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

NATO science for peace and security series. D, Information and communication security

Beyond Quantum Threats: Bridging Fully Homomorphic Encryption Schemes

Mugurel Barcau, George Gugulea, Cristian Lupaşcu, Vicenţiu Pașol, Mihai Togan, George Cătălin Ţurcaş

Published Feb 19, 2024• 2 citations
Publisher

Abstract

In the advent of quantum computing, fully homomorphic encryption (FHE), whose security is based on the hardness of lattice problems, gains significant importance due to its quantum-resistant nature. This work provides a comprehensive survey of recent advancements in bridges between FHE schemes, with an emphasis on practical applications.
DOI
10.3233/nicsp240012

Related papers

Analysis of quantum fully homomorphic encryption schemes (QFHE) and hierarchial memory management for QFHE

Shreya Girish Savadatti, Aswani Kumar Cherukuri, Annapurna Jonnalagadda +1 more

Homomorphic encryption is a recent and fundamental breakthrough in modern cryptography, which allows the performance of operations on encrypted data without unveiling the data. Leveraging quantum mechanics principles, quantum computers can potentially solve certain computational problems exponentially faster than classical computers. This immense computational power offers new possibilities for various fields, including cryptography. The rapid evolution of both these fields has led to the development of quantum fully homomorphic encryption (QFHE), which makes the capabilities of classical HE extend into the quantum domain. However, many existing QFHE schemes require significant memory due to complex calculations and fault-tolerance needs. This paper contributes in two ways. First, we provide a comprehensive survey of two specific QFHE schemes, discussing their underlying principles, mathematical frameworks, security aspects, and practical applications. We also explore the challenges posed by quantum computing and how QFHE addresses these to achieve both security and computational efficiency. Second, we propose a new hierarchical memory management system for QFHE, which includes a “quantum cache” (a specialized memory storage for quantum data) and a “reinforcement learning agent” (an intelligent system that learns from experience to optimize decisions). This system dynamically manages data movement between the cache and classical memory, improving memory efficiency and potentially boosting computational performance.

Complex & Intelligent Systems•Apr 23, 2025•12 citations

Lattice-based FHE as secure as PKE

Zvika Brakerski, Vinod Vaikuntanathan

We show that (leveled) fully homomorphic encryption (FHE) can be based on the hardness of O(n1.5+ε)-approximation for lattice problems (such as GapSVP) under quantum reductions for any ε 〉 0 (or O(n2+ε)-approximation under classical reductions). This matches the best known hardness for "regular" (non-homomorphic) lattice based public-key encryption up to the ε factor. A number of previous methods had hit a roadblock at quasipolynomial approximation. (As usual, a circular security assumption can be used to achieve a non-leveled FHE scheme.)

Conference on Innovations in Theoretical Computer Science•Jan 12, 2014•272 citations

Investigations of Fully Homomorphic Encryption (IFHE)

Nigel Paul Smart

Abstract : The IFHE project Investigation of Fully Homomorphic Encryption) originally set out to examine the security of FHE schemes, and the lattice hard problems on which they are based. This turned out to be relatively difficult, mainly due to the complexity of building software libraries which could support the advanced mathematics needed to perform experiments on modern multi-core processors. For example the NTL library is now (2015) able to support multi - threaded applications, but only if used with bleeding edge compilers on the latest Intel hardware. Thus the initial plan was perhaps a little ahead of its time. However, by leveraging additional sources of funding; most notably from the UKs EPSRC and the EUs ERC, the Bristol team was able to make substantial headway in other areas related to the PROCEED program which were not originally envisaged. These are centred around; General techniques for Fully Homomorphic Encryption Practical methods for actively secure Multi -Party Computation General theory behind Multi -Party Computation. This report documents the progress made by the Bristol team.

•May 1, 2015•2 citations

A Research on the Application Comparison of NTRU in Typical Fully Homomorphic Encryption Scheme

Xu Zhao, Zheng Yuan

Fully homomorphic encryption (FHE) allows arbitrary computations to be performed directly on encrypted data and is a core technology for privacy computing and secure cloud computing. The Number Theory Research Unit (NTRU) has become a research topic in this field by virtue of its lattice-based anti-quantum security, efficient polynomial operation characteristics and natural multi-key homomorphism capability. In this paper, we systematically review the key advances of NTRU-based FHE, covering the directions of the design of FHE, the optimization of bootstrapping techniques, and the application to FHE for multi-key approaches. Furthermore, the innovativeness and practical application challenges of the schemes are analyzed, and the future research trends are envisioned.

International Symposium on AI and Cybersecurity (ISAICS)•Oct 24, 2025•0 citations

A Comprehensive Survey on Lattice-based Cryptography and Homomorphic Encryption

Wenjie He, Jing Wang, Yuan Gao

With the popularization of cloud computing model, the outsourcing of data storage and computing services has become an indispensable trend, which lead to the related data security and privacy protection issues that have attracted extensive attention in the industry. Fully homomorphic encryption, as an encryption technology that can process ciphertext information without exposing plaintext information, has natural user data security and privacy protection characteristics. Meanwhile, the excellent quantum-resistant performance and homomorphic properties of lattice ciphers have made lattice-based homomorphic encryption schemes a much-attend research hotspot in the field of cryptography in recent years. In this paper we mainly introduce the status of all-pass encryption and several typical references for the research of lattice-based all-homomorphic cryptography.

