Modified Multi-Key Fully Homomorphic Encryption Based on NTRU Cryptosystem without Key-Switching

The Multi-Key Fully Homomorphic Encryption (MKFHE) based on the NTRU cryptosystem is an important alternative to the post-quantum cryptography due to its simple scheme form,high efficiency,and fewer ciphertexts and keys.In 2012,Lopez-Alt et al.proposed the first NTRU-type MKFHE scheme,the LTV12 scheme,using the key-switching and modulus-reduction techniques,whose security relies on two assumptions:the Ring Learning With Error (RLWE) assumption and the Decisional Small Polynomial Ratio (DSPR) assumption.However,the LTV12and subsequent NTRU-type schemes are restricted to the family of power-of-2 cyclotomic rings,which may affect the security in the case of subfield attacks.Moreover,the key-switching technique of the LTV12 scheme requires a circular application of evaluation keys,which causes rapid growth of the error and thus affects the circuit depth.In this paper,an NTRU-type MKFHE scheme over prime cyclotomic rings without key-switching is proposed,which has the potential to resist the subfield attack and decrease the error exponentially during the homomorphic evaluating process.First,based on the RLWE and DSPR assumptions over the prime cyclotomic rings,a detailed analysis of the factors affecting the error during the homomorphic evaluations in the LTV12 scheme is provided.Next,a Low Bit Discarded&Dimension Expansion of Ciphertexts (LBD&DEC) technique is proposed,and the inherent homomorphic multiplication decryption structure of the NTRU is proposed,which can eliminate the key-switching operation in the LTV12 scheme.Finally,a leveled NTRU-type MKFHE scheme is developed using the LBD&DEC and modulus-reduction techniques.The analysis shows that the proposed scheme compared to the LTV12 scheme can decrease the magnitude of the error exponentially and minimize the dimension of ciphertexts.

A Fully Homomorphic Encryption Scheme with Better Key Size

Fully homomorphic encryption is faced with two problems now. One is candidate fully homomorphic encryption schemes are few. Another is that the efficiency of fully homomorphic encryption is a big question. In this paper, we propose a fully homomorphic encryption scheme based on LWE, which has better key size. Our main contributions are： （1） According to the binary-LWE recently, we choose secret key from binary set and modify the basic encryption scheme proposed in Linder and Peikert in 2010. We propose a fully homomorphic encryption scheme based on the new basic encryption scheme. We analyze the correctness and give the proof of the security of our scheme. The public key, evaluation keys and tensored ciphertext have better size in our scheme. （2） Estimating parameters for fully homomorphic encryption scheme is an important work. We estimate the concert parameters for our scheme. We compare these parameters between our scheme and Bral2 scheme. Our scheme have public key and private key that smaller by a factor of about logq than in Bral2 scheme. Tensored ciphertext in our scheme is smaller by a factor of about log2q than in Bral2 scheme. Key switching matrix in our scheme is smaller by a factor of about log3q than in Bra12 scheme.

A secure outsourced Turing- equivalent computation scheme against semi-honest workers using fully homomorphic encryption

A scheme that can realize homomorphic Turing- equivalent privacy-preserving computations is proposed, where the encoding of the Turing machine is independent of its inputs and running time. Several extended private information retrieval protocols based on fully homomorphic encryption are designed, so that the reading and writing of the tape of the Turing machine, as well as the evaluation of the transition function of the Turing machine, can be performed by the permitted Boolean circuits of fully homomorphic encryption schemes. This scheme overwhelms the Turing-machine-to- circuit conversion approach, which also implements the Turing-equivalent computation. The encoding of a Turing- machine-to-circuit conversion approach is dependent on both the input data and the worst-case runtime. The proposed scheme efficiently provides the confidentiality of both program and data of the delegator in the delegator-worker model of outsourced computation against semi-honest workers.

