• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.3
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• pp.191-200
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• 2002

In this paper, we present the method transforming the interval functions into the truncated difference functions for multi-variable multi-valued functions and implementing the truncated difference functions to the multiple valued logic circuits with uniform patterns using the current mirror circuits and the inhibit circuits by current-mode CMOS. Also, we apply the presented methods to the implementation of circuits for additive truth table of 2-variable 4-valued MOD(4) and multiplicative truth table of 2-variable 4-valued finite fields GF(4). These circuits are simulated under 2${\mu}{\textrm}{m}$ CMOS standard technology, 15$mutextrm{A}$ unit current, and 3.3V power supply voltage using PSpice. The simulation results have shown the satisfying current characteristics. Both implemented circuits using current-mode CMOS have the uniform Patterns and the regularity of interconnection. Also, it is expansible for the variables of multiple valued logic functions and are suitable for VLSI implementation.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.10
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• pp.507-511
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• 2005

We have derived the linear complexity of a binary sequence generated by a Feedback with Carry Shift Regiater(FCSR) under the following condition: q is a power of a prime such that $q=r^e,\;(e{\geq}2)$ and r=2p+1, where both r and p are 2-prime. Also, a summation generator creates sequence from addition with carry of LFSR(Linear Feedback Shift Register) sequences. Similarly, it is possible to generate keystream by bitwise exclusive-oring on two FCSR sequences. In this paper, we described the cryptographic properties of a sequence generated by the FCSRs in view of the linear complexity.

• Proceedings of the Korea Information Processing Society Conference
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• 2010.11a
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• pp.1760-1762
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• 2010

본 논문에서 3치가산기와 승산기(multiplier)는 전류모드 CMOS에 의해서 구현된다. 첫째, 3치 T-gate를 집적회로 설계의 유효 가용성을 갖고 있는 전류모드 CMOS를 이용하여 구현한다. 둘째, 3치 T-gates를 이용해 회로가 유한체 GF (3)에 대하여 2변수 3치 가산표 (2-variable ternary addition table) 및 구구표 (multiplication table)가 실현되도록 구현한다. 마지막으로, 이러한 동작 회로들은 1.5 CMOS 표준 기술과 $15{\mu}A$ 단위전류(unit current) 및 3.3V 소스 전압 (VDD voltage)에 의해 활성화 된다. 활성화 결과는 만족할 만한 전류 특성을 나타냈다. 전류 모드 CMOS에 의하여 실행되는 3치가산기 및 승산기는 단순하며 와이어 라우팅(wire routing)에 대하여 정규적이고, 또한 셀 배열 (cell array)과 함께 모듈성 (modularity)의 특성을 갖고 있다.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.8 s.338
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• pp.15-26
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• 2005

In this paper, we propose an efficient $GF(2^m)$ multi-segment multiplier architecture and study its application to elliptic curve cryptography processors. The multi-segment based ECC datapath has a very small combinational multiplier to compute partial products, most of its internal data buses are word-sized, and it has only a single m bit multiplexer and a single m bit register. Hence, the resource requirements of the proposed ECC datapath can be minimized as the segment number increases and word-size is decreased. Hence, as compared to the ECC processor based on digit-serial multiplication, the proposed ECC datapath is more efficient in resource usage. The resource requirement of ECC Processor implementation depends not only on the number of basic hardware components but also on the complexity of interconnection among them. To show the realistic area efficiency of proposed ECC processors, we implemented both the ECC processors based on the proposed multi-segment multiplication and digit serial multiplication and compared their FPGA resource usages. The experimental results show that the Proposed multi-segment multiplication method allows to implement ECC coprocessors, requiring about half of FPGA resources as compared to digit serial multiplication.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.5
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• pp.179-187
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• 2003

Recently efficient implementation of finite field operation has received a lot of attention. Among the GF($2^m$) arithmetic operations, multiplication process is the most basic and a critical operation that determines speed-up hardware. We propose a hardware architecture using Mastrovito method to reduce processing time. Existing Mastrovito multipliers using the special generating trinomial p($\chi$)=$x^m$+$x^n$+1 require $m^2$-1 XOR gates and $m^2$ AND gates. The proposed multiplier needs $m^2$ AND gates and $m^2$＋($n^2$-3n)/2 XOR gates that depend on the intermediate term xn. Time complexity of existing multipliers is $T_A$+( (m-2)/(m-n) +1+ log$_2$(m) ) $T_X$ and that of proposed method is $T_X$＋(1＋ log$_2$(m-1)＋ n/2 ) )$T_X$. The proposed architecture is efficient for the extension degree m suggested as standards: SEC2, ANSI X9.63. In average, XOR space complexity is increased to 1.18% but time complexity is reduced 9.036%.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.23 no.3
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• pp.359-370
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• 2013

Lin and Chan proposed a reversible secret image sharing scheme in 2010. The advantages of their scheme are as follows: the low distortion ratio, high embedding capacity of shadow images and usage of the reversible. However, their scheme has some problems. First, the number of participants is limited because of modulus prime number m. Second, the overflow can be occurred by additional operations (quantized value and the result value of polynomial) in the secret sharing procedure. Finally, if the coefficient of (t-1)th degree polynomial become zero, (t-1) participants can access secret data. In this paper, an improved reversible secret image sharing scheme which solves the problems of Lin and Chan's scheme while provides the low distortion ratio and high embedding capacity is proposed. The proposed scheme solves the problems that are a limit of a total number of participants, and occurrence of overflow by new polynomial operation over GF($2^8$). Also, it solve problem that the coefficient of (t-1)th degree polynomial become zero by fixed MSB 4-bit constant. In the experimental results, PSNR of their scheme is decreased with the increase of embedding capacity. However, even if the embedding capacity increase, PSNR value of about 45dB or more is maintained uniformly in the proposed scheme.