Elliptic Curve Cryptography is a public key encryption technique that is based on the elliptic curve theory which can be used to generate cryptographic keys which are smaller, faster and much more efficient. This technology can be used alongside the commonly used public key encryption methods such as RSA and Diffie-Hellman.
Let’s look into a bit about the origins of elliptic curve cryptography. Several functions and properties of it have been studied mathematically for about 150 years now. Although, the use of elliptic curves in cryptography had not been introduced till 1985, and is now used extensively in security protocols.
To get a basic understanding of what an elliptic curve looks like, check this out:
Now, what is Elliptic Curve Cryptography and how does it work? As you can see, the elliptic curve is a set of points which satisfies the equation y2 = x3 +ax +b. If you take a number(lets say, alpha) and multiply it with a point on the elliptic curve (beta), you will get your answer(lets say, gamma) which lies on the curve itself.
But, how does this help in cryptography? Well, even if you have the alpha beta and gamma value, it is extremely difficult to figure out the alpha value. It is easy to perform but supremely difficult to reverse. In Spite of several years of
research by mathematicians, they have not been able to formulate an algorithm to solve this problem.
Elliptic curve cryptography is applied in several areas such as the U.S. government uses it to protect internal communications, it provides signatures in Apple’s iMessage service, it’s used to prove ownership of bitcoins.
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