Representing Ed25519 p curve in hexadecimal byte string

Question

I am interested in representing p = 2^255 - 19 in the Ed255519 curve as hexadecimal byte representation.

When I was looking through the original NaCL source code written by DJB, I saw a code fragment that says:

static const unsigned int minusp[32] = {
 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128
} ;

Am I safe to assume that this is the 32 byte integer representation of p = 2^255 - 19 and all I need to do is translate the 32 byte integers into 32 byte hexadecimal string representation ?

How should I represent the p for Ed25519 in hexadecimal string ?

Answer 1

The constant is named minusp, thus it's $-p \pmod {2^{256}}$, or $2^{255} + 19$, encoded in little-endian.

Assuming you want the hex string in big-endian, which is the way numbers are usually written, you get:

$p = 2^{255}-19$ = 7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED

$2^{256} - p = 2^{255}+19$ = 8000000000000000000000000000000000000000000000000000000000000013