An Improved Multiple to One Fully Homomorphic Encryption on the Integers

The public key of the integer homomorphic encryption scheme which was proposed by Van Dijk et al. is long, so the scheme is almost impossible to use in practice. By studying the scheme and Coron’s public key compression technique, a scheme which is able to encrypt n bits plaintext once was obtained. The scheme improved the efficiency of the decrypting party and increased the number of encrypting parties, so it meets the needs of cloud computing better. The security of the scheme is based on the approximate GCD problem and the sparse-subset sum problem.

An Unbounded Fully Homomorphic Encryption Scheme Based on Ideal Lattices and Chinese Remainder Theorem

We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational solution to an old problem proposed by Rivest, Adleman, and Dertouzos [1] in 1978, and to some new problems that appeared in Peikert [2] as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the breakthrough work [3] of Gentry in 2009. Gentry’s bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Our construction of an unbounded FHE scheme is straightforward and can handle unbounded homomorphic computation on any refreshed ciphertexts without bootstrapping transformation technique.

Novel Homomorphic Encryption for Mitigating Impersonation Attack in Fog Computing

Fog computing is a rapidly growing technology that aids in pipelining the possibility of mitigating breaches between the cloud and edge servers.It facil-itates the benefits of the network edge with the maximized probability of offering interaction with the cloud.However,the fog computing characteristics are suscep-tible to counteract the challenges of security.The issues present with the Physical Layer Security(PLS)aspect in fog computing which included authentication,integrity,and confidentiality has been considered as a reason for the potential issues leading to the security breaches.In this work,the Octonion Algebra-inspired Non-Commutative Ring-based Fully Homomorphic Encryption Scheme(NCR-FHE)was proposed as a secrecy improvement technique to overcome the impersonation attack in cloud computing.The proposed approach was derived through the benefits of Octonion algebra to facilitate the maximum security for big data-based applications.The major issues in the physical layer security which may potentially lead to the possible security issues were identified.The potential issues causing the impersonation attack in the Fog computing environment were identified.The proposed approach was compared with the existing encryption approaches and claimed as a robust approach to identify the impersonation attack for the fog and edge network.The computation cost of the proposed NCR-FHE is identified to be significantly reduced by 7.18%,8.64%,9.42%,and 10.36%in terms of communication overhead for varying packet sizes,when compared to the benchmarked ECDH-DH,LHPPS,BF-PHE and SHE-PABF schemes.

Targeted Fully Homomorphic Encryption Based on a Double Decryption Algorithm for Polynomials

Several public-key encryption schemes used to solve the problem of ciphertext data processing on the fly are discussed. A new targeted fully homomorphic encryption scheme based on the discrete logarithm problem is presented. Public-key encryption cryptosystems are classified to examine homomorphic encryption. Without employing techniques proposed by Gentry such as somewhat homomorphic and bootstrapping techniques, or relinearization technique proposed by Brakerski et al., a new method called ＂Double Decryption Algorithm＂ is employed in our cryptography to satisfy a fully or targeted fully homomorphic property. Inspired by EIGamal and BGN cryptography, we obtain the desired fully homomorphic property by selecting a new group and adding an extra component to the ciphertext. Proof of semantic security is also demonstrated.

A Novel Fully Homomorphic Encryption Scheme Bsed on LWE

Although the learning with errors（LWE）-based full homomorphic encryption scheme was the first example of deviation from the original Gentry＇s blueprint, the scheme did not give detailed conversion process of circuit layer structure, and must rely on bootstrapping technique to achieve full homomorphism. Therefore, through modifying the re-linearization technique proposed by the above scheme, a technique called non-matrix key switching is presented, which includes key switching with re-linearization and pure key switching. The complex matrix operations of existing key switching technique are removed. Combining this technique with modulus switching, a （leveled） fully homomorphic encryption scheme without bootstrapping from LWE is constructed. In order to make circuit layer structure clear, the scheme gives detailed refresh door operation. Finally, we use bootstrapping to upgrade arithmetic circuit to any layer, and make the homomorphic computing capability of the scheme have nothing to circuit depth.

