Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Homomorphic inference of deep neural networks for zero-knowledge verification of nuclear warheads

Gabriel V. Turturica, Violeta Iancu

Published May 8, 2023• 2 citations
Publisher

Abstract

Disarmament treaties have been the driving force towards reducing the large nuclear stockpile assembled during the Cold War. Further efforts are built around verification protocols capable of authenticating nuclear warheads while preventing the disclosure of confidential information. This type of problem falls under the scope of zero-knowledge protocols, which aim at multiple parties agreeing on a statement without conveying any information beyond the statement itself. A protocol capable of achieving all the authentication and security requirements is still not completely formulated. Here we propose a protocol that leverages the isotopic capabilities of NRF measurements and the classification abilities of neural networks. Two key elements guarantee the security of the protocol, the implementation of the template-based approach in the network's architecture and the use of homomorphic inference. Our results demonstrate the potential of developing zero-knowledge protocols for the verification of nuclear warheads using Siamese networks on encrypted spectral data.

DOI
10.1038/s41598-023-34679-7

Related papers

Nuclear disarmament verification via resonant phenomena

Jake J. Hecla, Areg Danagoulian

Nuclear disarmament treaties are not sufficient in and of themselves to neutralize the existential threat of the nuclear weapons. Technologies are necessary for verifying the authenticity of the nuclear warheads undergoing dismantlement before counting them toward a treaty partner's obligation. Here we present a concept that leverages isotope-specific nuclear resonance phenomena to authenticate a warhead's fissile components by comparing them to a previously authenticated template. All information is encrypted in the physical domain in a manner that amounts to a physical zero-knowledge proof system. Using Monte Carlo simulations, the system is shown to reveal no isotopic or geometric information about the weapon, while readily detecting hoaxing attempts. This nuclear technique can dramatically increase the reach and trustworthiness of future nuclear disarmament treaties.

arXiv:1709.09736•Nature Communications•Mar 28, 2018•27 citations

A Physical Zero-Knowledge Proof and Unclonable Sensors for Nuclear Warhead Verification

Sébastien Philippe

Future nuclear arms-control agreements may call for reductions of the total number of nuclear weapons and warheads in the world arsenals. Such agreements would require new trusted verification mechanisms to confirm that items presented to inspectors are nuclear warheads and not spoofs. Proliferation and national security concerns require, however, that inspectors gain no warhead design information through this process. To address this paradox, considerable efforts have been directed towards the development of "information barriers." These barriers consist of automated measurement systems that process sensitive information but only display the results of internal analysis in a binary valid/invalid manner. These systems are, by their nature, at risk of electronic tampering and snooping – and their trusted implementation has so far proved extremely difficult to realize. This thesis takes radically different directions to address this challenge. It demonstrates new approaches to information protection and trusted instruments for nuclear warhead verification that are based on the cryptographic concepts of zero-knowledge proofs and physically unclonable functions. To the author's knowledge, this thesis provides the first demonstration of a zero-knowledge physical measurement technique. Using fast neutron differential radiography and superheated emulsion detectors, such a technique can show two objects have identical geometry and opacity to 14-MeV neutrons without revealing what these properties are. This zero-knowledge feature no longer holds when the objects compared are significantly different. Such a technique could form the basis of a template-matching verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. The thesis then introduces and demonstrates key elements of an optical physical unclonable function sensitive to neutrons and based on superheated emulsions. Such sensors are unique objects that cannot be cloned or simulated. The data they produce are a function of both their internal disordered structure and the physical quantity they measure. Due to their sensitivity against any structural variation, including through neutron irradiation, it is possible to show that they – or the data they have recorded -- have not been tampered with. Such sensors could be used by adversarial parties in sensitive facilities without the risk of being compromised.

