• Title/Summary/Keyword: Binary finite field

Search Result 33, Processing Time 0.025 seconds

Design of Binary Sequences with Optimal Cross-correlation Values (최적의 상호상관관계를 갖는 이진 수열의 설계)

  • Choi, Un-Sook;Cho, Sung-Jin
    • The Journal of the Korea institute of electronic communication sciences
    • /
    • v.6 no.4
    • /
    • pp.539-544
    • /
    • 2011
  • Balanced binary sequences of period $2^n-1(n{\geq}1)$ having the two-valued autocorrelation function have many applications in spread-spectrum communications system. In this paper we propose new nonlinear binary sequences which are constructed from Legendre sequences with the same cross-correlation as the sequences proposed by Cho. These sequences include the m-sequences, GMW sequences, Kasami sequences and No sequences which are described in terms of the trace function over a finite field. Also the proposed sequences have more low cross-correlation distribution than the quadratic form sequences proposed by Klapper.

A Design of Point Scalar Multiplier for Binary Edwards Curves Cryptography (이진 에드워즈 곡선 암호를 위한 점 스칼라 곱셈기 설계)

  • Kim, Min-Ju;Jeong, Young-Su;Shin, Kyung-Wook
    • Journal of the Korea Institute of Information and Communication Engineering
    • /
    • v.26 no.8
    • /
    • pp.1172-1179
    • /
    • 2022
  • This paper describes a design of point scalar multiplier for public-key cryptography based on binary Edwards curves (BEdC). For efficient implementation of point addition (PA) and point doubling (PD) on BEdC, projective coordinate was adopted for finite field arithmetic, and computational performance was improved because only one inversion was involved in point scalar multiplication (PSM). By applying optimizations to hardware design, the storage and arithmetic steps for finite field arithmetic in PA and PD were reduced by approximately 40%. We designed two types of point scalar multipliers for BEdC, Type-I uses one 257-b×257-b binary multiplier and Type-II uses eight 32-b×32-b binary multipliers. Type-II design uses 65% less LUTs compared to Type-I, but it was evaluated that it took about 3.5 times the PSM computation time when operating with 240 MHz. Therefore, the BEdC crypto core of Type-I is suitable for applications requiring high-performance, and Type-II structure is suitable for applications with limited resources.

Efficient Serial Gaussian Normal Basis Multipliers over Binary Extension Fields

  • Kim, Yong-Tae
    • The Journal of the Korea institute of electronic communication sciences
    • /
    • v.4 no.3
    • /
    • pp.197-203
    • /
    • 2009
  • Finite field arithmetic is very important in the area of cryptographic applications and coding theory, and it is efficient to use normal bases in hardware implementation. Using the fact that $GF(2^{mk})$ having a type-I optimal normal basis becomes the extension field of $GF(2^m)$, we, in this paper, propose a new serial multiplier which reduce the critical XOR path delay of the best known Reyhani-Masoleh and Hasan's serial multiplier by 25% and the number of XOR gates of Kwon et al.'s multiplier by 2 based on the Reyhani-Masoleh and Hasan's serial multiplier for type-I optimal normal basis.

  • PDF

Efficient Hardware Montgomery Modular Inverse Module for Elliptic Curve Cryptosystem in GF(p) (GF(p)의 타원곡선 암호 시스템을 위한 효율적인 하드웨어 몽고메리 모듈러 역원기)

  • Choi, Piljoo;Kim, Dong Kyue
    • Journal of Korea Multimedia Society
    • /
    • v.20 no.2
    • /
    • pp.289-297
    • /
    • 2017
  • When implementing a hardware elliptic curve cryptosystem (ECC) module, the efficient design of Modular Inverse (MI) algorithm is especially important since it requires much more computation than other finite field operations in ECC. Among the MI algorithms, binary Right-Shift modular inverse (RS) algorithm has good performance when implemented in hardware, but Montgomery Modular Inverse (MMI) algorithm is not considered in [1, 2]. Since MMI has a similar structure to that of RS, we show that the area-improvement idea that is applied to RS is applicable to MMI, and that we can improve the speed of MMI. We designed area- and speed-improved MMI variants as hardware modules and analyzed their performance.

Hardware Design of Finite Field Divider Using Modified Extended Euclidian Algorithm (개선된 확장 유클리드 알고리듬을 이용한 유한체 나눗셈 연산기의 하드웨어 설계)

  • Lee K.H.;Kang M.S.
    • Proceedings of the Korean Information Science Society Conference
    • /
    • 2005.11a
    • /
    • pp.64-66
    • /
    • 2005
  • 본 논문에서는 GF($2^m$) 상에서 나눗셈 연산을 위한 고속 알고리듬을 제안하고, 제안한 알고리듬을 기본으로 한 나눗셈 연산기의 하드웨어 설계 및 구현에 관하여 기술한다. 나눗셈을 위한 모듈러 연산은 개선된 이진 확장 유클리드 알고리듬 (Binary Extended Euclidian algorithm) 을 기본으로 하고 있다 성능비교 결과로부터 제안한 방법은 기존 방법에 비해 지연시간이 약 $26.7\%$ 정도 개선됨을 확인하였다.

