  Quantum key distribution (QKD) promises provably secure cryptography, even to
attacks from an all-powerful adversary. However, with quantum computing
development lagging behind QKD, the assumption that there exists an adversary
equipped with a universal fault-tolerant quantum computer is unrealistic for at
least the near future. Here, we explore the effect of restricting the
eavesdropper's computational capabilities on the security of QKD, and find that
improved secret key rates are possible. Specifically, we show that for a large
class of discrete variable protocols higher key rates are possible if the
eavesdropper is restricted to a unitary operation from the Clifford group.
Further, we consider Clifford-random channels consisting of mixtures of
Clifford gates. We numerically calculate a secret key rate lower bound for BB84
with this restriction, and show that in contrast to the case of a single
restricted unitary attack, the mixture of Clifford based unitary attacks does
not result in an improved key rate.
