  We consider a variant of the BB84 protocol for quantum cryptography, the
prototype of tomographically incomplete protocols, where the key is generated
by one-way communication rather than the usual two-way communication. Our
analysis, backed by numerical evidence, establishes thresholds for
eavesdropping attacks on the raw data and on the generated key at quantum bit
error rates of 10% and 6.15%, respectively. Both thresholds are lower than the
threshold for unconditional security in the standard BB84 protocol.
