What is meant by elliptic curve cryptography?

What is meant by elliptic curve cryptography?

Elliptic Curve Cryptography (ECC) is a key-based technique for encrypting data. ECC focuses on pairs of public and private keys for decryption and encryption of web traffic. ECC is frequently discussed in the context of the Rivest–Shamir–Adleman (RSA) cryptographic algorithm.

What uses elliptic curve cryptography?

Elliptic curves are applicable for encryption, digital signatures, pseudo-random generators and other tasks. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic-curve factorization.

What is the function of elliptic curve?

Elliptic curves over finite fields are used in some cryptographic applications as well as for integer factorization. Typically, the general idea in these applications is that a known algorithm which makes use of certain finite groups is rewritten to use the groups of rational points of elliptic curves.

What is equation of elliptic curve?

This equation defines an elliptic curve. y2 = x3 + Ax + B, for some constants A and B. Below is an example of such a curve. An elliptic curve over C is a compact manifold of the form C/L, where L = Z + ωZ is a lattice in the complex plane.

Who invented elliptic curve cryptography?

Elliptic curve cryptography was introduced in 1985 by Victor Miller and Neal Koblitz who both independently developed the idea of using elliptic curves as the basis of a group for the discrete logarithm problem. [16, 20].

What is the zero point of an elliptic curve?

When in (projective) Weierstrass form, an elliptic curve always contains exactly one point of infinity, ( 0 , 1 , 0 ) (“the point at the ends of all lines parallel to the -axis”), and the tangent at this point is the line at infinity and intersects the curve at ( 0 , 1 , 0 ) with multiplicity three.

Where is ECC used?

ECC is an alternative to the Rivest-Shamir-Adleman (RSA) cryptographic algorithm and is most often used for digital signatures in cryptocurrencies, such as Bitcoin and Ethereum, as well as one-way encryption of emails, data and software.

Why is it called an elliptic curve?

These curves are called elliptic curves. So elliptic curves are the set of points that are obtained as a result of solving elliptic functions over a predefined space.

Who discovered elliptic curves?

Properties and functions of elliptic curves have been studied in mathematics for 150 years. Use of elliptic curves in cryptography was not known till 1985. Elliptic curve cryptography is introduced by Victor Miller and Neal Koblitz in 1985 and now it is extensively used in security protocol.

Why was ECC created?

Elliptic Curve Cryptography (ECC) was discovered in 1985 by Victor Miller (IBM) and Neil Koblitz (University of Washington) as an alternative mechanism for implementing public-key cryptography.

How many points is an elliptic curve?

There are ten points on this elliptic curve, counting ∞. Example: Add the points (1,1) + (2,5) on the curve whose points were just listed. 2 = 13 ≡ 6 (mod 7) and y3 ≡ 4(1−6)−1 ≡ 0 (mod 7), so the sum is (6,0). Example: Double the point (2,2) on the same curve.

Why is it called elliptic curve?