• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.539-545
• /
• 1994

Let $q = p^r$, where p is a prime. A polynomial $f(x) \in GF(q)[x]$ is called a permutation polynomial (PP) over GF(q) if the numbers f(a) where $a \in GF(Q)$ are a permutation of the a's. In other words, the equation f(x) = a has a unique solution in GF(q) for each $a \in GF(q)$. More generally, $f(x_1, \cdots, x_n)$ is a PP in n variables if $f(x_1,\cdots,x_n) = \alpha$ has exactly $q^{n-1}$ solutions in $GF(q)^n$ for each $\alpha \in GF(q)$. Mullen ([3], [4], [5]) has studied the concepts of local permutation polynomials (LPP's) over finite fields. A polynomial $f(x_i, x_2, \cdots, x_n) \in GF(q)[x_i, \codts,x_n]$ is called a LPP if for each i = 1,\cdots, n, f(a_i,\cdots,x_n]$ is a PP in $x_i$ for all $a_j \in GF(q), j \neq 1$.Mullen ([3],[4]) found a set of necessary and three variables over GF(q) in order that f be a LPP. As examples, there are 12 LPP's over GF(3) in two indeterminates ; $f(x_1, x_2) = a_{10}x_1 + a_{10}x_2 + a_{00}$ where $a_{10} = 1$ or 2, $a_{01} = 1$ or x, $a_{00} = 0,1$, or 2. There are 24 LPP's over GF(3) of three indeterminates ; $F(x_1, x_2, x_3) = ax_1 + bx_2 +cx_3 +d$ where a,b and c = 1 or 2, d = 0,1, or 2.

• Journal of the Korean Recycled Construction Resources Institute
• /
• v.8 no.4
• /
• pp.387-394
• /
• 2020

In this research, a physical property test of CLSM, which can safely and effectively utilize a great number of industrial byproducts and waste types, was used to review the applicability of GBFS, FNS, and FGB, as well as their field applicabilities as cavity fillers, and the following conclusions have been reached. first, For CLSM utilizing GBFS, FNS, and FGB, it was revealed that a proper mixing of over 30% of GBFS and FNS or within 5% of FGB is effective in improving the fluidity for field application. second, It was revealed that GF15B5 can suppress bleeding at a similar level as the base, whereas GF30B5 can do so at about 0.17% compared to the base. It was also verified that GF15, GF30, and GF45 can suppress bleeding at about 0.2%, 0.26%, and 0.3%, respectively, compared to the base. third, Both GF15B5 and GF30B5 exceeded 0.4MPa in 7day strength tests to satisfy the field application and, also, the rates of increase of their initial strengths were found to be 323% and 233% higher than the base, respectively. Meanwhile, the 7day strength test of GF, which utilizes GBFS and FNS, also reached over 0.2MPa for field application, and it was revealed that GF15, GF30, and GF45 show 160%, 237%, and 185% higher strength increase rates, respectively, compared to the base.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.1C
• /
• pp.8-13
• /
• 2006

A new RS(Reed Solomon) Decoder design method, using Galois Subfield GF($2^4$) Multiplier, is described. The Decoder is designed using Normalized error position stored ROM. Here New Inverse Calculator in GF($2^8$) is designed, which is simpler and faster than the classical GF($2^8$) direct inverse calculator, using the Galois Subfield GF($2^4$) Arithmatic operator.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.6 no.4
• /
• pp.97-106
• /
• 1996

In this paper, we define an equivalence relation on the group of all permutations over the finite field GF($2^n$) and show each equivalence class has common cryptographic properties. And, we classify all exponent permutations over GF($2^7$) and GF($2^8$). Then, three applications of our results are described. We suggest a method for designing $n\;{\times}\;2n$ S(ubstitution)-boxes by the concatenation of two exponent permutations over GF($2^n$) and study the differential and linear resistance of them. And we can easily indicate that the conjecture of Beth in Eurocrypt '93 is wrong, and discuss the security of S-box in LOKI encryption algorithm.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.25 no.5
• /
• pp.979-984
• /
• 2015

