New Quantum Protocol Lets Secret Calculations Survive Cheating Participants

Quantum cryptography has long promised a future in which sensitive computations can be carried out collectively without any single party learning the others’ secrets. A new study published in Quantum Information Processing pushes that promise further by tackling one of the field’s most stubborn practical problems: what happens when the group of participants changes mid-computation, and what happens when a participant who has just been expelled decides to sabotage the result. Researchers Fulin Li, Rongpei Li, Yixin Sun and Shixin Zhu of the School of Mathematics at Hefei University of Technology have designed a verifiable, dynamic quantum secure multi-party multiplication protocol built on homomorphic encryption, and their security analysis suggests it can withstand precisely the attacks that exploit this vulnerable transition period.

Secure multi-party computation is a branch of cryptography in which several parties jointly compute a function over their private inputs without revealing those inputs to one another. In the quantum version of this problem, quantum states and quantum operations supplement or replace classical techniques to provide security guarantees rooted in the laws of physics rather than in assumptions about computational hardness. Multiplication is a particularly important target operation: once parties can multiply their secret values securely, they can build a wide range of more elaborate privacy-preserving applications, from secure auctions and electronic voting to privacy-preserving machine learning and distributed statistical analysis. The new protocol addresses multiplication directly, allowing multiple participants to combine their secret inputs into a shared product while keeping every individual input hidden.

The central technical innovation lies in the protocol’s use of the multiplicative homomorphic property of the RSA encryption algorithm. Homomorphic encryption allows arithmetic to be performed directly on encrypted data: a party can encrypt a value, and the structure of the encryption ensures that combining ciphertexts corresponds to combining the underlying plaintexts. In the multiplicative case, the product of two ciphertexts decrypts to the product of the two plaintexts. This property means participants can contribute encrypted shares of their secrets, the encrypted shares can be multiplied together, and only the final decrypted result reveals anything about the combined product—never the individual contributions. By anchoring the protocol in RSA’s well-understood multiplicative homomorphism, the authors inherit a mature cryptographic foundation while layering quantum techniques on top for input protection and verification.

What distinguishes this work from earlier quantum secure multiplication protocols is its verifiability. In many existing schemes, participants simply have to trust that the final result is correct. If a malicious participant injects a corrupted share, or if noise and error creep into the process, the output may be silently wrong. The new protocol allows every participant to check the integrity of the final computation result and to detect any error affecting correctness, whether that error was introduced intentionally by a cheater or unintentionally by some failure in the process. Verification transforms the protocol from a trust-based arrangement into an auditable one, which is essential for any realistic deployment involving parties who may have conflicting interests.

The dynamic aspect of the protocol is equally significant. Real-world collaborations are rarely static: organizations join consortiums, employees leave companies, and partners withdraw from joint ventures. A secure multi-party protocol that must be restarted from scratch every time the participant list changes would be impractically rigid. The new scheme supports dynamic updates, meaning participants can be added or removed while the computation’s security guarantees are preserved. This flexibility, however, creates a dangerous loophole that the authors explicitly confront: a participant who is being revoked has a clear incentive to cheat during the update process, corrupting the computation on the way out. The protocol’s verification mechanism is specifically designed to detect deceptive behavior by revoked participants during these dynamic updates, closing an attack window that earlier dynamic protocols left open.

The authors describe this threat as a dishonest revocation attack, and their security analysis demonstrates that the protocol resists it alongside a series of other typical external and internal attacks. External attacks, in the quantum setting, include eavesdropping attempts in which an outsider tries to extract information from the quantum states exchanged between honest participants; the protocol’s quantum components are designed so that such interference leaves detectable traces. Internal attacks are subtler and often more damaging, since they come from participants who hold legitimate credentials but choose to deviate from the protocol to learn others’ inputs or to bias the result. By combining homomorphic encryption with verification checks, the protocol ensures that neither class of adversary can compromise either the privacy of the inputs or the correctness of the product without being caught.

Efficiency matters as much as security in this domain, because quantum protocols can impose heavy computational and communication burdens. The authors report that their scheme achieves relatively low computational costs compared with existing multiplication protocols, making it a more practical candidate for real applications. The reliance on classical RSA homomorphic operations for the arithmetic core, rather than on expensive quantum computations for every step, helps keep the overhead manageable, while quantum resources are deployed where they add the most security value. The result, the authors argue, is a protocol that offers enhanced practicality and meaningful security guarantees at a computational price that realistic deployments could afford.

The work builds on a substantial body of prior research in quantum secure multi-party computation. Earlier protocols have addressed secure summation using single photons, quantum Fourier transforms, Grover’s search algorithm and mutually unbiased bases, and secure multiplication has been explored through secret sharing and hybrid quantum-classical approaches. Previous work by members of the same team introduced a (k, n)-threshold dynamic quantum secure multiparty multiplication protocol and a verifiable threshold quantum secure multiparty summation protocol, and the present study extends that lineage by adding verifiable result integrity to the dynamic multiplication setting through homomorphic encryption. The broader field also draws on foundational results in quantum state determination, secret sharing with d-level systems, and analyses of practical attacks such as Trojan-horse attacks on quantum communication systems, all of which inform the threat model the new protocol is designed to survive.

The implications extend beyond the immediate technical contribution. As quantum computers edge closer to threatening classical public-key cryptography, and as organizations increasingly need to compute jointly over sensitive data—financial positions, medical records, proprietary models—protocols that combine quantum security with classical efficiency are likely to attract growing attention. A verifiable, dynamic multiplication protocol offers a building block for such systems: it demonstrates that participant churn need not be a security liability, and that even a departing adversary with every reason to cheat can be prevented from corrupting a shared computation. The research was supported by the National Natural Science Foundation of China, and the authors declare no conflict of interest. While laboratory-scale quantum networks and practical homomorphic quantum deployments remain works in progress, this protocol represents a concrete step toward secure multi-party computation that is simultaneously quantum-resistant in its guarantees, flexible in its membership, and honest in its arithmetic.

Subject of Research: A verifiable dynamic quantum secure multi-party multiplication protocol based on RSA homomorphic encryption that resists cheating by revoked participants.

Article Title: Verifiable dynamic quantum secure multi-party multiplication protocol based on homomorphic encryption

Article References: Li, F., Li, R., Sun, Y., & Zhu, S. (2026). Verifiable dynamic quantum secure multi-party multiplication protocol based on homomorphic encryption. Quantum Information Processing, 25(10), Article 317. https://doi.org/10.1007/s11128-026-05347-2

Image Credits: AI Generated

DOI: 10.1007/s11128-026-05347-2

Keywords: quantum cryptography, secure multi-party computation, homomorphic encryption, RSA, verifiability, dynamic protocols, multiplication protocol, dishonest revocation attack, quantum information, privacy-preserving computation, Quantum Information Processing, Hefei University of Technology