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Bootstrapping Optimization Techniques for the FINAL Fully Homomorphic Encryption Scheme

INFORMATION 2025年第3期16卷 200-200页

作者： Wu, Meng Zhao, Xiufeng Song, Weitao Informat Engn Univ Coll Cryptog Engn Zhengzhou 450001 Peoples R China

With the advent of cloud computing and the era of big data, there is an increasing focus on privacy computing. Consequently, homomorphic encryption, being a primary technique for achieving privacy computing, is held in high regard. Nevertheless, the efficiency of homomorphic encryption schemes is significantly impacted by bootstrapping. Enhancing the efficiency of bootstrapping necessitates a dual focus: reducing the computational burden of outer product operations integral to the process while rigorously constraining the noise generated by bootstrapping within predefined threshold limits. The FINAL scheme is a fully homomorphic encryption scheme based on the number theory research unit (NTRU) and learning with errors (LWE) assumptions. The performance of the FINAL scheme is better than that of the TFHE scheme, with faster bootstrapping and smaller bootstrapping and key-switching keys. In this paper, we introduce ellipsoidal Gaussian sampling to generate keys f and g in the bootstrapping of the FINAL scheme, so that the standard deviations of keys f and g are different and reduce the bootstrapping noise by 76%. However, when q is fixed, the boundary for bootstrapping noise remains constant. As a result, larger decomposition bases are used in bootstrapping to reduce the total number of polynomial multiplications by 47%, thus improving the efficiency of the FINAL scheme. The optimization scheme outperforms the original FINAL scheme with 33.3% faster bootstrapping, and the memory overhead of blind rotation keys is optimized by 47%.

关键词： number theory research unit bootstrapping fully homomorphic encryption learning with errors

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Adaptive Hardcore Bit and Quantum Key Leasing over Classical Channel from LWE with Polynomial Modulus 30th

Adaptive Hardcore Bit and Quantum Key Leasing over Classical...

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30th International Conference on the Theory and Application of Cryptology and Information Security

作者： Duong Hieu Phan Wen, Weiqiang Yan, Xingyu Zheng, Jinwei Telecom Paris LTCI Inst Polytech Paris Paris France Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China

ISBN: (纸本)9789819609468;9789819609475

Quantum key leasing, also known as public key encryption with secure key leasing (PKE-SKL), allows a user to lease a (quantum) secret key to a server for decryption purpose, with the capability of revoking the key afterwards. In the pioneering work by Chardouvelis et al. (arXiv:2310.14328), a PKE-SKL scheme utilizing classical channels was successfully built upon the noisy trapdoor claw-free (NTCF) family. This approach, however, relies on the superpolynomial hardness of learning with errors (LWE) problem, which could affect both efficiency and security of the scheme. In our work, we demonstrate that the reliance on superpolynomial hardness is unnecessary, and that LWE with polynomial-size modulus is sufficient to achieve the same goal. Our approach enhances both efficiency and security, thereby improving the practical feasibility of the scheme on near-term quantum devices. To accomplish this, we first construct a noticeable NTCF (NNTCF) family with the adaptive hardcore bit property, based on LWE with polynomial-size modulus. To the best of our knowledge, this is the first demonstration of the adaptive hardcore bit property based on LWE with polynomial-size modulus, which may be of independent interest. Building on this foundation, we address additional challenges in prior work to construct the first PKE-SKL scheme satisfying the following properties: ( i) the entire protocol utilizes only classical communication, and can also be lifted to support homomorphism. (ii) the security is solely based on LWE assumption with polynomial-size modulus. As a demonstration of the versatility of our noticeable NTCF, we show that an efficient proof of quantumness protocol can be built upon it. Specifically, our protocol enables a classical verifier to test the quantumness while relying exclusively on the LWE assumption with polynomialsize modulus.

关键词： Trapdoor claw-free functions Adaptive hardcore bit Secure key leasing Proofs of quantumness learning with errors

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A Compact Multi-Identity Fully Homomorphic Encryption Scheme Without Fresh Ciphertexts

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APPLIED SCIENCES-BASEL 2025年第1期15卷 473-473页

作者： Wang, Ziwei Huang, Ruwei Wei, Xiyi Guangxi Univ Sch Comp & Elect Informat Nanning 530004 Peoples R China

The lattice-based multi-identity fully homomorphic encryption scheme combines the quantum security of lattice cryptography with the advantage of identity-based encryption. However, existing schemes face challenges such as large key sizes, inefficient ciphertext expansion processes, and reliance on outdated trapdoor designs, limiting their compactness and practicality. In this study, we propose a novel Compact Multi-Identity Fully Homomorphic Encryption Scheme (WZ-MIBFHE) that eliminates the need for fresh ciphertexts during expansion. First, we construct a compact identity-based encryption scheme by combining the YJW23 trapdoor and ABB10 under the standard model, proving its IND-sID-CPA security. The scheme is then adapted to ensure correctness and security when integrated with the decomposition method for ciphertext expansion. This adaptation also utilizes approximation errors to reduce overall noise. Finally, we expand the modified IBE scheme's ciphertext using the decomposition method to construct the WZ-MIBFHE scheme. Compared to existing methods, WZ-MIBFHE reduces the lattice dimension to nlogq+logbq, improves public and private key sizes, and significantly lowers ciphertext expansion rates by removing the need for fresh ciphertexts. These improvements enhance both the compactness and efficiency of the scheme, making it a promising solution for multi-identity homomorphic encryption.

