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相关概念视频

Scalar Notation01:28

Scalar Notation

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Scalar notation is a useful method for simplifying calculations involving vectors. When vectors are added or subtracted, their components can be added or subtracted separately using scalar notation. For instance, force, a vector quantity, can be broken down into its x and y components, called rectangular components, and then the magnitude and direction of these components can be determined using trigonometric functions.
Consider a man pulling a rope from a hook in the northeast direction. The...
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Scalar Product (Dot Product)01:11

Scalar Product (Dot Product)

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The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
The scalar product of two vectors is obtained by multiplying...
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Scalar and Vectors01:22

Scalar and Vectors

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In mechanics, commonly used terms like force, speed, velocity, and work can be classified as either scalar or vector quantities. A scalar is a physical quantity that can be described by its magnitude alone and does not require any directional components. Examples of scalar quantities are mass, area, and length.
Scalar quantities with the same physical units can be added or subtracted according to the usual algebra rules for numbers. For example, a class ending 10 min earlier than 50 min lasts...
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Introduction to Scalars01:21

Introduction to Scalars

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Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts 50 min," or "the gas tank in my car holds 65 L," or "the distance between the two posts is 100 m." A physical quantity that can be specified completely in this manner is called a scalar quantity. The word "scalar" is a synonym for "number." Time, mass, distance, length, volume,...
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Scalar and Vector Triple Products01:06

Scalar and Vector Triple Products

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Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors....
2.3K
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

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Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
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相关实验视频

Updated: Jun 9, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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基于重新编码的区域时间效率高的安全尺度乘法架构.

Zhantao Zhang1, Weijiang Wang1,2, Jingqi Zhang1

  • 1School of Integrated Circuits and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, China.

Micromachines
|October 26, 2024
PubMed
概括
此摘要是机器生成的。

本研究介绍了一种新的,低延迟和低面积的圆曲线标尺乘法 (ECSM) 架构,用于安全的移动通信. 该设计增强了对功率分析攻击的安全性,并在FPGA上实现了高效的性能,使其适合高安全性计算需求.

关键词:
圆曲线密码学 (ECC) 是一种圆曲线的标量乘法 (ECSM)现场可编程门阵列 (FPGA)素数场 (GF) 是一个素数场.采样功率分析 (SPA) 的方法

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相关实验视频

Last Updated: Jun 9, 2025

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06:42

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Operation of the Collaborative Composite Manufacturing CCM System
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科学领域:

  • 密码学和计算机工程学
  • 硬件安全和性能优化 硬件安全和性能优化

背景情况:

  • 在移动通信中对安全和高效的数字签名的需求日益增加,推动了对轻量级加密解决方案的需求.
  • 圆曲线加密 (ECC) 提供了高安全性,减少了计算开销,使其成为资源有限环境的理想选择.
  • 圆曲线标尺乘法 (ECSM) 是ECC的一个基本操作,其高效实施对于整体性能至关重要.

研究的目的:

  • 提出一个新的圆曲线标尺乘法 (ECSM) 架构,优化低延迟和低面积.
  • 加强ECSM的安全性,以防止简单功率分析 (SPA) 和差异功率分析 (DPA) 等侧通道攻击.
  • 为了实现一个具有竞争力的区域时间产品 (ATP) 实用硬件实现.

主要方法:

  • 使用子算法作为ECSM架构的基础.
  • 整合了重新编码-k和随机化-Z算法,以加强对SPA和DPA的抵抗力.
  • 开发了一种多功能,低面积的架构,优化了数据依赖性,以实现高效执行.
  • 采用交叉模块乘法和修改的二进制逆算法来减少时钟周期延迟和增加频率.

主要成果:

  • 在Xilinx Virtex-7 FPGA上为256位素场GF实施了拟议的ECSM架构(p).
  • 实现了 7351 片的低资源使用率.
  • 实现单个ECSM计算时间为0.74毫秒,导致区域时间产物 (ATP) 为5.41.
  • 与现有最先进的设计相比,证明了竞争性性能和增强的安全性.

结论:

  • 提出的ECSM架构有效地平衡了低延迟,低区域和高安全性.
  • 该设计非常适合要求计算速度和强大的安全性,如安全移动通信的应用程序.
  • 这项工作为未来研究高效和安全的ECC硬件实现提供了重要的见解和灵感.