• Title/Summary/Keyword: Point Multiplication

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High Throughput Multiplier Architecture for Elliptic Cryptographic Applications

  • Swetha, Gutti Naga;Sandi, Anuradha M.
    • International Journal of Computer Science & Network Security
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    • v.22 no.9
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    • pp.414-426
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    • 2022
  • Elliptic Curve Cryptography (ECC) is one of the finest cryptographic technique of recent time due to its lower key length and satisfactory performance with different hardware structures. In this paper, a High Throughput Multiplier architecture is introduced for Elliptic Cryptographic applications based on concurrent computations. With the aid of the concurrent computing approach, the High Throughput Concurrent Computation (HTCC) technology that was just presented improves the processing speed as well as the overall efficiency of the point-multiplier architecture. Here, first and second distinct group operation of point multiplier are combined together and synthesised concurrently. The synthesis of proposed HTCC technique is performed in Xilinx Virtex - 5 and Xilinx Virtex - 7 of Field-programmable gate array (FPGA) family. In terms of slices, flip flops, time delay, maximum frequency, and efficiency, the advantages of the proposed HTCC point multiplier architecture are outlined, and a comparison of these advantages with those of existing state-of-the-art point multiplier approaches is provided over GF(2163), GF(2233) and GF(2283). The efficiency using proposed HTCC technique is enhanced by 30.22% and 75.31% for Xilinx Virtex-5 and by 25.13% and 47.75% for Xilinx Virtex-7 in comparison according to the LC design as well as the LL design, in their respective fashions. The experimental results for Virtex - 5 and Virtex - 7 over GF(2233) and GF(2283)are also very satisfactory.

On Implementations of Algorithms for Fast Generation of Normal Bases and Low Cost Arithmetics over Finite Fields (유한체위에서 정규기저의 고속생성과 저비용 연산 알고리즘의 구현에 관한 연구)

  • Kim, Yong-Tae
    • The Journal of the Korea institute of electronic communication sciences
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    • v.12 no.4
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    • pp.621-628
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    • 2017
  • The efficiency of implementation of the arithmetic operations in finite fields depends on the choice representation of elements of the field. It seems that from this point of view normal bases are the most appropriate, since raising to the power 2 in $GF(2^n)$ of characteristic 2 is reduced in these bases to a cyclic shift of the coordinates. We, in this paper, introduce our algorithm to transform fastly the conventional bases to normal bases and present the result of H/W implementation using the algorithm. We also propose our algorithm to calculate the multiplication and inverse of elements with respect to normal bases in $GF(2^n)$ and present the programs and the results of H/W implementations using the algorithm.

Human Cytomegalovirus Replication and $Ca^{2+}$ Response in Human Cell Lines of Neuronal Origin (신경세포에서의 Human Cytomegalovirus 증식과 이에 따른 세포내 유리칼슘 농도 변화)

  • Kang, Kyung-Hee;Lee, Chan-Hee
    • The Journal of Korean Society of Virology
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    • v.26 no.1
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    • pp.1-8
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    • 1996
  • Human cytomegalovirus (HCMV) replication and $Ca^{2+}$ response in human cell lines of neuronal origin were investigated. SK-N-SH (neuroblastoma cells) and A172 cells (glioblastoma cells) were used. SK-N-SH cells were permissive for HCMV multiplication with a delay of one day compared to virus multiplication in human embryo lung (HEL) cells. The delay of HCMV multiplication in SK-N-SH cells appeared to be correlated with a delay in the $Ca^{2+}$ response. The cytoplasmic free $Ca^{2+}$ concentration ($[Ca^{2+}]_i$) began to increase at 12 h p.i. in HCMV-infected SK-N-SH cells, while $[Ca^{2+}]_i$ increase in HCMV-infected HEL cells was observed as early as 3 h p.i. On the whole, the level of the increase in $[Ca^{2+}]_i$ in SK-N-SH cells was about 30% of that in HEL cells. On the other hand, in A172 cells infected with HCMV, neither production of infectious virus nor detectable increase in $[Ca^{2+}]_i$ was observed. Treatment with TPA of HCMV-infected SK-N-SH cells resulted in $[Ca^{2+}]_i$ increase at 6 h p.i. The stimulatory effect of TPA on HCMV- induced $[Ca^{2+}]_i$ increase continued until 12 h p.i., but TPA failed to stimulate the $Ca^{2+}$ response in SK-N-SH cells at 24 h p.i., suggesting that the effect of TPA had disappeared in SK-N-SH cells at that time point. In conclusion, SK-N-SH cells are permissive for HCMV replication and the delay in $Ca^{2+}$ response may be a consequence of the lower responsiveness of SK-N-SH cells than HEL cells to HCMV infection.