•Jan 1, 2018•1 citation

Zero Knowledge Proofs in Quantum Networks

Tuhin Paul, Srijani Das, Manasi Patra +1 more

Zero-knowledge proofs (ZKPs) enable the verification of a statement without revealing any information beyond its validity and constitute a fundamental primitive in cryptography and information theory. However, existing constructions rely on computational assumptions and are predominantly confined to bipartite settings, leaving their information-theoretic realization in bipartite or network scenarios largely unexplored. Here we develop a framework for zero-knowledge verification based on the indistinguishability of quantum states under operational constraints. Exploiting the fundamental limitations imposed by local operations, we show that a verifier is inherently restricted from extracting information about the underlying state while retaining the ability to verify correctness. We construct explicit protocols for multiparty quantum networks that achieve information-theoretic security, ensuring that no subset of collaborating parties can gain knowledge beyond the validity of the statement, independent of their joint computational power.

quant-pharXiv:2609.35339•Sep 29, 2026•0 citations

ZERO KNOWLEDGE PROTOCOL: CHALLENGES AND OPPORTUNITIES.

Peter Marleau, E. Brubaker, Nathan R. Hilton +4 more

Glaser, Barak, and Goldston recently described an approach for nuclear warhead verification based on the cryptographic concept of a zero-knowledge protocol (ZKP).The verification approach included both procedural elements and a physical implementation.A group of Sandia National Laboratories researchers, whose expertise include radiation instrumentation design and development, cryptography, and arms control verification implementation, jointly reviewed the paper and identified specific challenges to implementing the approach as well as some opportunities.This paper compares the ZKP concept as presented by Glaser et al., to other warhead verification concepts and approaches described in the literature.The paper also summarizes challenges and opportunities for elements of this (new) approach.We note that ZKP as used in cryptography is a useful model for the arms control verification problem, but find that the direct analogy to arms control breaks down quickly.For example, fault tolerance in cryptographic ZKP is achieved by brute force repetition of the challenge/response procedure; in arms control, repeated measurements can be expensive.The ZKP methodology fits within the general class of template-based verification techniques, where template in this case refers to a reference measurement that is used for comparison.Template methods in general confirm that a given object is like another object that has already been accepted as a warhead by some other means.This can be a powerful verification approach, but requires independent means to trust the authenticity of the reference warhead -a standard that may be difficult to achieve.Note that this use of template differs from that of Glaser et al., who use the term to describe the accepted reference warhead.In the ZKP approach as described, the reference warhead must be presentwith inspector confidence in its provenance-at each subsequent confirmation measurement.This imposes significant additional constraints on maintaining continuity of knowledge of the reference between inspections.Despite some technical challenges, the concept of last-minute selection of the pre-loads and equipment could be a valuable component of a verification regime.In addition, the neutron transmission image using a bubble detector array is an interesting idea that can be considered for template measurements independently of ZKP..

•Jun 1, 2015•0 citations

Reverse Delegated Training and Private Inference via Perfectly-Secure Quantum Homomorphic Encryption

Sergio A. Ortega, Miguel A. Martin-Delgado

Quantum machine learning in cloud environments requires protecting sensitive data while enabling remote computation. Here we demonstrate the first realistic implementations of a perfectly-secure quantum homomorphic encryption (QHE) scheme applied to quantum neural networks (QNN). Using efficient Clifford+$T$ decomposition, we implement quantum convolutional neural networks for two complementary scenarios: (i) reverse delegated training, where encrypted data from multiple providers trains a user's network via federated aggregation; (ii) private inference, where users process encrypted data with remote quantum networks. Moreover, analysis of server circuit privacy reveals probabilistic model protection through Pauli gate concealment. These results establish perfectly-secure QHE as a practical framework for multi-party quantum machine learning.

quant-pharXiv:2602.12712•Feb 16, 2026•0 citations

Zero knowledge proof for secure two-party computation with malicious adversaries in distributed networks

