Semantic Security with Infinite Dimensional Quantum Eavesdropping Channel

Abstract

We propose a new proof method for direct coding theorems for wiretap channels where the eavesdropper has access to a quantum version of the transmitted signal on an infinite-dimensional Hilbert space and the legitimate parties communicate through a classical channel or a classical input, quantum output (cq) channel. The transmitter input can be subject to an additive cost constraint, which specializes to the case of an average energy constraint. This method yields errors that decay exponentially with increasing block lengths. Moreover, it provides a guarantee of a quantum version of semantic security, which is an established concept in classical cryptography and physical layer security. Therefore, it complements existing works which either do not prove the exponential error decay or use weaker notions of security. The main part of this proof method is a direct coding result on channel resolvability which states that there is only a doubly exponentially small probability that a standard random codebook does not solve the channel resolvability problem for the cq channel. Semantic security has strong operational implications meaning essentially that the eavesdropper cannot use its quantum observation to gather any meaningful information about the transmitted signal. We also discuss the connections between semantic security and various other established notions of secrecy.

References in corpus (15)

• Rényi Divergence and Kullback-Leibler Divergence
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Noisy channel coding via privacy amplification and information reconciliation
• Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
• Energy-constrained private and quantum capacities of quantum channels
• Quantum trade-off coding for bosonic communication
• Position-based coding and convex splitting for private communication over quantum channels
• Quantum wiretap channel with non-uniform random number and its exponent and equivocation rate of leaked information
• Entropic characteristics of subsets of states
• Public and private resource trade-offs for a quantum channel
• Quantum Keyless Privacy vs. Quantum Key Distribution for Space Links
• Capacities of Quantum Amplifier Channels
• Semantic Security for Quantum Wiretap Channels
• Non-additivity in classical-quantum wiretap channels
• Noisy Feedback and Loss Unlimited Private Communication