Conventionally G is used to denote the standard Generator.
H is then some point whereby the discrete log is not known with respects to G;
H = yG where y is unknown.
A pedersen commitment would normally then be
P = aG + bH. Where b is blinder and a is the value you wish to commit to.
In monero, we have
P = bG + aH.
How would the mathematics break if I used the first definition? My initial guess is that it would not, unless maybe there are places in the code where this role is switched again.
That leads me onto my next question; Are there places in the code where the role of G and H are switched?
Follow-up to this, page35 on zero to monero: https://www.getmonero.org/library/Zero-to-Monero-1-0-0.pdf
Describes the process of going from the private spend key to public spend key:
publicSpend = privateSpend * G is the G used here, different from the G used in the Pedersen commitment?
- If the numbers were switched, we would also switch the maths to match it, for example the commitment to zero would become
- Assume that x and y are both unknown for
H = yGand
H = xH