Position-based quantum cryptography over untrusted networks

Abstract

In this paper, we propose quantum position-verification schemes where all the channels are untrusted except the position of the prover and distant reference stations of verifiers. We review and analyze the existing QPV schemes containing some pre-shared data between the prover and verifiers. Most of these schemes are based on non-cryptographic assumptions, that is, quantum/classical channels between the verifiers are secure. It seems impractical in the environment fully controlled by adversaries and would lead to security compromise in practical implementations. However, our proposed formulism for quantum position-verification is more robust, secure and according to the standard assumptions of cryptography. Furthermore, once the position of the prover is verified, our schemes establish secret keys in parallel and can be used for authentication and secret communication between the prover and verifiers.

The Quantum Car

“…1 Since then many works related to QLV have appeared in the literature, e.g. [8][9][10][11][12][13][14][15], largely focusing on information-theoretic security issues under different conditions. As I discuss more later, it is widely accepted that under known attacks, QLV is effectively secure.…”

Unconditionally secure commitment in position-based quantum cryptography

“…Let's label BSM results of C as classical 2N-bit string . This measurement of C projects the qubits in possession of A and B into Bell states instantly, unknown to everyone at the moment 33 .…”

“…Now if C applies randomly chosen operators {( σ z σ x ) 1 , ( σ z ) 2 , ( σ x ) 3 } on qubits received from A, then the entangled states shared between A and C will become , unknown to everyone now. If B and his agent C share randomly prepared entangled state and C gets BSM results then swapped entangled state between A and B will be , unknown to everyone 33 . Now in the revealing phase, if A announces exact Bell states (her committed bit 1) and C announces his applied unitary operators and BSM results, then B can get exact swapped state , and so the values of He then gets the verified state .…”

“…In this article, we present a commitment scheme based on position-verification and non-local quantum correlations, different from all previously proposed schemes in literature. Position-based quantum cryptography [22][23][24][25][26][27][28][29][30][31][32][33] has remained a conundrum for many years, but recently we proposed a quantum scheme for secure positioning 34 that can be useful in implementing other cryptographic tasks 35 . This strategy for studying cryptography uses teleportation 36 and entanglement swapping 37 in an interesting and new fashion.…”

“…33 . Now in the revealing phase, if A announces exact Bell states bit 1) and C announces his applied unitary operators and BSM results, then B can get exact swapped state…”