I am reading about Schnorr signature and I though what if we calculate response as $r = \alpha + c + k$ instead of $r = \alpha + c*k$? Will it make scheme more insecure? Are there any name for this scheme?
So, signing: $k = privatekey, \alpha = random, c = HASH(message, \alpha*G, k*G), r = \alpha + c + k, signature = (\alpha*G, r)$