Xiaoyi Yang, Meijuan Huang

Distributed networks remarkably enhance the convenience of network connectivity. How to achieve efficient cooperative computation while preserving data privacy is a challenge in the scenario of distributed networks. Secure computation, as the key technology of information security and privacy protection in the distributed networks, attracts more and more attention. In the paper, we develop the protocols of secure two-party computation in the presence of malicious adversaries which are constructed with homomorphic probabilistic cryptosystem, and propose four honest-verifier zero-knowledge proof protocols to detect two cheating behaviours of the malicious adversary. The proposed protocols are more targeted than the existing work. The analysis shows that the proposed protocols are complete, sound and zero-knowledge. As an application, we show how to use our protocols in a secure two-party protocol to detect cheating, which can make it secure in the presence of malicious adversaries.

International Journal of Computational Science and Engineering•Jan 1, 2018•1 citation
Disarmament treaties have been the driving force towards reducing the large nuclear stockpile assembled during the Cold War. Further efforts are built around verification protocols capable of authenticating nuclear warheads while preventing the disclosure of confidential information. This type of problem falls under the scope of zero-knowledge protocols, which aim at multiple parties agreeing on a statement without conveying any information beyond the statement itself. A protocol capable of achieving all the authentication and security requirements is still not completely formulated. Here we propose a protocol that leverages the isotopic capabilities of NRF measurements and the classification abilities of neural networks. Two key elements guarantee the security of the protocol, the implementation of the template-based approach in the network's architecture and the use of homomorphic inference. Our results demonstrate the potential of developing zero-knowledge protocols for the verification of nuclear warheads using Siamese networks on encrypted spectral data.
Nuclear disarmament treaties are not sufficient in and of themselves to neutralize the existential threat of the nuclear weapons. Technologies are necessary for verifying the authenticity of the nuclear warheads undergoing dismantlement before counting them toward a treaty partner's obligation. Here we present a concept that leverages isotope-specific nuclear resonance phenomena to authenticate a warhead's fissile components by comparing them to a previously authenticated template. All information is encrypted in the physical domain in a manner that amounts to a physical zero-knowledge proof system. Using Monte Carlo simulations, the system is shown to reveal no isotopic or geometric information about the weapon, while readily detecting hoaxing attempts. This nuclear technique can dramatically increase the reach and trustworthiness of future nuclear disarmament treaties.
Future nuclear arms-control agreements may call for reductions of the total number of nuclear weapons and warheads in the world arsenals. Such agreements would require new trusted verification mechanisms to confirm that items presented to inspectors are nuclear warheads and not spoofs. Proliferation and national security concerns require, however, that inspectors gain no warhead design information through this process. To address this paradox, considerable efforts have been directed towards the development of "information barriers." These barriers consist of automated measurement systems that process sensitive information but only display the results of internal analysis in a binary valid/invalid manner. These systems are, by their nature, at risk of electronic tampering and snooping – and their trusted implementation has so far proved extremely difficult to realize. This thesis takes radically different directions to address this challenge. It demonstrates new approaches to information protection and trusted instruments for nuclear warhead verification that are based on the cryptographic concepts of zero-knowledge proofs and physically unclonable functions. To the author's knowledge, this thesis provides the first demonstration of a zero-knowledge physical measurement technique. Using fast neutron differential radiography and superheated emulsion detectors, such a technique can show two objects have identical geometry and opacity to 14-MeV neutrons without revealing what these properties are. This zero-knowledge feature no longer holds when the objects compared are significantly different. Such a technique could form the basis of a template-matching verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. The thesis then introduces and demonstrates key elements of an optical physical unclonable function sensitive to neutrons and based on superheated emulsions. Such sensors are unique objects that cannot be cloned or simulated. The data they produce are a function of both their internal disordered structure and the physical quantity they measure. Due to their sensitivity against any structural variation, including through neutron irradiation, it is possible to show that they – or the data they have recorded -- have not been tampered with. Such sensors could be used by adversarial parties in sensitive facilities without the risk of being compromised.
