# What is the 'base point' (G) from the whitepaper and how is it represented as a single hex value?

The white paper introduces `G`, aka the base point, as `G = (x, −4/5)`.
I have two questions:

1. what is `x`? Is this the `x` from the elliptic curve (is it a variable)? If so, how is a private key `aG` computed?
2. A point has two coordinates (x and y). How is a point represented as a 256-bit value?

## 1 Answer

`G` is the base point of the Ed25519 elliptic curve. The `x` coordinate is not written explicitly because it can be found back using the `y` coordinate, the sign of `x` and the equation of the curve (`x` is positive for `G`).

Points on the Ed25519 curve are represented by 32 bytes. These 32 bytes are in fact the little-endian representation of a 256-bit number.

• bits 0 to 254 for the `y` coordinate
• bit 255 indicates the sign of the `x` coordinate

Therefore the hex string representing `G` is `5866666666666666666666666666666666666666666666666666666666666666`.

There are more info about this base point in https://crypto.stackexchange.com/questions/27392/base-point-in-ed25519