• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.847-864
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• 2013

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.907-928
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• 2015

We show in many cases that the Siegel-Ramachandra invariants generate the ray class fields over imaginary quadratic fields. As its application we revisit the class number one problem done by Heegner and Stark, and present a new proof by making use of inequality argument together with Shimura's reciprocity law.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.131-146
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• 2018

We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.6 s.336
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• pp.67-74
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• 2005

Crypto-systems have difficulties in designing hardware due to the various standards. We propose a programmable and configurable architecture for cryptography coprocessors to accommodate various crypto-systems. The proposed architecture has a 32 bit I/O interface and internal bus width, and consists of a programmable finite field arithmetic unit, an input/output unit, a register file, and a control unit. The crypto-system is determined by the micro-codes in memory of the control unit, and is configured by programming the micro-codes. The coprocessor has a modular structure so that the arithmetic unit can be replaced if a substitute has an appropriate 32 bit I/O interface. It can be used in many crypto-systems by re-programming the micro-codes for corresponding crypto-system or by replacing operation units. We implement an elliptic curve crypto-processor using the proposed architecture and compare it with other crypto-processors