Zero-knowledge proofs (ZKPs) enable the verification of a statement without revealing any information beyond its validity and constitute a fundamental primitive in cryptography and information theory. However, existing constructions rely on computational assumptions and are predominantly confined to bipartite settings, leaving their information-theoretic realization in bipartite or network scenarios largely unexplored. Here we develop a framework for zero-knowledge verification based on the indistinguishability of quantum states under operational constraints. Exploiting the fundamental limitations imposed by local operations, we show that a verifier is inherently restricted from extracting information about the underlying state while retaining the ability to verify correctness. We construct explicit protocols for multiparty quantum networks that achieve information-theoretic security, ensuring that no subset of collaborating parties can gain knowledge beyond the validity of the statement, independent of their joint computational power.
Glaser, Barak, and Goldston recently described an approach for nuclear warhead verification based on the cryptographic concept of a zero-knowledge protocol (ZKP).The verification approach included both procedural elements and a physical implementation.A group of Sandia National Laboratories researchers, whose expertise include radiation instrumentation design and development, cryptography, and arms control verification implementation, jointly reviewed the paper and identified specific challenges to implementing the approach as well as some opportunities.This paper compares the ZKP concept as presented by Glaser et al., to other warhead verification concepts and approaches described in the literature.The paper also summarizes challenges and opportunities for elements of this (new) approach.We note that ZKP as used in cryptography is a useful model for the arms control verification problem, but find that the direct analogy to arms control breaks down quickly.For example, fault tolerance in cryptographic ZKP is achieved by brute force repetition of the challenge/response procedure; in arms control, repeated measurements can be expensive.The ZKP methodology fits within the general class of template-based verification techniques, where template in this case refers to a reference measurement that is used for comparison.Template methods in general confirm that a given object is like another object that has already been accepted as a warhead by some other means.This can be a powerful verification approach, but requires independent means to trust the authenticity of the reference warhead -a standard that may be difficult to achieve.Note that this use of template differs from that of Glaser et al., who use the term to describe the accepted reference warhead.In the ZKP approach as described, the reference warhead must be presentwith inspector confidence in its provenance-at each subsequent confirmation measurement.This imposes significant additional constraints on maintaining continuity of knowledge of the reference between inspections.Despite some technical challenges, the concept of last-minute selection of the pre-loads and equipment could be a valuable component of a verification regime.In addition, the neutron transmission image using a bubble detector array is an interesting idea that can be considered for template measurements independently of ZKP..
Quantum machine learning in cloud environments requires protecting sensitive data while enabling remote computation. Here we demonstrate the first realistic implementations of a perfectly-secure quantum homomorphic encryption (QHE) scheme applied to quantum neural networks (QNN). Using efficient Clifford+TTT decomposition, we implement quantum convolutional neural networks for two complementary scenarios: (i) reverse delegated training, where encrypted data from multiple providers trains a user's network via federated aggregation; (ii) private inference, where users process encrypted data with remote quantum networks. Moreover, analysis of server circuit privacy reveals probabilistic model protection through Pauli gate concealment. These results establish perfectly-secure QHE as a practical framework for multi-party quantum machine learning.
Distributed networks remarkably enhance the convenience of network connectivity. How to achieve efficient cooperative computation while preserving data privacy is a challenge in the scenario of distributed networks. Secure computation, as the key technology of information security and privacy protection in the distributed networks, attracts more and more attention. In the paper, we develop the protocols of secure two-party computation in the presence of malicious adversaries which are constructed with homomorphic probabilistic cryptosystem, and propose four honest-verifier zero-knowledge proof protocols to detect two cheating behaviours of the malicious adversary. The proposed protocols are more targeted than the existing work. The analysis shows that the proposed protocols are complete, sound and zero-knowledge. As an application, we show how to use our protocols in a secure two-party protocol to detect cheating, which can make it secure in the presence of malicious adversaries.