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Montgomery Multiplier with Very Regular Behavior

  • Yoo-Jin Baek
    • International Journal of Internet, Broadcasting and Communication
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    • v.16 no.1
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    • pp.17-28
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    • 2024
  • As listed as one of the most important requirements for Post-Quantum Cryptography standardization process by National Institute of Standards and Technology, the resistance to various side-channel attacks is considered very critical in deploying cryptosystems in practice. In fact, cryptosystems can easily be broken by side-channel attacks, even though they are considered to be secure in the mathematical point of view. The timing attack(TA) and the simple power analysis attack(SPA) are such side-channel attack methods which can reveal sensitive information by analyzing the timing behavior or the power consumption pattern of cryptographic operations. Thus, appropriate measures against such attacks must carefully be considered in the early stage of cryptosystem's implementation process. The Montgomery multiplier is a commonly used and classical gadget in implementing big-number-based cryptosystems including RSA and ECC. And, as recently proposed as an alternative of building blocks for implementing post quantum cryptography such as lattice-based cryptography, the big-number multiplier including the Montgomery multiplier still plays a role in modern cryptography. However, in spite of its effectiveness and wide-adoption, the multiplier is known to be vulnerable to TA and SPA. And this paper proposes a new countermeasure for the Montgomery multiplier against TA and SPA. Briefly speaking, the new measure first represents a multiplication operand without 0 digits, so the resulting multiplication operation behaves in a very regular manner. Also, the new algorithm removes the extra final reduction (which is intrinsic to the modular multiplication) to make the resulting multiplier more timing-independent. Consequently, the resulting multiplier operates in constant time so that it totally removes any TA and SPA vulnerabilities. Since the proposed method can process multi bits at a time, implementers can also trade-off the performance with the resource usage to get desirable implementation characteristics.

The 12 Channel TDM/FDM Translator with Polyphase Network and Fast DCT (다상회로와 고속DCT를 이용한 12채널의 TDM/FDM변환)

  • 박종연
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.9 no.4
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    • pp.170-178
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    • 1984
  • For the reduction of the 12-channel TDM/FDM translation time the 14-point fast DCT algorithm is used and the polyphase network which translates the prototype filter into the channel filters required in each channel is designed. For the prototype filter the degree of the numerator is 168 and the coefficients have symmetry values, the degree of the numerator is 6. Such a prototype filter is consistant with the CCITT requirements. In this case the required multiplication rate is CCITT requirements. In this case the required multiplication rate is $0.12267{\times}10^2$ multiplications/sec. channel and reduces to about 15-40% of the rate required in the exising systems. The proposed 12-channel TDM/FDM translation system is simulated using a demodulation system with a computer (PRIME 750) and the results show that the proposed conversion method is valid.

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Accurate Measurement of Residual Stresses of Glass Rods by Photoelasticity (광탄성법에 의한 유리봉 잔류응력의 정밀측정)

  • Baek, Tae-Hyun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.5
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    • pp.1524-1533
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    • 1996
  • Risidual stress of cylindrical glass rods are measured by photoelasticity to study the variation of stresses with respect to heat treatment temperatures. In order to measure the stresses accurately, fringe sharpening and multiplication techniques are applied to the determination of photoelastic fringe orders. Filon's separationmethod is used to resolve circumferential and redial stress ocmponents from isochromatic fringes which are the same as in-plane maximum shearing stresses. According to the photoelastic measurements, residual stress is increased as the heat treatment temperature of the rods is raised from $560^{\circ}C$ to $650^{\circ}C$ All the circumferential stress components are changed from tensile stresses to compressive ones at approximate $R_m$/$R_o$ = 0.6, where $R_o$/ is outer radius and $R_m$any measured radius. This analysis shows that residual stresses of the glass rods approach zero if the rods are heat-treated near the strain point.

