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Document Cofactor multiplied base points? #706

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@stevefan1999-personal

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@stevefan1999-personal

Derived from #705 and some discussion online, I find this constant particularly useful:

const ED25519_BASEPOINT_POINT_MUL_BY_COFACTOR: EdwardsPoint = EdwardsPoint{
    X: FieldElement51::from_limbs([2233581206391315, 847321536719855, 1143763522071466, 2176635986873503, 544015092356874]),
    Y: FieldElement51::from_limbs([810168548829118, 1091277158180317, 1905862677914949, 871313444918061, 2245667822025877]),
    Z: FieldElement51::from_limbs([207037345464830, 1993080251615457, 560932193579569, 999626924140364, 754134581836708]),
    T: FieldElement51::from_limbs([606549093027129, 120708372070681, 50079640475349, 1940797268843777, 623236962379938])
};

This is because in my way to generate ed25519 keys:

let ED25519_BASEPOINT_POINT_MUL_BY_COFACTOR = ED25519_BASEPOINT_POINT.mul_by_cofactor(); // Not constant at the moment

let mut rng = Rng::new();
let expanded_sk: [u8; 32] = 
    Sha512::default()
        .chain_update({
            let mut sk = SecretKey::default();
            rng.fill(&mut sk);
            sk
        })
        .finalize()[..32]
        .try_into()
        .unwrap();
let mut count: usize = 0;
let mut pk = ED25519_BASEPOINT_POINT.mul_clamped(expanded_sk);

loop {
    // foo(pk.compress().to_bytes());
    count += 1;
    pk += ED25519_BASEPOINT_POINT_MUL_BY_COFACTOR;
}
// expanded_sk += 8 * count;

The performance improved the generation by 3 orders of magnitude, so now the Edwards point compression is the only hot path now. Is it possible to do addition arithmetic on compressed Edwards point directly?

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