COMPRESSION POINTS IN ELLIPTIC MONTGOMERY AND EDWARDS CURVES

What is it about?

Compression point is a new way that allows efficient storage while still keeping the same amount of information. In this paper, we will focus on working with compression point to reduce the memory size. Usually, any points in elliptic curves are represented by two elements x and y of a finite field and thus require large memory size. So, these methods are divided into two main categories: x-point compression and y-point compression. We will work with elliptic curves in Weierstrass, Montgomery, and Edwards form, discussing their overall characteristics. In this paper, we present the state for all these methods with the cost of these operations compared with classical methods to help users choose the right method for each specific case.

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Why is it important?

We provided details and important improvements of new methods of compression of two points with affine coordinates. We see that our methods can achieve twice implementation efficiency compared with the classical method i,e it will save 50% of memory size. So with this work, we have detailed result that can help us to choose the suitable curve to work with.

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