Recently, position-based quantum cryptography has been claimed to be
unconditionally secure. In contrary, here we show that the existing proposals
for position-based quantum cryptography are, in fact, insecure if entanglement
is shared among two adversaries. Specifically, we demonstrate how the
adversaries can incorporate ideas of quantum teleportation and quantum secret
sharing to compromise the security with certainty. The common flaw to all
current protocols is that the Pauli operators always map a codeword to a
codeword (up to an irrelevant overall phase). We propose a modified scheme
lacking this property in which the same cheating strategy used to undermine the
previous protocols can succeed with a rate at most 85%. We conjecture that the
modified protocol is unconditionally secure and prove this to be true when the
shared quantum resource between the adversaries is a two- or three- level
system