• Korean Journal of Mathematics
• /
• v.27 no.3
• /
• pp.723-734
• /
• 2019

We study the negative trinomial table T' of $(x^2+x+1)^{-n}$ and its t/u-slope diagonals for any t, u > 0. We investigate recurrence formula of the t/u-slope diagonal sums of T' and find interrelationships with t/u-slope diagonal sums of the trinomial table T.

• Communications of the Korean Mathematical Society
• /
• v.24 no.2
• /
• pp.239-245
• /
• 2009

We estimate the positive real zeros of certain trinomial equations and then deduce zeros bounds of some lacunary polynomials.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.1
• /
• pp.1-17
• /
• 2011

A new method for option pricing based on the trinomial tree method is introduced. The new method calculates the local average of option prices around a node at each time, instead of computing prices at each node of the trinomial tree. Local averaging has a smoothing effect to reduce oscillations of the tree method and to speed up the convergence. The option price and the hedging parameters are then obtained by the compact scheme and the Richardson extrapolation. Computational results for the valuation of European and American vanilla and barrier options show superiority of the proposed scheme to several existing tree methods.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.41 no.5
• /
• pp.29-36
• /
• 2004

This study focuses on the arithmetical methodology and hardware implementation of low-system-complexity multiplier over GF(2$^{m}$ ) using the trinomial of degree a The proposed parallel-in parallel-out operator is composed of MR, PP, and MS modules, each can be established using the regular array structure of AND and XOR gates. The proposed multiplier is composed of $m^2$ 2-input AND gates and $m^2$-1 2-input XOR gates, and the propagation delay is $T_{A}$+(1+[lo $g_2$$^{m}$ ]) $T_{x}$ . Comparison result of the related multipliers of GF(2$^{m}$ ) are shown by table, it reveals that our operator involve more regular and generalized then the others, and therefore well-suited for VLSI implementation. Moreover, our multiplier is more suitable for any other GF(2$^{m}$ ) operational applications.s.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.13 no.2
• /
• pp.383-390
• /
• 2018

Since cellular automata(CA) is superior to LFSR in randomness, it is applied as an alternative of LFSR in various fields. However, constructing CA corresponding to a given polynomial is more difficult than LFSR. Cattell et al. and Cho et al. showed that irreducible polynomials are CA-polynomials. And Cho et al. and Sabater et al. gave a synthesis method of 90/150 CA corresponding to the power of an irreducible polynomial, which is applicable as a shrinking generator. Swan characterizes the parity of the number of irreducible factors of a trinomial over the finite field GF(2). These polynomials are of practical importance when implementing finite field extensions. In this paper, we show that the trinomial $x^{2^n-1}+X+1$ ($n{\geq}2$) are CA-polynomials. Also the trinomial $x^{2^a(2^n-1)}+x^{2^a}+1$ ($n{\geq}2$, $a{\geq}0$) are CA-polynomials.

• Communications for Statistical Applications and Methods
• /
• v.14 no.1
• /
• pp.81-92
• /
• 2007

This paper consider trinomial group testing concerned with classification of N given units into one of k disjoint categories. In this paper, we propose Bayesian inference for estimating individual category proportions using the trinomial group testing model proposed by Bar-Lev et al. (2005). We compared a relative efficience (RE) based on the mean squared error (MSE) of MLE and Bayes estimators with various prior information. The impact of different prior specifications on the estimates is also investigated using selected prior distribution. The impact of different priors on the Bayes estimates is modest when the sample size and group size we large.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.4
• /
• pp.573-584
• /
• 2016

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. Such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them T-functions are probably invertible transformations and are very useful in stream ciphers. In this paper we will characterize a secure trinomial on ${\mathbb{Z}}_{2^n}$ which generates an n-bit word sequence without consecutive elements of period $2^n$.

• Journal of Korean Society for Quality Management
• /
• v.26 no.3
• /
• pp.31-45
• /
• 1998

This paper proposes a method of designing one-sided cumulative scored control charts to control the process mean with a normally distributed quality characteristic. The average run length(ARL) is obtained from the average sample number of sequential probability ratio test(SPRT) on trinomial distribution. Using the analogy between cumulative scored control chart and SPRT for trinomial observations, a procedure is presented to determine three control chart parameters; lower and u, pp.r scoring boundaries and action limit. The parameters are determined by minimizing the ARL when the process is out of control with prespecified ARL when the process is in control.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.8 no.2
• /
• pp.27-36
• /
• 1998

최근들어 타원곡선 암호법(ECC)이 RSA암호법을 대체할 것으로 기대되면서ECC의 연산속도를 결정하는 중요한 요소인 유한체의 연산 속도에 관심이 고조되고 있다. 본 논문에서는 Modified 최적 정규 기저의 성질 규명과 GF(q)(q=2$^{k}$ , k=8또는 16)위에서 GF(q$^{m}$ )(m: 홀수)의 Mofdified trinomial 기가 존재하는 m들을 제시하고, GF(r$^{n}$ )위에서 GF(r$^{nm}$ )dml Modified 최적 정규기저와 Modified trinomial 기저를 이용한 연산의 회수와 각 기저를 이용한 연산의 회수와 각 기저를 이용한 유한체 GF(q$^{m}$ )의 연산을 S/W화한 결과를 비교 하였다.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.11 no.2
• /
• pp.37-44
• /
• 2001

In this paper, an efficient architecture for the ECC multiplier in GF(2") is proposed. We give a design example for the irreducible trinomials $x_{193}\;+\;x_{15}\;+\;1$. In hardware implementations, it is often desirable to use the irreducible trinomial equations. A digit-serial multiplier with a digit size of 32 is proposed, which has more advantages than the 193bit serial LFSR architecture. The proposed multiplier is verified with a VHDL description using an elliptic curve addition. The elliptic curve used in this implementation is defined by Weierstrass equations. The measured results show that the proposed multiplier it 0.3 times smaller than the bit-serial LFSR multiplier.lier.