I don't agree that 'secret' is merely used as an antonym of 'by public show of hands'. Surely the promise inherent in the usage 'secret ballot' is that nobody can be permitted, by any possible means, to ascertain how one has voted, as such knowledge or information could be misused by a subsequent totalitarian governmental set-up, a vindictive employer, &c. I still feel that, once this safeguard is breached by the recording of one's identification details in relation to the ballot paper, this safeguard is lost.
In any event, how, precisely, is the retention of this information in any accessible form supposed to guard against election fraud? I remain unconvinced as to the necessity, and exceedingly dubious as to the probity, of the practice.