Towards-Unconditional-Uncloneable-Encryption

Associated Manuscript

This GitHub page is associated to the following manuscript:

• Manuscript: 📃 Towards Unconditional Uncloneable Encryption
• Authors: 👤 Pierre Botteron, 👤 Anne Broadbent, 👤 Eric Culf, 👤 Ion Nechita, 👤 Clément Pellegrini, and 👤 Denis Rochette.

Content

./
|__ conjecture/: Core of package. 
|  |-- `NPA1.m`: Matlab package of the npa hierarchy level 1 of Section 4.2 of the paper.
|  |-- `NPA2.m`: Matlab package of the npa hierarchy level 2 of Section 4.3 of the paper.
|  |-- `seesaw.nb`: Mathematica package of the seesaw method of Section 4.4 of the paper.
|-- `README.md`: This file.

No-Cloning Game for a 1-bit Message

Alice encrypts a uniformly random message $m \in \{0,1\}$ using key $k$, into a quantum state $\rho_{m,k}$. She transmits it to a Pirate modeled by a CPTP map $\Phi: \mathcal{B} ( \mathcal{H}_A ) \to \mathcal{B} ( \mathcal{H}_B \otimes \mathcal{H}_C )$. Bob and Charlie are then given the registers for $\mathcal{H}_{B}$ and $\mathcal{H}_C$, respectively, as well as a copy of $k$. They output $m_{B}$, $m_{C} \in \{0, 1\}$, respectively, and win if and only if $m = m_B = m_C$. Uncloneable-Indistinguishability holds if the winning probability is bounded by $1/2 + \text{negl}(\lambda)$ for $\lambda$ some security parameter.

Conjecture

Upper bounds on the winning probability in the no-cloning game involving three adversaries $(P, B, C)$ for our candidate scheme for Uncloneable Encryption with $K$ keys. The solid line (red) is the conjectured upper bound, the dashed line (cyan) corresponds to the upper bound derived from NPA level 1, the circles (teal) are the numerical upper bounds obtained from NPA level 2, and the square (black) is the numerical result obtained using the seesaw optimization method on $K=18$.

Reference

@misc{https://doi.org/10.48550/arxiv.2410.23064,
  doi = {10.48550/ARXIV.2410.23064},
  url = {https://arxiv.org/abs/2410.23064},
  author = {Botteron, Pierre and Broadbent, Anne and Culf, Eric and Nechita, Ion and Pellegrini, Clément and Rochette, Denis},
  title = {Towards Unconditional Uncloneable Encryption},
  publisher = {arXiv},
  year = {2024},
}