Secure Scheme for Locating Disease-Causing Genes Based on Multi-Key Homomorphic Encryption

Genes have great significance for the prevention and treatment of some diseases.A vital consideration is the need to find a way to locate pathogenic genes by analyzing the genetic data obtained from different medical institutions while protecting the privacy of patients’genetic data.In this paper,we present a secure scheme for locating disease-causing genes based on Multi-Key Homomorphic Encryption(MKHE),which reduces the risk of leaking genetic data.First,we combine MKHE with a frequency-based pathogenic gene location function.The medical institutions use MKHE to encrypt their genetic data.The cloud then homomorphically evaluates specific gene-locating circuits on the encrypted genetic data.Second,whereas most location circuits are designed only for locating monogenic diseases,we propose two location circuits(TH-intersection and Top-q)that can locate the disease-causing genes of polygenic diseases.Third,we construct a directed decryption protocol in which the users involved in the homomorphic evaluation can appoint a target user who can obtain the final decryption result.Our experimental results show that compared to the JWB+17 scheme published in the journal Science,our scheme can be used to diagnose polygenic diseases,and the participants only need to upload their encrypted genetic data once,which reduces the communication traffic by a few hundred-fold.

An Improved Ciphertext Retrieval Scheme Based on Fully Homomorphic Encryption

In order to guarantee the user's privacy and the integrity of data when retrieving ciphertext in an untrusted cloud environment, an improved ciphertext retrieval scheme was proposed based on full homomorphic encryption. This scheme can encrypt two bits one time and improve the efficiency of retrieval. Moreover, it has small key space and reduces the storage space. Meanwhile, the homomorphic property of this scheme was proved in detail. The experimental results and comparisons show that the proposed scheme is characterized by increased security, high efficiency and low cost.

Big Data analytics for privacy through ND-homomorphic encryption

Rapidly rising the quantity of Big Data is an opportunity to flout the privacy of people. Whenhigh processing capacity and massive storage are required for Big Data, distributed networkshave been used. There are several people involved in these activities, the system may contributeto privacy infringements frameworks have been developed for the preservation of privacy atvarious levels (e.g. information age, information the executives and information preparing) asfor the existing pattern of huge information. We plan to frame this paper as a literature surveyof these classifications, including the Privacy Processes in Big Data and the presentation of theAssociate Challenges. Homomorphic encryption is particularised aimed at solitary single actionon the ciphered information. Homomorphic enciphering is restrained to an honest operation onthe encoded data. The reference to encryption project fulfils many accurate trading operationson coded numerical data;therefore, it protects the written in code-sensible information evenmore.

An Efficient Encrypted Speech Retrieval Based on Unsupervised Hashing and B+ Tree Dynamic Index

Existing speech retrieval systems are frequently confronted with expanding volumes of speech data.The dynamic updating strategy applied to construct the index can timely process to add or remove unnecessary speech data to meet users’real-time retrieval requirements.This study proposes an efficient method for retrieving encryption speech,using unsupervised deep hashing and B+ tree dynamic index,which avoid privacy leak-age of speech data and enhance the accuracy and efficiency of retrieval.The cloud’s encryption speech library is constructed by using the multi-threaded Dijk-Gentry-Halevi-Vaikuntanathan(DGHV)Fully Homomorphic Encryption(FHE)technique,which encrypts the original speech.In addition,this research employs Residual Neural Network18-Gated Recurrent Unit(ResNet18-GRU),which is used to learn the compact binary hash codes,store binary hash codes in the designed B+tree index table,and create a mapping relation of one to one between the binary hash codes and the corresponding encrypted speech.External B+tree index technology is applied to achieve dynamic index updating of the B+tree index table,thereby satisfying users’needs for real-time retrieval.The experimental results on THCHS-30 and TIMIT showed that the retrieval accuracy of the proposed method is more than 95.84%compared to the existing unsupervised hashing methods.The retrieval efficiency is greatly improved.Compared to the method of using hash index tables,and the speech data’s security is effectively guaranteed.

