Discrete Rotational Symmetry and Quantum Key Distribution Protocols
  We study the role of discrete rotational symmetry in quantum key distribution by generalizing the well-known Bennett-Brassard 1984 (BB84) and Scarani-Acin-Ribordy-Gisin 2004 (SARG04) protocols. We observe that discrete rotational symmetry results in the protocol's invariance to continuous rotations, thus leading to a simplified relation between bit and phase error rates and consequently a straightforward security proof. 
David Shirokoff, Chi-Hang Fred Fung, and Hoi-Kwong Lo