  • PDF

Hygrothermoelasticity in a porous cylinder under nonlinear coupling between heat and moisture

  • Ishihara, Masayuki;Yoshida, Taku;Ootao, Yoshihiro;Kameo, Yoshitaka
    • Structural Engineering and Mechanics
    • /
    • v.75 no.1
    • /
    • pp.59-69
    • /
    • 2020
  • The purpose of this study is to develop practical tools for the mechanical design of cylindrical porous media subjected to a broad gap in a hygrothermal environment. The planar axisymmetrical and transient hygrothermoelastic field in a porous hollow cylinder that is exposed to a broad gap of temperature and dissolved moisture content and is free from mechanical constraint on all surfaces is investigated considering the nonlinear coupling between heat and binary moisture and the diffusive properties of both phases of moisture. The system of hygrothermal governing equations is derived for the cylindrical case and solved to illustrate the distributions of hygrothermal-field quantities and the effect of diffusive properties on the distributions. The distribution of the resulting stress is theoretically analyzed based on the fundamental equations for hygrothermoelasticity. The safety hazard because of the analysis disregarding the nonlinear coupling underestimating the stress is illustrated. By comparing the cylinder with an infinitesimal curvature with the straight strip, the significance to consider the existence of curvature, even if it is infinitesimally small, is demonstrated qualitatively and quantitatively. Moreover, by investigating the bending moment, the necessities to consider an actual finite curvature and to perform the transient analysis are illustrated.

Non-cooperative interference radio localization with binary proximity sensors

  • Wu, Qihui;Yue, Liang;Wang, Long;Ding, Guoru
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.9 no.9
    • /
    • pp.3432-3448
    • /
    • 2015
  • Interference can cause serious problems in our daily life. Traditional ways in localizing a target can't work well when it comes to the source of interference for it may take an uncooperative or even resistant attitude towards localization. To tackle this issue, we take the BPSN (Binary Proximity Sensor Networks) and consider a passive way in this paper. No cooperation is needed and it is based on simple sensor node suitable for large-scale deployment. By dividing the sensing field into different patches, when enough patches are formed, good localization accuracy can be achieved with high resolution. Then we analyze the relationship between sensing radius and localization error, we find that in a finite region where edge effect can't be ignored, the trend between sensing radius and localization error is not always consistent. Through theoretical analysis and simulation, we explore to determine the best sensing radius to achieve high localization accuracy.

Coupled Turbulent Flow, Heat and Solute Transport in Continuous Casting Processes with EMBR (EMBR을 이용한 연속주조공정에서 난류 유동, 상변화 및 매크로 편석에 대한 연구)

  • Kang, Kwan-Gu;Ryou, Hong-Sun;Hur, Nahm-Keon
    • Proceedings of the KSME Conference
    • /
    • 2004.04a
    • /
    • pp.1195-1200
    • /
    • 2004
  • A fully coupled fluid flow, heat, and solute transport model was developed to investigate turbulent flow, solidification, and macrosegregation in a continuous casting process of steel slab with EMBR. Transport equations of mass, momentum, energy, and species for a binary iron-carbon alloy system were solved using a continuum model. The electromagnetic field was described by the Maxwell equations. A finite-volume method was employed to solve the conservation equations associated with appropriate boundary conditions. The effects of intensity of magnetic field and carbon segregation were investigated. The electromagnetic field reduces the velocity of molten flow in the mold and an increase in the percentage of C in steel results in a decrease of carbon segregation ratio.

  • PDF

Construction of Jacket Matrices Based on q-ary M-sequences (q-ary M-sequences에 근거한 재킷 행렬 설계)

  • S.P., Balakannan;Kim, Jeong-Ki;Borissov, Yuri;Lee, Moon-Ho
    • Journal of the Institute of Electronics Engineers of Korea TC
    • /
    • v.45 no.7
    • /
    • pp.17-21
    • /
    • 2008
  • As with the binary pseudo-random sequences q-ary m-sequences possess very good properties which make them useful in many applications. So we construct a class of Jacket matrices by applying additive characters of the finite field $F_q$ to entries of all shifts of q-ary m-sequence. In this paper, we generalize a method of obtaining conventional Hadamard matrices from binary PN-sequences. By this way we propose Jacket matrix construction based on q-ary M-sequences.

A New Digital Image Steganography Approach Based on The Galois Field GF(pm) Using Graph and Automata

  • Nguyen, Huy Truong
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.13 no.9
    • /
    • pp.4788-4813
    • /
    • 2019
  • In this paper, we introduce concepts of optimal and near optimal secret data hiding schemes. We present a new digital image steganography approach based on the Galois field $GF(p^m)$ using graph and automata to design the data hiding scheme of the general form ($k,N,{\lfloor}{\log}_2p^{mn}{\rfloor}$) for binary, gray and palette images with the given assumptions, where k, m, n, N are positive integers and p is prime, show the sufficient conditions for the existence and prove the existence of some optimal and near optimal secret data hiding schemes. These results are derived from the concept of the maximal secret data ratio of embedded bits, the module approach and the fastest optimal parity assignment method proposed by Huy et al. in 2011 and 2013. An application of the schemes to the process of hiding a finite sequence of secret data in an image is also considered. Security analyses and experimental results confirm that our approach can create steganographic schemes which achieve high efficiency in embedding capacity, visual quality, speed as well as security, which are key properties of steganography.