• Proceedings of the IEEK Conference
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• 2002.06b
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• pp.277-280
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• 2002

This paper analyze the characteristics of three multipliers in finite fields GF(2m) from the point of view of processing time and area complexity. First, we analyze structure of three multipliers; 1) LSB-first systolic array, 2) LFSR structure, and 3) CA structure. To make performance analysis, each multiplier was modeled in VHDL and was synthesized for FPGA implementation. The simulation results show that LFSR structure is best from the point of view of area complexity, and LSB systolic array is best from the point of view of processing time per clock.

• Proceedings of the IEEK Conference
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• 2002.06e
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• pp.79-82
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• 2002

In this paper, we proposed a multiplicative algorithm for two polynomials in existence coefficients over finite field GF(3$^{m}$ ). Using the proposed multiplicative algorithm, we constructed the multiplier of modular architecture with parallel in-output. The proposed multiplier is composed of (m+1)$^2$identical cells, each cell consists of single mod(3) additional gate and single mod(3) multiplicative gate. Proposed multiplier need single mod(3) multiplicative gate delay time and m mod(3) additional gate delay time not clock. Also, the proposed architecture is simple, regular and has the property of modularity, therefore well-suited for VLSI implementation.

• Microbiology and Biotechnology Letters
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• v.13 no.1
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• pp.59-64
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• 1985

In order to utilize Citrus peel as fermentative substrate of microorganisms, enzymatic saccharification of Citrus peel by the crude enzyme of Aspergillus sp. GF 015 isolated and identified from nature was investigated. When the fungus was cultured at $27^{\circ}C$ for 3 days in wheat bran medium containing 0.6% $NH_4NO_3$ and 0.05% $KH_2PO_4$, the maximal production of the enzyme was observed. Optimal conditions for enzymatic reaction of crude enzyme were 15ml(97.5 unit)/g of enzyme solution to Citrus peel powder ratio, pH4.0, $45^{\circ}C$ of temperature and 12 hours of reaction time. As the result of saccharifying Citrus peel under optimum conditions, reducing sugar on the weight of dry matter was formed 60.2% and saccharifying rate was 76.3%. The sugar solution obtained were mainly composed of glucose, xylose and galacturonic acid. Hydrolyzing enzymes produced by Aspergillus sp. GF 015 were pectinase, cellulase and xylanase.

• Journal of the korean academy of Pediatric Dentistry
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• v.25 no.2
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• pp.323-334
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• 1998

The purpose of this study was to compare the microleakage of the amalgam and the gallium alloy when several lining materials were applied. The ANA 2000, high copper lathecut type amalgam(AM group) and Gallium Alloy GF II (GF group) were used. The fifty extracted sound molars were randomly assigned to AM group and GF group, and the buccal and lingual class V cavities with a size $3{\times}2{\times}2mm$ were prepared. The prepared cavities were randomly assigned to group 1 : no liner used control, group 2 : Copalite, group 3 : Panavia 21, group 4 : All-bond 2, and group 5 : Superbond C&B. After liner placement and amalgam filling, the specimens were stored in $37^{\circ}C$ normal saline for 24 hours and then thermocycled from $5^{\circ}C$ to $55^{\circ}C$ thousand times. The specimens were stored in the 1% methylene blue solution for 24 hours and sectioned and examined by stereomicroscope. The results obtained from this study can be summarized as follows : 1. In the GF group, microleakage values of group 2, 3, 4, 5 were significantly lower than that of group 1 (p<0.05). 2. In the AM group, microleakage values of group 3 and 4 were significantly lower than that of group 1 (p<0.05), but microleakage values of group 2 and 5 did not differ from that of group 1 (p>0.05). 3. The GF group was similar(group, 1 3, 4) or superior(group 2, 5) to the AM group in the aspect of the microleakage.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.05a
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• pp.686-689
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• 2009

This paper describes a scalar multiplier for Elliptic curve cryptography. The scalar multiplier has 163-bits key size which supports the specifications of smart card standard. To reduce the computational complexity of scalar multiplication on finite field $GF(2^{163})$, the Non-Adjacent-Format (NAF) conversion algorithm based on complementary recoding is adopted. The scalar multiplier core synthesized with a $0.35-{\mu}m$ CMOS cell library has 32,768 gates and can operate up to 150-MHz@3.3-V. It can be used in hardware design of Elliptic curve cryptography processor for smart card security.

