Quantum Privacy-Preserving Price E-Negotiation

TL;DR

The paper addresses privacy-preserving price e-negotiation (3PEN) by introducing Q3PEN, a quantum protocol that uses oracle operations, a qubit comparator, and quantum counting to compare prices and count qualifying products. It provides rigorous correctness guarantees (Theorem 1) and privacy protections for both participants, leveraging Holevo bounds and a quantum bit-string commitment (KQ03). The protocol achieves significantly reduced communication complexity, scaling as $O(\log N)$ compared with classical $O(N)$ schemes, and a framework is described for extending to multi-party scenarios. Overall, Q3PEN offers a secure, efficient quantum approach to private e-negotiation in electronic commerce with provable security properties and scalability.

Abstract

Privacy-preserving price e-negotiation (3PEN) is an important topic of secure multi-party computation (SMC) in the electronic commerce field, and the key point of its security is to guarantee the privacy of seller's and buyer's prices. In this study, a novel and efficient quantum solution to the 3PEN problem is proposed, where the oracle operation and the qubit comparator are utilized to obtain the comparative results of buyer's and seller's prices, and then quantum counting is executed to summarize the total number of products which meets the trading conditions. Analysis shows that our solution not only guarantees the correctness and the privacy of 3PEN, but also has lower communication complexity than those classical ones.

Figures (6)

• Figure 1: The six-step procedure of Q3PEN protocol.
• Figure 2: The oracle operation Alice or Bob applied on the initial state $\frac{1}{{\sqrt N }}\sum\limits_{i = 1}^{N} {\left| i \right\rangle \otimes {{\left| 0 \right\rangle }^{ \otimes d}}}$. Here $n = \left\lceil {\log (N + 1)} \right\rceil$.
• Figure 3: The circuit of the oracle operation applied on state $\frac{1}{{\sqrt N }}\sum\limits_{i = 1}^{N} {\left| i\right\rangle \left| {{a_i}} \right\rangle \left| {{b_i}} \right\rangle \otimes \left| 0 \right\rangle }$.
• Figure 4: The circuit of one-qubit comparator comparing two qubits. Here, $\times$ is the NOT gate, and $\bullet$ in the Toffloi gate denotes the negative-control qubit conditional being set to one, while $\oplus$ represents the target qubit.
• Figure 5: The circuit of multi-qubit comparator comparing ${a_i}$ and ${b_i}$. ${U_c}$ is the one-qubit comparator described in Fig. 3, and $\circ$ denotes the positive-control qubit conditional being set to zero.