椭圆曲线密码学导论pdf

历史 (History)

The use of elliptic curves in cryptography was advised independently by Neal Koblitz and Victor S. Miller in 1985. Elliptic curve cryptography algorithms entered large use from 2004 to 2005.

1985年， Neal Koblitz和Victor S. Miller分别建议在加密中使用椭圆曲线。从2004年到2005年，椭圆曲线加密算法开始大量使用。

介绍 (Introduction)

It is a public key encryption technique in cryptography which depends on the elliptic curve theory which helps us to create faster, smaller, and most efficient or valuable cryptographic keys.

它是一种依赖于椭圆曲线理论的加密技术中的公共密钥加密技术，可帮助我们创建更快，更小，最有效或最有价值的加密密钥。

It generates keys with the help of the properties of the Elliptic curve equation in mathematics rather than the traditional method of generation as the product of very large prime numbers is multiplied.

它借助数学中椭圆曲线方程式的属性来生成键，而不是传统的生成方法，因为乘以非常大的素数的乘积就可以生成键。

The technology can be used in various technologies with most public-key encryption methods, like RSA, and Diffie-Hellman.

可以使用大多数公钥加密方法将这种技术用于各种技术，例如RSA和Diffie-Hellman。

According to some researchers, ECC can find a level of security with a "164-bit" key that other systems require a "1,024-bit" key to achieve. Because ECC helps to publish equivalent security with less computing power in crypto and battery resource usage for ECC, it is becoming widely used for mobile applications or any other applications.

根据一些研究人员的说法，ECC可以使用其他系统需要“ 1,024位”密钥才能实现的“ 164位”密钥来找到安全级别。 因为ECC有助于以较少的计算能力发布等效的安全性，而ECC的加密和电池资源使用量却越来越少，因此它已被广泛用于移动应用程序或任何其他应用程序。

ECC was invented or developed by "Certicom" who was a big mobile e-business security provider who provides security and was recently licensed the security by "Hifn", a manufacturer of integrated circuitry (IC) and network security products for use.

ECC由“ Certicom”发明或开发，“ Certicom”是一家提供安全性的大型移动电子商务安全提供商，最近获得了集成电路(IC)和网络安全产品制造商“ Hifn”的许可。

RSA has been producing its own latest version of ECC. Eventually, Many manufacturers, including Cylink, VeriFone Motorola, TRW, Pitney Bowes,3COM, and Siemens have provided support for ECC in their products for better use in the future.

RSA一直在生产自己的最新版本的ECC。 最终，包括Cylink，VeriFone摩托罗拉，TRW，Pitney Bowes，3COM和Siemens在内的许多制造商在其产品中都为ECC提供了支持，以便将来更好地使用。

The objective and functions of elliptic curves have been studied in mathematics for 150 years for use in the future. These use within cryptography was first discovered in 1985, (individually) by "Neal Koblitz" from the University of Washington, and "Victor Miller" at IBM for business university. An elliptic curve is not similar to an ellipse or we can say in oval shape but is created or represented as a looping line intersecting or interacting two axes (lines on a graph used to indicate the position of a point in the graph).

椭圆曲线的目的和功能已经在数学上进行了150年的研究，以备将来使用。 密码术中的这些用法是1985年由华盛顿大学的“ Neal Koblitz”和商业大学的IBM的“ Victor Miller”首次发现的(单独)。 椭圆曲线与椭圆并不相似，或者可以说是椭圆形，但可以创建或表示为与两个轴相交或相互作用的环线(图形上用于指示图形中点位置的线)。

ECC is depends on properties of a particular type of equation uses for to created from the mathematical group (a set of values for that operations can be used or performed on any two members of the group of settings to produce a third member in the group) derived from points where the line intersects the axes as x oy y-axis. Multiplying a point on the curve of a graph by a number will produce another point on the curve of the graph, but it is very complex or difficult to find what number was used in this, eventually, if you know the original point and the result from that equation or formula.

ECC取决于用于从数学组中创建的特定类型方程式的属性(该操作的一组值可以在设置组的任何两个成员上使用或执行，以在该组中产生第三个成员)从直线与x y轴相交的点得出。 将图形曲线上的一个点乘以一个数字会在图形曲线上产生另一个点，但是要知道原始点和结果，最终很难找到其中使用的数字，这非常复杂或困难。从等式或公式。

Equations depend on elliptic curves have a functionality that is very valuable or useful for cryptography purposes,

取决于椭圆曲线的方程式具有非常有价值的功能或对密码学有用的功能，

• They are relatively easy to perform,

  它们相对容易执行，

• and, extremely difficult to reverse.

  并且，极难逆转。

ECC的主要优点 (Key Benefits of ECC)

ECC key is very useful or helpful for the present generation as more people are moving to the Smartphone, so there are more chances to get a virus or hack the phone. As the use or utilization of smartphones extends to grow of the population, there is an emerging need for more comfort or flexible encryption for businesses to meet with huge increasing security requirements for this.

随着越来越多的人使用智能手机，ECC密钥对于现代人来说非常有用或有用，因此有更多机会感染病毒或入侵手机。 随着智能手机的使用或使用范围随着人口的增长而扩展，对企业越来越需要舒适或灵活的加密技术来满足对此日益增长的安全性要求。

更强的按键 (Stronger Keys)

It is the latest encryption technique that offers stronger security. If we see the comparison to the RSA and DSA algorithms, then only 256-bit ECC is just equal or comparable to 3072-bit RSA key, the main reason behind keeping short key is the uses of huge computational power, secure and fast connection, ideal for Smartphone and tablet for future use. It is harder to break ‘for hackers’ compare to RSA and DSA, which means the ECC algorithm ensures or secure the web site and infrastructure safety than traditional methods for product f large numbers in a more secure manner in the future.

它是提供更强安全性的最新加密技术。 如果我们看到了与RSA和DSA算法的比较，那么只有256位ECC等于或与3072位RSA密钥相当，保持短密钥的主要原因是使用巨大的计算能力，安全和快速的连接，智能手机和平板电脑供将来使用的理想选择。 与RSA和DSA相比，“为黑客而战”更难破解，这意味着ECC算法比传统的针对大量产品的方法能够以更安全的方式确保或保护网站和基础设施的安全。

较短的按键大小 (Shorter Key Size)

It is certificated to allow key size to remain small while providing a higher level of security to the system. ECC certificates key to create technique was entirely different from other algorithms, while on the use of a public key for encryption and a private key for decryption in the cryptography technology.

经过认证可以使密钥大小保持较小，同时为系统提供更高级别的安全性。 ECC证书创建技术的密钥与其他算法完全不同，而密码技术中使用的是加密的公共密钥和解密的私有密钥。

翻译自: https://www.includehelp.com/cryptography/elliptic-curve-cryptography.aspx

椭圆曲线密码学导论pdf