# What Are Elliptic Curves And What Is Their Use In Crypto?

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Elliptic curve cryptography(ECC) is one of the most powerful tools but least understood. It is important to understand the technology behind our security system. ECC is the next generation of public key cryptography and is used extensively for data encryption.

## What Are Elliptic Curves?

Elliptic Curves are defined by the equation (y^2=x^3+ax+b) where a and b are constants and x,y are coordinates on the curve. Suppose there are two points on the Elliptic curve P and Q then the third and interaction point of the curve can be denoted as P*Q. Some of the properties of the Elliptic curves are Closure, Associativity, Identity and Invertibility.

Elliptic Curves has many properties which makes them very useful for cryptography. One of the most valuable properties of the Elliptic Curve is Point Addition. The addition of two points on the curve to get the third point is Point Addition. Another valuable property of the Elliptic curve is Point Doubling which is used most commonly in cryptography.

Elliptic cryptography majorly relies on the Elliptic Curve Discrete Logarithm Problem(ECDLP). It states that it is hard to solve for X if we know (Y=G^X MOD P) where G is some known integer P is a prime number. This problem is hard because there’s no known way to efficiently find (X) without trying every possible combination.

## What Are Some Of The Uses Of Elliptic Curves?

Elliptic Curves has various real world applications like Banking and online payments. ECC can be used to protect data, authenticate connections and also in chat encryptions. Purchase on ecommerce sites using debit or credit cards is protected through the Elliptic Curves.

ECC requires smaller keys than other methods to achieve the same level of security. It can be important in scenarios where less storage is available. ECC also offers the same security with less computing power than others. It is also used in low computing power devices like Mobile phones.

#### Summary

Elliptic curves are one of the most important tools in the field of cryptography which helps to secure the network. It is used in various applications which helps to secure our data and in various cryptocurrency. There are various other similar tools which can help to secure the data and network efficiently.

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