Is there any weak message for an ECDSA signature? Suppose ECDSA is used without hashing the message, but directly using a short message (say 10-bytes long) as the value z (using the definitions at http://en.wikipedia.org/wiki/Elliptic_Curve_DSA) because we need extremely fast signing with ECDSA in a specific embedded platform. We also pre-compute kG and k^-1 values.

Are there any weak z values such that the signature can be forged ?
[Partial answer] In  Generic Groups, Collision Resistance, and ECDSA by D. Brown (see http://cacr.uwaterloo.ca/techreports/2002/corr2002-06.ps or http://eprint.iacr.org/2002/026) on page 17, you have a lot of information about the kind of hash functions that can be used with ECDSA. In your case, taking the identity function as hash and looking at the results you find that two of the proposed weaknesses are particularly relevant to your case:


$z=0$ is a weak value (see Zero-Finder-Resistant Hash)
If the probability that a random number modulo the curve order belongs to your acceptable range of $z$ values is not too low, there also is an attack (see One-Way Hash Function). With 10 bytes long values as suggested, the probability is sufficiently low and you can probably ignore this attack.