Composable security against collective attacks of a modified BB84 QKD protocol with information only in one basis

Quantum Cryptography uses the counter-intuitive properties of Quantum Mechanics for performing cryptographic tasks in a secure and reliable way. The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: collective attacks and joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids a classical information-theoretical analysis and proves a fully composable security. We show that this modified BB84 protocol is as secure against collective attacks as the original BB84 protocol, and that it requires more bits for testing.