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What is the purpose of the elliptic curve?

Elliptic curves are especially important in number theory, and constitute a major area of current research; for example, they were used in Andrew Wiless proof of Fermats Last Theorem. They also find applications in elliptic curve cryptography (ECC) and integer factorization.

What is so special about elliptic curves?

The elliptic curve L-function plays a very important role in modern number theory. Perhaps the most celebrated theorem of our era is the fact that elliptic curves over the rationals are modular: that is, the L-function of an elliptic curve defined over the rationals is equal to the L-function of a cusp form.

What is the formula for the elliptic curve?

In most situations, an Elliptic Curve E is the graph of an equation of the form y2 = x3 + Ax + B, where A and B are constants. This is called the Weierstrass equation for an elliptic curve.

What are the advantages of ECC?

Advantages of ECC: Smaller keys, ciphertexts and signatures. Very fast key generation. Fast signatures. Moderately fast encryption and decryption. Signatures can be computed in two stages, allowing latency much lower than inverse throughput. Good protocols for authenticated key exchange (FH-ECMQV et al)

What is the theory of elliptic curves?

Elliptic curves are curves defined by a certain type of cubic equation in two variables. The set of rational solutions to this equation has an extremely interesting structure, including a group law. The theory of elliptic curves was essential in Andrew Wiles proof of Fermats last theorem.

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What is an elliptic curve in simple terms?

An elliptic curve is not an ellipse, or oval shape, but it is represented as a looping line intersecting two axes, which are lines on a graph used to indicate the position of a point. The curve is completely symmetric, or mirrored, along the x-axis of the graph.

Why is elliptic curve better?

1) Elliptic Curves provide security equivalent to classical systems (like RSA), but uses fewer bits. 2) Implementation of elliptic curves in cryptography requires smaller chip size, less power consumption, increase in speed, etc.

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