Editing Schnorr signature (section)

==Short Schnorr signatures==

The aforementioned process achieves a ''t''-bit security level with 4''t''-bit signatures. For example, a 128-bit security level would require 512-bit (64-byte) signatures. The security is limited by discrete logarithm attacks on the group, which have a complexity of the ''square-root'' of the group size.

In Schnorr's original 1991 paper, it was suggested that since collision resistance in the hash is not required, shorter hash functions may be just as secure, and indeed recent developments suggest that a ''t''-bit security level can be achieved with 3''t''-bit signatures.<ref name="Neven"/> Then, a 128-bit security level would require only 384-bit (48-byte) signatures, and this could be achieved by truncating the size of ''e'' until it is half the length of the ''s'' bitfield.