• The KIPS Transactions:PartA
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• v.12A no.3 s.93
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• pp.235-242
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• 2005

In this paper, we propose a new division circuit for $GF(2^m)$ applications. The proposed division circuit is based on a modified the binary GCD algorithm and produce division results at a rate of one per 2m-1 clock cycles. Analysis shows that the proposed circuit gives $47\%$ and $20\%$ improvements in terms of speed and hardware respectively. In addition, since the proposed circuit does not restrict the choice of irreducible polynomials and has regularity and modularity, it provides a high flexibility and scalability with respect to the field size m. Thus, the proposed divider. is well suited to low-area $GF(2^m)$ applications.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.8
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• pp.67-74
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• 2008

A compact and high-performance AES(Advanced Encryption Standard) encryption/decryption processor is designed by applying various hardware sharing and optimization techniques. In order to achieve minimized hardware complexity, sharing the S-Boxes for round transformation with the key scheduler, as well as merging and reusing datapaths for encryption and decryption are utilized, thus the area of S-Boxes is reduced by 25%. Also, the S-Boxes which require the largest hardware in AES processor is designed by applying composite field arithmetic on $GF(((2^2)^2)^2)$, thus it further reduces the area of S-Boxes when compared to the design based on $GF(2^8)$ or $GF((2^4)^2)$. By optimizing the operation of the 64-bit round transformation and round key scheduling, the round transformation is processed in 3 clock cycles and an encryption of 128-bit data block is performed in 31 clock cycles. The designed AES processor has about 15,870 gates, and the estimated throughput is 412.9 Mbps at 100 MHz clock frequency.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.3
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• pp.41-48
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• 2004

Finite field multiplication and division are important arithmetic operation in error-correcting codes and cryptosystems. The elements of the finite field GF($2^m$) are represented by bases with a primitive polynomial of degree m over GF(2). We can be easily realized for multiplication or computing multiplicative inverse in GF($2^m$) based on a normal basis representation. The number of product terms of logic function determines a complexity of the Messay-Omura multiplier. A normal basis exists for every finite field. It is not easy to find the optimal normal element for a given primitive polynomial. In this paper, the generating method of normal basis is investigated. The normal bases whose product terms are less than other bases for multiplication in GF($2^m$) are found. For each primitive polynomial, a list of normal elements and number of product terms are presented.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.42 no.10 s.340
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• pp.17-24
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• 2005

This paper propose a new generation method of GRM coefficients using the circulation property of polarity over GF(3). The general method to derive GRM coefficients are obtain the filled polarity of GRM coefficients using RM expansion and expand it for the polarities. Since the general method has many operations when the number of the variables are incremented. Proposed method in this paper simplifies the generation procedure and reduces a number of operators compare to parallel type because of the cyclic property of polarity. Comparing to the proposed papers, the proposed method use only adders without multiplier. So it improves the complexity of the system with efficient composition of the circuits.

• Asian-Australasian Journal of Animal Sciences
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• v.21 no.9
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• pp.1361-1366
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• 2008

One-hundred and twenty Ischia grey rabbits, traditionally raised in pits, were equally divided after weaning (32 days) into three groups: group C, housed in cages (4 rabbits/cage) and fed a commercial concentrate; group GF, housed as C group and fed grasses collected on the island and crushed faba beans supplemented with an appropriate mineral vitamin mix; group P, housed in pits (8 rabbits/pit) and fed as GF group. Feed intake was recorded daily and live weight monthly up to slaughter (92 days). At slaughter, 10 rabbits per group were used to measure carcass and meat traits. The carcasses were weighed and measured according to the standard procedures and meat samples from the Longissimus dorsi and left hind leg were analysed for water holding capacity and chemical composition, respectively. During the entire trial, group C consumed significantly (p<0.01) a higher quantity of feed than the other groups (126.1 vs. 63.4 and 66.5 g/d, resp. for groups C, GF and P) and at slaughter showed a significantly (p<0.01) higher body weight (2,529.7 vs. 1,324.4 and 1,375.4 g, resp. for groups C, GF and P). Significant differences (p<0.01) were found also for dressing out percentage (68.6 vs. 66.6 and 66.9%, resp. for groups C, GF and P) and for meat chemical composition, in particular lipid percentage (4.13 vs. 1.84 and 1.93%, resp., for groups C, GF and P, p<0.01) and moisture (73.7 vs. 76.4 and 76.3%, resp. for groups C, GF and P, p<0.01). The results suggest the opportunity to obtain heavier animals raised in the pits if their diets were integrated with commercial feed.