A Study on the Adaptability and Cytotoxicity of Porcelain Bonded Ni-Cr Alloy (도재소부용 Ni-Cr합금의 적합성과 세포독성에 관한 연구)

  • Choi, Boo-Byung;Shin, Myung-Chull
    • The Journal of Korean Academy of Prosthodontics
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    • v.20 no.1
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    • pp.7-17
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    • 1982
  • In order to investigate the internal adaptability and cytotoxicity for porcelain fused to metal Ni-Cr alloy, two commercial alloys (Generic Gold-R alloy, Aalba Dent- Valloy)were employed and compared with new developed beryllium free Ni-Cr alloy (KIST-K alloy). After cementation of each crown to abutment die before and after ceramic bonding respectively, dies were mounted to epoxy resin and the internal space was measured between crown and die of each point on sagittal section. The results were as follows: 1) The results show that the space between the crown and the die was largest at the incisal edge, followed by the shoulder or the bevel and chamfer. The least was to be in the axial surface. 2) There were no significant difference in the adaptability of the compared alloys. 3) On day 2 of the experiment the cell multiplication was slightly inhibited by R and K alloys. However, observations taken at day 4 and 7 showed normal cell multiplication process compared to control group. 4) Alloy V exhibited the most severe cell toxicity among the alloys tested on day 2. By day 4 and 7 it showed a decrease level in toxicity, however it did not exhibit normal cell growth as compared to control group.

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High Performance Integer Multiplier on FPGA with Radix-4 Number Theoretic Transform

  • Chang, Boon-Chiao;Lee, Wai-Kong;Goi, Bok-Min;Hwang, Seong Oun
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.16 no.8
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    • pp.2816-2830
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    • 2022
  • Number Theoretic Transform (NTT) is a method to design efficient multiplier for large integer multiplication, which is widely used in cryptography and scientific computation. On top of that, it has also received wide attention from the research community to design efficient hardware architecture for large size RSA, fully homomorphic encryption, and lattice-based cryptography. Existing NTT hardware architecture reported in the literature are mainly designed based on radix-2 NTT, due to its small area consumption. However, NTT with larger radix (e.g., radix-4) may achieve faster speed performance in the expense of larger hardware resources. In this paper, we present the performance evaluation on NTT architecture in terms of hardware resource consumption and the latency, based on the proposed radix-2 and radix-4 technique. Our experimental results show that the 16-point radix-4 architecture is 2× faster than radix-2 architecture in expense of approximately 4× additional hardware. The proposed architecture can be extended to support the large integer multiplication in cryptography applications (e.g., RSA). The experimental results show that the proposed 3072-bit multiplier outperformed the best 3k-multiplier from Chen et al. [16] by 3.06%, but it also costs about 40% more LUTs and 77.8% more DSPs resources.

Position Correction Method for Misaligned Hall-Effect Sensor of BLDC Motor using BACK-EMF Estimation (역기전력 추정법을 이용한 브러시리스 직류 전동기의 홀센서 상전류 전환시점 보상 방법)

  • Park, Je-Wook;Kim, Jong-Hoon;Kim, Jang-Mok
    • The Transactions of the Korean Institute of Power Electronics
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    • v.17 no.3
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    • pp.246-251
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    • 2012
  • This paper proposes a new position compensation method for misaligned Hall-effect sensors of BLDCM(Brushless DC Motor). If the Hall-effect sensors are installed at wrong position, the exact rotor position cannot be obtained. Therefore, when the BLDCM is controlled with this wrong position, the torque ripple can be increased and the average torque also decreases. The back-EMF of BLDCM can be obtained by using the voltage equation and by multiplying the back-EMF constant and rotor speed. At a constant speed, the estimated back-EMF by using the multiplication of the back-EMF constant and rotor speed is constant, but the estimated back-EMF from the voltage equation decreases at the commutation point because the line-to-line back-EMF of two conducting phases is start to decrease at this point. Therefore, by using the difference between these two estimated back-EMFs, the commutation point of the phase current can be determined and position compensation can be carried out. The proposed position correction method doesn't require additional hardware circuit and can be easily implemented. The validity of the proposed position compensation method is verified through several experiments.

A Study on Detecting Optimal Corner Points using Morphology and Human Visual Concept (수리 형태학과 인간의 시각적 개념을 이용한 최적의 코너 점 추출을 위한 연구)

  • Jeong, Gi-Ryong
    • Journal of Navigation and Port Research
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    • v.28 no.3
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    • pp.233-238
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    • 2004
  • Comer point is a very important information to a pattern recognition of image processing. And so, many researchers develope various detecting comer point algoritms. But, there are some problems to get comer points by 8 directional chain code when the degree of edge line is not integer multiplication of 45 degree. So, we propose a new algorithm which is combined with morphology and human visual conception for optimal comer points without the above defects. We get a good simulation result by this proposed algorithm Ana so, we think this algorithm is very useful to FA(factory automation} and ship's radar system to know some coastal area from its image.