Practical Unclonable Encryption with Continuous Variables

TL;DR

The paper introduces the first continuous-variable unclonable encryption scheme, extending the quantum encryption of classical messages to CV systems by encoding a classical codeword into squeezed coherent states whose squeezing directions serve as the secret key. A rigorous security analysis connects the cloning game to a CV monogamy-of-entanglement game, yielding an explicit bound that ensures exponentially small success probability for adversaries. The authors also address practical viability by analyzing squeezing levels and channel imperfections, showing robustness under realistic noise and loss. This work advances practical quantum cryptography by enabling unclonable encryption within existing optical infrastructure and provides a foundation for future CV-based unclonable primitives.

Abstract

We propose the first continuous-variable (CV) unclonable encryption scheme, extending the paradigm of quantum encryption of classical messages (QECM) to CV systems. In our construction, a classical message is first encrypted classically and then encoded using an errorcorrecting code. Each bit of the codeword is mapped to a CV mode by creating a coherent state which is squeezed in the q or p quadrature direction, with a small displacement that encodes the bit. The squeezing directions are part of the encryption key. We prove unclonability in the framework introduced by Broadbent and Lord, via a reduction of the cloning game to a CV monogamy-of-entanglement game. Furthermore, we demonstrate that our scheme can be readily implemented with current technology. By incorporating realistic imperfections such as channel noise and detector inefficiencies, we show that the protocol remains robust under these conditions.

Figures (4)

• Figure 1: Schematic representation of the unclonable encryption game.
• Figure 2: We plot (\ref{['allowedasymp']}) as a function of the squeezing $r$ and displacement $\alpha$. As illustrated, asymptotically the scheme is secure only for $r>3.5$ for some values of $\alpha$.
• Figure 3: Bit error rate (\ref{['eq:ber_noisy']}) for different parameters (channel parameters in SNU).
• Figure 4: Winning probabilities in the unclonability game for various schemes. The ideal curve is the simple guessing probability $\left(\frac{1}{2}\right)^n$. The wining probability of the conjugate coding scheme is at most $\left(\frac{1}{2} + \frac{1}{2\sqrt{2}}\right)^n$. For our CV scheme we plotted $2^{-n+\tau(\lambda)}$ (\ref{['result']}) with parameters $r=3.6, \alpha=0.4$ and allow bit flips $t=3.5\%$ of ciphertext size.

Theorems & Definitions (12)

• Definition 2.1
• Definition 2.2: Cloning attack
• Definition 2.3
• Lemma 2.5
• Theorem 3.1
• proof
• Lemma 4.2
• proof
• Lemma 4.3
• proof