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# Elliptic Curve Cryptography

Cryptography | Elliptic Curve Cryptography: In this tutorial, we will briefly study the basic Elliptic curve and its examples aim to capture. We will cover types of messages in Elliptic Curve Cryptography. By Monika Sharma Last updated : May 24, 2023

## Elliptic Curve Cryptography 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.

## Elliptic Curve Cryptography 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.

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.

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

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.

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.

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).

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.

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

• They are relatively easy to perform,
• and, extremely difficult to reverse.

## Key Benefits of Elliptic Curve Cryptography

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.

## Elliptic Curve Cryptography: 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.

## Elliptic Curve Cryptography: 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.