橢圓曲線密碼學導論pdf

歷史 (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分別建議在加密中使用橢圓曲線。從2004年到2005年，橢圓曲線加密算法開始大量使用。

介紹 (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.

它是一種依賴于橢圓曲線理論的加密技術中的公共密鑰加密技術，可幫助我們創建更快，更小，最有效或最有價值的加密密鑰。

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.

它借助數學中橢圓曲線方程式的屬性來生成鍵，而不是傳統的生成方法，因為乘以非常大的素數的乘積就可以生成鍵。

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

可以使用大多數公鑰加密方法將這種技術用于各種技術，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.

根據一些研究人員的說法，ECC可以使用其他系統需要“ 1,024位”密鑰才能實現的“ 164位”密鑰來找到安全級別。 因為ECC有助于以較少的計算能力發布等效的安全性，而ECC的加密和電池資源使用量卻越來越少，因此它已被廣泛用于移動應用程序或任何其他應用程序。

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”發明或開發，“ Certicom”是一家提供安全性的大型移動電子商務安全提供商，最近獲得了集成電路(IC)和網絡安全產品制造商“ Hifn”的許可。

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一直在生產自己的最新版本的ECC。 最終，包括Cylink，VeriFone摩托羅拉，TRW，Pitney Bowes，3COM和Siemens在內的許多制造商在其產品中都為ECC提供了支持，以便將來更好地使用。

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).

橢圓曲線的目的和功能已經在數學上進行了150年的研究，以備將來使用。 密碼術中的這些用法是1985年由華盛頓大學的“ Neal Koblitz”和商業大學的IBM的“ Victor Miller”首次發現的(單獨)。 橢圓曲線與橢圓并不相似，或者可以說是橢圓形，但可以創建或表示為與兩個軸相交或相互作用的環線(圖形上用于指示圖形中點位置的線)。

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取決于用于從數學組中創建的特定類型方程式的屬性(該操作的一組值可以在設置組的任何兩個成員上使用或執行，以在該組中產生第三個成員)從直線與x y軸相交的點得出。 將圖形曲線上的一個點乘以一個數字會在圖形曲線上產生另一個點，但是要知道原始點和結果，最終很難找到其中使用的數字，這非常復雜或困難。從等式或公式。

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

取決于橢圓曲線的方程式具有非常有價值的功能或對密碼學有用的功能，

• They are relatively easy to perform,

  它們相對容易執行，

• and, extremely difficult to reverse.

  并且，極難逆轉。

ECC的主要優點 (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.

隨著越來越多的人使用智能手機，ECC密鑰對于現代人來說非常有用或有用，因此有更多機會感染病毒或入侵手機。 隨著智能手機的使用或使用范圍隨著人口的增長而擴展，對企業越來越需要舒適或靈活的加密技術來滿足對此日益增長的安全性要求。

更強的按鍵 (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.

它是提供更強安全性的最新加密技術。 如果我們看到了與RSA和DSA算法的比較，那么只有256位ECC等于或與3072位RSA密鑰相當，保持短密鑰的主要原因是使用巨大的計算能力，安全和快速的連接，智能手機和平板電腦供將來使用的理想選擇。 與RSA和DSA相比，“為黑客而戰”更難破解，這意味著ECC算法比傳統的針對大量產品的方法能夠以更安全的方式確保或保護網站和基礎設施的安全。

較短的按鍵大小 (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.

經過認證可以使密鑰大小保持較小，同時為系統提供更高級別的安全性。 ECC證書創建技術的密鑰與其他算法完全不同，而密碼技術中使用的是加密的公共密鑰和解密的私有密鑰。

翻譯自: https://www.includehelp.com/cryptography/elliptic-curve-cryptography.aspx

橢圓曲線密碼學導論pdf