关键词： fully homomorphic encryption identity-based encryption multi-identity learning with errors fresh ciphertext

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Implementing Homomorphic Encryption-Based Logic Locking in System-On-Chip Designs

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 2025年

作者： Ye, Ziyang Ikeda, Makoto Univ Tokyo Grad Sch Engn Dept Elect Engn & Informat Syst Tokyo 1138656 Japan

This study presents a logic-locking scheme based on the binary ring learning with error (bin-RLWE) algorithm, implemented in a reduced instruction set computer-five (RISC-V) system-on-chip (SoC) design. Unlike traditional logic-locking methods that require providing users with raw locking parameters, the proposed approach secures critical logic paths in the privilege switching process without exposing these sensitive parameters. The implemented locking module itself consumes 3519 lookup tables (LUTs) and 2645 registers, leading to an overall overhead of 6.0% in LUTs and 6.9% in registers compared to the baseline system. The unlock process requires about 2.6 mu s, introducing moderate performance impact and primarily affecting system-level operations while preserving user-level computational efficiency.

关键词： Logic Homomorphic encryption Switches Noise Hardware security Logic gates Very large scale integration Computational efficiency System-on-chip Software Cryptography hardware security homomorphic encryption learning with errors logic locking

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The informativeness of the gradient revisited

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Neural Networks 2025年 189卷 107517页

作者： Takhanov, Rustem Department of Mathematics Nazarbayev University 53 Kabanbay Batyr Ave. Astana010000 Kazakhstan

In the past decade gradient-based deep learning has revolutionized several applications. However, this rapid advancement has highlighted the need for a deeper theoretical understanding of its limitations. Research has shown that, in many practical learning tasks, the information contained in the gradient is so minimal that gradient-based methods require an exceedingly large number of iterations to achieve success. The informativeness of the gradient is typically measured by its variance with respect to the random selection of a target function from a hypothesis class. We use this framework and give a general bound on the variance in terms of a parameter related to the pairwise independence of the target function class and the collision entropy of the input distribution. Our bound scales as Õ(ɛ+e−[Formula presented]Ec), where Õ hides factors related to the regularity of the learning model and the loss function, ɛ measures the pairwise independence of the target function class and Ec is the collision entropy of the input distribution. To demonstrate the practical utility of our bound, we apply it to the class of learning with errors (LWE) mappings and high-frequency functions. In addition to the theoretical analysis, we present experiments to understand better the nature of recent deep learning-based attacks on LWE. © 2025

关键词： Barren plateau Informativeness of the gradient learning with errors Variance of the gradient

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Leveled Homomorphic Encryption in Certificateless Cryptosystem

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Chinese Journal of Electronics 2017年第6期26卷 1213-1220页

作者： CHEN Hu HU Yupu LIAN Zhizhu State Key Laboratory of Integrated Service Networks Xidian University Jiangsu Key Laboratory of Education Big Data Science and Engineering Jiangsu Normal University

To lower communication complexity, a Certificateless homomorphic encryption(CLHE) scheme based on the learning with errors(LWE) problem is constructed by introducing a new technique called probabilistic encoding with weakly homomorphic property. This technique can conveniently convert an intended message into two elements in a ring, which will be respectively encrypted under both public keys of a user in certificateless *** knowing both elements simultaneously, the original message can be easily recovered. It is hidden perfectly by the probabilistic property of encoding. This CLHE removes evaluation keys by using the approximate eigenvector method given by Gentry et al., which makes it into a pure CLHE. It is proven to be semantic secure in the Random oracle model(ROM). The results indicate it is able to homomorphically evaluate any functions in a class functions with given multiplicative depth L.

关键词： Certificateless cryptosystem Lattice cryptography Fully homomorphic encryption learning with errors Random oracle model

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An Automatic Analysis Approach Toward Indistinguishability of Sampling on the LWE Problem

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Tsinghua Science and Technology 2020年第5期25卷 553-563页

作者： Shuaishuai Zhu Yiliang Han Xiaoyuan Yang the College of Cryptography Engineering Engineering University of People's Armed PoliceXi'an 710086China the Key Laboratory of Network and Information Security under the People's Armed Police Engineering University of People's Armed PoliceXi'an 710086China

learning with errors (LWE) is one of the Non-Polynomial (NP)-hard problems applied in cryptographic primitives against quantum ***,the security and efficiency of schemes based on LWE are closely affected by the error sampling *** existing pseudo-random sampling methods potentially have security leaks that can fundamentally influence the security levels of previous cryptographic *** that these primitives are proved semantically secure,directly deducing the influences caused by leaks of sampling algorithms may be ***,we attempt to use the attack model based on automatic learning system to identify and evaluate the practical security level of a cryptographic primitive that is semantically proved secure in indistinguishable security *** this paper,we first analyzed the existing major sampling algorithms in terms of their security and ***,concentrating on the Indistinguishability under Chosen-Plaintext Attack (IND-CPA) security model,we realized the new attack model based on the automatic learning *** experimental data demonstrates that the sampling algorithms perform a key role in LWE-based schemes with significant disturbance of the attack advantages,which may potentially compromise security ***,our attack model is achievable with acceptable time and memory costs.

