Many quantum key distribution (QKD) schemes are based on sending and measuring qubits -- two-dimensional quantum systems. Yet, in practical realizations and experiments, the measuring devices at the receiver's (Bob) site commonly do not measure a two-dimensional system but rather a quantum space of a larger dimension. Such an enlargement sometimes results from imperfect devices. However, in various QKD protocols such enlargement exists even in the ideal scenario when all devices are assumed to be perfect. This issue is common, for instance, in QKD schemes implemented via photons, where the parties' devices are based on Mach-Zehnder interferometers, as these inherently enlarge the quantum space in use. We show how space enlargement at Bob's site exposes the implemented protocol to new kinds of attacks, attacks that have not yet been explicitly pinpointed nor rigorously analyzed. We name these the "reversed space attacks". A key insight in formalizing our attacks, is the idea of taking all states defining Bob's (large) measured space and reversing them in time in order to identify precisely the space that an eavesdropper may attack. We employ such attacks on two variants of intereferometric-based QKD recently experimented by several groups, and show how to get full information on the qubit sent by Alice, while inducing no errors at all. The technique we develop here has subsequently been used in a closely related work (Boyer, Gelles, and Mor, Physical Review A, 2014) to demonstrate a (weaker variant of) reversed-space attack on both interferometric-based and polarization-based QKD.