Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Breaking barriers in two-party quantum cryptography via stochastic semidefinite programming

Akshay Bansal, Jamie Sikora

TL;DR

This work addresses the inherent security gaps in two-party quantum cryptography by introducing a stochastic switching framework based on stochastic semidefinite programming, enabling protocols to randomly switch among tasks such as bit commitment, oblivious transfer, and weak coin flipping. By formulating cheating strategies as SDPs across multiple scenarios, the authors demonstrate both breadth (switching among different primitives) and depth (switching between variants of Rabin oblivious transfer) with concrete bounds showing improved average security, e.g., reduced Alice-cheating probabilities while preserving Bob’s bounds in several switches. They present the first quantum protocol for Rabin oblivious transfer via switching, and quantify cheating probabilities for various switch configurations, highlighting cases where switching yields improvements and cases where it does not or even harms security. The approach provides a flexible, solver-friendly methodology to design and analyze quantum cryptographic primitives, offering a pathway to more robust primitives in quantum networks even as it reveals intrinsic limitations and potential vulnerabilities. Overall, the stochastic-switching framework advances the understanding of how randomized task selection within a protocol can mitigate cheating advantages and broaden the repertoire of feasible quantum cryptographic constructions.

Abstract

In the last two decades, there has been much effort in finding secure protocols for two-party cryptographic tasks. It has since been discovered that even with quantum mechanics, many such protocols are limited in their security promises. In this work, we use stochastic selection, an idea from stochastic programming, to circumvent such limitations. For example, we find a way to switch between bit commitment, weak coin flipping, and oblivious transfer protocols to improve their security. We also use stochastic selection to turn trash into treasure yielding the first quantum protocol for Rabin oblivious transfer.

Breaking barriers in two-party quantum cryptography via stochastic semidefinite programming

TL;DR

This work addresses the inherent security gaps in two-party quantum cryptography by introducing a stochastic switching framework based on stochastic semidefinite programming, enabling protocols to randomly switch among tasks such as bit commitment, oblivious transfer, and weak coin flipping. By formulating cheating strategies as SDPs across multiple scenarios, the authors demonstrate both breadth (switching among different primitives) and depth (switching between variants of Rabin oblivious transfer) with concrete bounds showing improved average security, e.g., reduced Alice-cheating probabilities while preserving Bob’s bounds in several switches. They present the first quantum protocol for Rabin oblivious transfer via switching, and quantify cheating probabilities for various switch configurations, highlighting cases where switching yields improvements and cases where it does not or even harms security. The approach provides a flexible, solver-friendly methodology to design and analyze quantum cryptographic primitives, offering a pathway to more robust primitives in quantum networks even as it reveals intrinsic limitations and potential vulnerabilities. Overall, the stochastic-switching framework advances the understanding of how randomized task selection within a protocol can mitigate cheating advantages and broaden the repertoire of feasible quantum cryptographic constructions.

Abstract

In the last two decades, there has been much effort in finding secure protocols for two-party cryptographic tasks. It has since been discovered that even with quantum mechanics, many such protocols are limited in their security promises. In this work, we use stochastic selection, an idea from stochastic programming, to circumvent such limitations. For example, we find a way to switch between bit commitment, weak coin flipping, and oblivious transfer protocols to improve their security. We also use stochastic selection to turn trash into treasure yielding the first quantum protocol for Rabin oblivious transfer.
Paper Structure (55 sections, 5 theorems, 71 equations, 2 figures)

This paper contains 55 sections, 5 theorems, 71 equations, 2 figures.

Table of Contents

  1. Introduction
  2. A brief history of two-party cryptography
  3. Oblivious transfer.
  4. Bit commitment.
  5. Weak coin flipping.
  6. Strong coin flipping and die rolling.
  7. Our stochastic switching framework
  8. Is this a realistic setting?
  9. A familiar example where the stochastic switch is useful.
  10. Why would this improve security, and does it always?
  11. Modeling cheating Alice and cheating Bob.
  12. Where does this idea come from?
  13. Our results
  14. Breadth.
  15. Depth.
  16. ...and 40 more sections

Key Result

Theorem 1.1

There exists a simple protocol which performs bit commitment or oblivious transfer with There exists a simple protocol which performs bit commitment or weak coin flipping with There exists a simple protocol which performs weak coin flipping or oblivious transfer with There exists a simple protocol which performs bit commitment or weak coin flipping or oblivious transfer with

Figures (2)

  • Figure 1: Let $S_j$ denote the set of optimal first messages Alice could send in $\mathrm{Task}_j$. Then if two sets are disjoint, Alice would have to hedge her cheating attempts if Bob switches between those two tasks (e.g., $\mathrm{Task}_1$ and $\mathrm{Task}_2$). If the two sets have a nonempty intersection, Alice would have no difficulty cheating if Bob switches between those two tasks (e.g., $\mathrm{Task}_3$ and $\mathrm{Task}_4$).
  • Figure 2: A schematic of our Rabin oblivious transfer protocol. Bob can either decide to continue with the now-in-progress Protocol \ref{['protocol:ROT:measure']} or test and restart Protocol \ref{['protocol:ROT:measure']} from the beginning.

Theorems & Definitions (5)

  • Theorem 1.1: Switching between different protocols, informal
  • Theorem 1.2: A quantum protocol for Rabin oblivious transfer, informal
  • Theorem 1.3: A quantum protocol for an alternative Rabin oblivious transfer, informal
  • Lemma 1.4: A protocol in which the stochastic switch does not help, informal
  • Lemma 1.5: A protocol in which the stochastic switch hurts the overall security, informal