Q.18 What are Elliptic curve cryptosystems?

Answered: Q.18 What are Elliptic curve…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Q.18 What are Elliptic curve cryptosystems?

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An elliptic curve cryptosystem is an asymmetric/public key cryptosystem. It provides equal security with a similar key size as compared to RSA and other systems. It makes use of elliptic curves.

Elliptic curves are defined by some mathematical functions:-

$y^{2} = x^{3} + a x + b$ (equation of degree 3)

Symmetric to X-axis, if we draw a line it will touch a max of 3 points.

Let $E_{p} (a, b)$ be the elliptic curve.

Consider the equation $Q = K P$ , where Q and P are points on the curve and $k < n$ .

If K and P are given, it is easy to find Q but if Q and P are given, it would be difficult to find K.

This is called the Trapdoor function, i.e A->B is easy but B->A is very difficult.

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