is finitely generated then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q)$\cap$h(M))n(grad$(0_M){\cap}h(M)$) = (Q$\cap$h(M))n(grad$(0_M){\cap}Q{\cap}h(M)$). Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K $\neq$ M and $Q{\cap}K{\subseteq}M_g$ for all $g{\in}G$, then we prove that Q + K is almost semiprime in M.

• Journal of Sensor Science and Technology
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• v.17 no.2
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• pp.151-155
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• 2008

In this paper, it was investigated that the pattern recognition of multiplication environment of lactic acid bacteria in the process of curd yogurt preparation using household fermentation system, which was manufactured by combining incubator with sensor module, data processing circuit and computer. It will be sufficiently applicable to determine the maximum ratio of the amount of air to mixed milk for preparation of high quality yogurt.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.85-103
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• 2001

Suppose that Hand K are paired Hopf algebras and that A is an H - K - bicomodule algebra with multiplication which is a left H-comodule map and is a right K-comodule map. We define a new twisted algebra, $A^{\tau}$ and define $M^{\tau}$ for $M{\in}M_A^K$. We find an equivalent condition for $M^{\tau}{\in}M_{A^{\tau}}^K$. We show that the above defined twisted multiplication is the special case of Beattie's twist multiplication. We show that if K is commutative, then A is an H-module algebra and show that if $H^*$ is cocommutative then the construction of smash product appears as a special case of the new twist product.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.9
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• pp.62-69
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• 1996

In this paper, the bit-level 1-dimensional systolic array for modular multiplication is designed. First of all, the parallel algorithm and data dependence graph from walter's method based on montgomery algorithm suitable for array design for modular multiplication is derived. By the systematic procedure for systolic array design, four 1-dimensional systolic arrays are obtained and then are evaluated by various criteria. As it is modified the array which is derived form [0,1] projection direction by adding a control logic and it is serialized the communication paths of data A, optimal 1-dimensional systolic array is designed. It has constant I/O channels for expansile module and it is easy for fault tolerance due to unidirectional paths. It is suitable for RSA cryptosystem which deals iwth the large size and many consecutive message blocks.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.471-480
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• 2003

Let $\mathcal{R}$ be a commutative ring with 1, and Let M be a (left) R-module. M is said to be pointwise projective if for each epimorphism ${\alpha}:\mathcal{A}{\rightarrow}\mathcal{B}$, where A and $\mathcal{B}$ are any $\mathcal{R}$-modules, and for each homomorphism ${\beta}:\mathcal{M}{\rightarrow}\mathcal{B}$, then for every $m{\in}\mathcal{M}$, there exists a homomorphism ${\varphi}:\mathcal{M}{\rightarrow}\mathcal{A}$, which may depend on m, such that ${\alpha}{\circ}{\varphi}(m)={\beta}(m)$. Our mean concern in this paper is to study the relations between pointwise projectivemodules with cancellation modules and its geeralization.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.509-525
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• 2014

Let R be a commutative ring with identity. An R-module M is said to be w-projective if $Ext\frac{1}{R}$(M,N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w-semi-hereditary if every finite type ideal of R is w-projective. To characterize w-semi-hereditary rings, we introduce the concept of w-injective modules and study some basic properties of w-injective modules. Using these concepts, we show that R is w-semi-hereditary if and only if the total quotient ring T(R) of R is a von Neumann regular ring and $R_m$ is a valuation domain for any maximal w-ideal m of R. It is also shown that a connected ring R is w-semi-hereditary if and only if R is a Pr$\ddot{u}$fer v-multiplication domain.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.971-985
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• 2014

All modules considered in this note are over associative commutative rings with an identity element. We show that a ${\omega}$-local module M is Rad-supplemented if and only if M/P(M) is a local module, where P(M) is the sum of all radical submodules of M. We prove that ${\omega}$-local nonsmall submodules of a cyclic Rad-supplemented module are again Rad-supplemented. It is shown that commutative Noetherian rings over which every w-local Rad-supplemented module is supplemented are Artinian. We also prove that if a finitely generated Rad-supplemented module is cyclic or multiplication, then it is amply Rad-supplemented. We conclude the paper with a characterization of finitely generated amply Rad-supplemented left modules over any ring (not necessarily commutative).