In this paper, we proposed a Semi-Systolic multiplier of $GF(2^n)$ with Type II optimal Normal Basis. Comparing the complexity of the proposed multiplier with Chiou's multiplier proposed in 2012, it is saved $2n^2+44n+26$ in total transistor numbers and decrease 4 clocks in time delay. This means that, for $GF(2^{333})$ of the field recommended by NIST for ECDSA, the space complexity is 6.4% less and the time complexity of the 2% decrease. In addition, this structure has an advantage as applied to Chiou's method of concurrent error detection and correction in multiplication of $GF(2^n)$.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.531-538
• /
• 1997

In this paper, we show how to construct an optimal normal basis over finite field of high degree and compare two methods for fast operations in some finite field $GF(2^n)$. The first method is to use an optimal normal basis of $GF(2^n)$ over $GF(2)$. In case of n = st where s and t are relatively primes, the second method which regards the finite field $GF(2^n)$ as an extension field of $GF(2^s)$ and $GF(2^t)$ is to use an optimal normal basis of $GF(2^t)$ over $GF(2)$. In section 4, we tabulate implementation result of two methods.

• Korean Journal of Fisheries and Aquatic Sciences
• /
• v.22 no.4
• /
• pp.201-213
• /
• 1989

This study is just to be carried out to grasp the efficiency of jet stream excavating for the ground. Changing the dynamic pressure, nozzle diameter, distance off the ground, we measured the impulse, the excavated depth, the excavated width. According as each dynamic pressure increases from 100 to $500gf/cm^2$, the impulse of the jet stream increases from 43 to 114gf, from 52 to 227gf, from 114 to 506gf, from 137 to 768gf, in 4, 6, 8, 10mm nozzles respectively, but it makes no difference in the value of distance within 50cm off ground. The excavated depth increases at the invariable rate in accordance with nozzle diameter, dynamic pressure, nozzle distance. We obtain the equations relevant to the ground I, II as follows: $$L_I=[0.01(H/r-100) -0.43\cdot\iota+11.78]{\cdot}D/4$$ $$L_{II}=[0.03(H/r-100) -0.34\cdot\iota+6.39]{\cdot}D/4$$ where, $L_I,\;L_{II}$ are respectively the excavated depths of the ground I, II, cm; H is the dynamic pressure, $gf/cm^2\;:\;\iota$ is the distance off the ground, cm; D is Nozzle diameter, mm; r is the specific weight, $1gf/cm^2$.

• Journal of the Korean Society of Fisheries and Ocean Technology
• /
• v.39 no.4
• /
• pp.262-268
• /
• 2003

This paper describes the effect of loading rate, specimen geometries and material properties for Mode I interlaminar fracture toughness of hybrid composite by using double cantilever beam (DCB) specimen. In the range of loading rate 0.2-20mm/min, there is found to be no significant effect of loading rate with the value of critical energy release rate (G_IC). The value of $G_IC$ for variation of initial crack length are nearly similar values when material properties are CF/CF and GF/GF, however, the value of $G_IC/$ are highest with the increasing initial crack length at CF/GF. The SEM photographs show good fiber distribution and interfacial bonding of hybrid composites when the moulding is the CF/GF

• The Journal of the Korea institute of electronic communication sciences
• /
• v.9 no.4
• /
• pp.409-416
• /
• 2014

In H/W implementation for the finite field, the use of normal basis has several advantages, especially the optimal normal basis is the most efficient to H/W implementation in $GF(2^m)$. The finite field $GF(2^m)$ with type I optimal normal basis(ONB) has the disadvantage not applicable to some cryptography since m is even. The finite field $GF(2^m)$ with type II ONB, however, such as $GF(2^{233})$ are applicable to ECDSA recommended by NIST. In this paper, we propose a bit-parallel multiplier over $GF(2^m)$ having a type II ONB, which performs multiplication over $GF(2^m)$ in the extension field $GF(2^{2m})$. The time and area complexity of the proposed multiplier is the same as or partially better than the best known type II ONB bit-parallel multiplier.

• Journal of IKEEE
• /
• v.7 no.1 s.12
• /
• pp.56-62
• /
• 2003

In this paper, we designed a adder and a multiplier using current mode T-gate on $GF(2^2)$. The T-gate is consisted of current mirror and pass transistor, the designed 4-valued T-gate used adder and multiplier on $GF(2^2)$. We designed its under 1.5um CMOS standard technology. The unit current of the circuits is 15㎂, and power supply is 3.3V VDD. The proposed current mode CMOS operator have a advantage of module by T-gate`s arrangement, and so we easily implement multi-valued operator.