If Alice wants to prove to Bob that she is the owner of the private key, xwithout exposing xThey can use the Schnorr identification protocol with public functions sG = kG + exG And a private scalar function s = k +ex. In these features G This is the static generator point. k A hidden nonce chosen by Alice to protect. x so as not to reveal it to Bob e A nonce that Bob chooses to trust. kG (If someone pretends to hold it, it can’t be counted. x).
This all makes sense to me, but I wonder why. e is multiplied x Instead of just following the same addition operator k. So the equation is: sG = kG + eG + xG and s = k + e + x. k There is a very good reason to use addition. x It’s hidden. I can’t think of a meaningful difference in the goals of the protocols if: e If we multiply or add, wouldn’t we be missing a key concept?