International Academic Exchange Conference on Science and Technology Innovation (IAECST)•Dec 8, 2023•1 citation

Lattice-Based FHE as Secure as PKE.

Zvika Brakerski, Vinod Vaikuntanathan

We show that (leveled) fully homomorphic encryption (FHE) can be based on the hardness of Õ(n1.5+ɛ)-approximation for lattice problems (such as GapSVP) under quantum reductions for any ɛ> 0 (or Õ(n2+ɛ)-approximation under classical reductions). This matches the best known hardness for “regular ” (non-homomorphic) lattice based public-key encryption up to the ɛ factor. A number of previous methods had hit a roadblock at quasipolynomial approximation. (As usual, a circular security assumption can be used to achieve a non-leveled FHE scheme.) Our approach consists of three main ideas: Noise-bounded sequential evaluation of high fan-in operations; Circuit sequentialization using Barrington’s Theorem; and finally, successive dimension-modulus reduction.

Other repository•Jan 1, 2013•3 citations
Homomorphic encryption is a recent and fundamental breakthrough in modern cryptography, which allows the performance of operations on encrypted data without unveiling the data. Leveraging quantum mechanics principles, quantum computers can potentially solve certain computational problems exponentially faster than classical computers. This immense computational power offers new possibilities for various fields, including cryptography. The rapid evolution of both these fields has led to the development of quantum fully homomorphic encryption (QFHE), which makes the capabilities of classical HE extend into the quantum domain. However, many existing QFHE schemes require significant memory due to complex calculations and fault-tolerance needs. This paper contributes in two ways. First, we provide a comprehensive survey of two specific QFHE schemes, discussing their underlying principles, mathematical frameworks, security aspects, and practical applications. We also explore the challenges posed by quantum computing and how QFHE addresses these to achieve both security and computational efficiency. Second, we propose a new hierarchical memory management system for QFHE, which includes a “quantum cache” (a specialized memory storage for quantum data) and a “reinforcement learning agent” (an intelligent system that learns from experience to optimize decisions). This system dynamically manages data movement between the cache and classical memory, improving memory efficiency and potentially boosting computational performance.
We show that (leveled) fully homomorphic encryption (FHE) can be based on the hardness of O(n1.5+ε)-approximation for lattice problems (such as GapSVP) under quantum reductions for any ε 〉 0 (or O(n2+ε)-approximation under classical reductions). This matches the best known hardness for "regular" (non-homomorphic) lattice based public-key encryption up to the ε factor. A number of previous methods had hit a roadblock at quasipolynomial approximation. (As usual, a circular security assumption can be used to achieve a non-leveled FHE scheme.)
Abstract : The IFHE project Investigation of Fully Homomorphic Encryption) originally set out to examine the security of FHE schemes, and the lattice hard problems on which they are based. This turned out to be relatively difficult, mainly due to the complexity of building software libraries which could support the advanced mathematics needed to perform experiments on modern multi-core processors. For example the NTL library is now (2015) able to support multi - threaded applications, but only if used with bleeding edge compilers on the latest Intel hardware. Thus the initial plan was perhaps a little ahead of its time. However, by leveraging additional sources of funding; most notably from the UKs EPSRC and the EUs ERC, the Bristol team was able to make substantial headway in other areas related to the PROCEED program which were not originally envisaged. These are centred around; General techniques for Fully Homomorphic Encryption Practical methods for actively secure Multi -Party Computation General theory behind Multi -Party Computation. This report documents the progress made by the Bristol team.
Fully homomorphic encryption (FHE) allows arbitrary computations to be performed directly on encrypted data and is a core technology for privacy computing and secure cloud computing. The Number Theory Research Unit (NTRU) has become a research topic in this field by virtue of its lattice-based anti-quantum security, efficient polynomial operation characteristics and natural multi-key homomorphism capability. In this paper, we systematically review the key advances of NTRU-based FHE, covering the directions of the design of FHE, the optimization of bootstrapping techniques, and the application to FHE for multi-key approaches. Furthermore, the innovativeness and practical application challenges of the schemes are analyzed, and the future research trends are envisioned.
With the popularization of cloud computing model, the outsourcing of data storage and computing services has become an indispensable trend, which lead to the related data security and privacy protection issues that have attracted extensive attention in the industry. Fully homomorphic encryption, as an encryption technology that can process ciphertext information without exposing plaintext information, has natural user data security and privacy protection characteristics. Meanwhile, the excellent quantum-resistant performance and homomorphic properties of lattice ciphers have made lattice-based homomorphic encryption schemes a much-attend research hotspot in the field of cryptography in recent years. In this paper we mainly introduce the status of all-pass encryption and several typical references for the research of lattice-based all-homomorphic cryptography.
We show that (leveled) fully homomorphic encryption (FHE) can be based on the hardness of Õ(n1.5+ɛ)-approximation for lattice problems (such as GapSVP) under quantum reductions for any ɛ> 0 (or Õ(n2+ɛ)-approximation under classical reductions). This matches the best known hardness for “regular ” (non-homomorphic) lattice based public-key encryption up to the ɛ factor. A number of previous methods had hit a roadblock at quasipolynomial approximation. (As usual, a circular security assumption can be used to achieve a non-leveled FHE scheme.) Our approach consists of three main ideas: Noise-bounded sequential evaluation of high fan-in operations; Circuit sequentialization using Barrington’s Theorem; and finally, successive dimension-modulus reduction.