Is there a problem with signing a message like this?
p = the Elliptic Curve prime G = base point a = Alice’s private key A = aG = Alice’s public key e = hash(message) Jx = x coordinate of J
In my target 32-bit microcontroller I am using p-256 and SHA256. Thus e will typically be in 1..p-1.
e = hash(message) E = eG J = aE using Alice’s private key
and sends Jx as signature
e = hash(message) K = eA using Alice’s public key and validates Jx = Kx
The only problem I see is that e might be 0 or 1 or some value >= p. (If it is I have the flexibility to pad the message such that e is in a good range.)
Is there a problem if hash(msg) is greater or equal to the EC prime? Other than a few unusable values of e is there is a problem that makes this method less secure than ECDSA?