关键词： lattice-based cryptography learning with errors security model Non-Polynomial(NP)-hard problems

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Lattice-based autonomous path proxy re-encryption in the standard model

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Science China(Information Sciences) 2023年第10期66卷 184-195页

作者： Wenli XIE Jian WENG Yao TONG Xiaojian LIANG Lisha YAO Feixiang ZHAO College of Cyber Security Jinan University Guangzhou Fongwell Data Limited Company

Autonomous path proxy re-encryption(AP-PRE) is a type of PRE that implements control on the delegation path in a multi-hop PRE. AP-PRE forces the proxy to perform the transformation along a predefined path without revealing the underlying plaintext. There are several applications of AP-PRE,including electronic medical systems, data sharing, and email systems. However, as far as we know, the existing AP-PRE scheme is provably secure in the random oracle model under the classical number-theoretic assumption, which might be vulnerable to quantum computers. Therefore, it raises the intriguing question of how to construct a quantum-resistant AP-PRE scheme. In this study, we proposed an AP-PRE scheme based on the widely accepted quantum-resistant learning with errors(LWE) assumptions. Our scheme supports the polynomial length of the delegation path. Furthermore, our scheme is proved to be selective-path CPA(sCPA) secure in the standard model under LWE assumptions.

关键词： autonomous path proxy re-encryption proxy re-encryption lattice-based cryptography learning with errors controlled delegation

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On the Linearization of Human Identification Protocols: Attacks Based on Linear Algebra, Coding Theory, and Lattices

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2015年第8期10卷 1643-1655页

作者： Asghar, Hassan Jameel Steinfeld, Ron Li, Shujun Kaafar, Mohamed Ali Pieprzyk, Josef Natl ICT Australia Sydney NSW 2015 Australia Monash Univ Fac Informat Technol Clayton Sch Informat Technol Clayton Vic 3800 Australia Univ Surrey Fac Engn & Phys Sci Dept Comp Guildford GU2 7XH Surrey England Queensland Univ Technol Fac Sci & Engn Sch Elect Engn & Comp Sci Brisbane Qld 4000 Australia

Human identification protocols are challenge-response protocols that rely on human computational ability to reply to random challenges from the server based on a public function of a shared secret and the challenge to authenticate the human user. One security criterion for a human identification protocol is the number of challenge-response pairs the adversary needs to observe before it can deduce the secret. In order to increase this number, protocol designers have tried to construct protocols that cannot be represented as a system of linear equations or congruences. In this paper, we take a closer look at different ways from algebra, lattices, and coding theory to obtain the secret from a system of linear congruences. We then show two examples of human identification protocols from literature that can be transformed into a system of linear congruences. The resulting attack limits the number of authentication sessions these protocols can be used before secret renewal. Prior to this paper, these protocols had no known upper bound on the number of allowable sessions per secret.

关键词： Human identification protocols learning with errors linear system of congruences

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Leveled Fully Homomorphic Signcryption From Lattices

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IEEE ACCESS 2023年 11卷 35232-35242页

作者： Jin, Xiaodan Wang, Fuqun Zhang, Renjun Lian, Bin Chen, Kefei Hangzhou Normal Univ Sch Math Hangzhou 311121 Peoples R China Hangzhou Normal Univ Key Lab Cryptog Zhejiang Prov Hangzhou 311121 Peoples R China NingboTech Univ Sch Informat Sci & Engn Ningbo 315199 Peoples R China

With the continuous and rapid development of Cloud Computing, Big Data and Internet of Things, it is extremely critical to protect data with homomorphism, privacy and integrity. For this, Rezaeibagha et al. proposed a new cryptographic primitive, called homomorphic signcryption. However, the current homomorphic signcryption schemes either only support linear computation or are built on non-standard assumption. Therefore, it is interesting to design a leveled fully homomorphic signcryption (FHSC) scheme from the standard assumption. In this work, we present a leveled FHSC scheme from lattices. For this, we exert classical sign-then-encrypt method and surmount the difficulty of homomorphic multiplicative evaluation in the way of encrypting every elements. Moreover, we prove its indistinguishability against chosen plaintext attacks (IND-CPA) and strong unforgeability (SUF) under hard problems of standard lattices.

关键词： Cryptography Standards Lattices Data privacy Internet of Things Homomorphic encryption Organizations Fully homomorphic signcryption learning with errors short integer solution

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