全同态加密研究进展

随着数字化进程的加速推进,数据安全和隐私保护问题备受关注.数据加密一直是解决该问题的重要手段,但加密存储和传输较为常见,一旦涉及计算往往需要先解密,以明文形式计算后再加密.全同态加密(fully homomorphic encryption,FHE)将加密延展到计算层面,无需解密即可以完成密文的处理任务,有保护数据安全和用户隐私的天然特性.首个FHE方案于2009年由Gentry提出,自此FHE方案一直备受业界和学界的关注.从FHE方案的构造思想、不同研究阶段及面临的问题等方面梳理分析了FHE 10余年的研究进展,从算法库实践、标准化进展以及典型应用场景等方面介绍了FHE的应用进展,并提出未来研究的方向建议.

基于余数系统的小间隔插值拟合自举方法

针对近似同态加密方案自举耗时过大的问题提出了一种基于余数系统的小区间插值拟合自举方法。通过在多个小区间内对模函数进行插值拟合避免因拟合多项式次数过高产生自举时间过长或计算精度降低的问题,并通过结合余数系统提高计算过程中模乘运算的模逆运算效率。选用拉格朗日插值多项式对小区间内的正弦函数进行插值拟合。通过多个低次多项式复合计算实现比较函数,并提出了一种区间判断算法来识别密文所在区间。最终在24比特精度下,同态计算过程中模运算耗时下降到HEAAN库的8%,在计算槽的数量为65536时,平均每槽的模运算时间为0.028 ms。

新形态对称密码算法研究

安全多方计算、全同态加密和零知识证明是解决数据安全问题的重要密码技术,其快速发展和应用需求驱动,引发了新形态对称密码的设计与安全性分析.本文系统介绍适宜安全多方计算、全同态加密和零知识证明的新形态对称密码算法.首先梳理新形态对称密码算法的应用需求和设计目标;然后归类介绍新形态对称密码算法的设计理念和最新的安全性评估结果;最后总结探讨新形态对称密码算法的设计特点以及面临的问题.

全同态加密软硬件加速研究进展

全同态加密(FHE)是一种重计算、轻交互的多方安全计算协议。在基于全同态加密的计算协议中,尽管计算参与方之间无需多轮交互与大量通信,加密状态下的密态数据处理时间通常是明文计算的10~3~10~6倍,极大地阻碍了这类计算协议的实际落地;而密态数据上的主要处理负担是大规模的并行密码运算和运算所必须的密文及密钥数据搬运需求。该文聚焦软、硬件两个层面上的全同态加密加速这一研究热点,通过系统性地归类及整理当前领域中的文献,讨论全同态加密计算加速的研究现状与展望。

全同态加密技术的研究现状及发展路线综述

随着物联网、云计算、人工智能的应用与普及,数据安全与隐私保护成为人们关注的焦点。全同态加密,作为隐私安全问题的有效解决办法,允许对加密数据执行任意同态计算,是一种强大的加密工具,具有广泛的潜在应用。该文总结了自2009年以来提出全同态加密方案,并根据方案的核心技术划分成4条技术路线,分析讨论了各类方案的关键构造,算法优化进程和未来发展方向。首先,全面介绍了全同态加密相关的数学原理,涵盖了全同态加密方案的基础假设和安全特性。随后,按照4条全同态加密方案的技术路线,归纳了加密方案的结构通式,总结了自举算法的核心步骤,讨论了最新研究进展,并在此基础上综合分析比较了各类方案的存储效率及运算速度。最后,展示了同态算法库对每条技术路线下加密方案的应用实现情况,分析了在当前时代背景下全同态加密方案的机遇与挑战,并对未来的研究前景做出了展望。

基于错误学习的全同态加密技术研究现状与挑战

全同态加密方案是一种具备数据机密性和安全性的加密方案,同时还能够对密文进行计算操作。在云计算时代,全同态加密方案能够满足私有信息检索、多方安全计算等多种应用需求。错误学习与全同态加密的结合,迅速推动了全同态加密方案的发展,并引出了多种技术工具,如密钥交换和模交换等具有理论和实际应用意义的技术。自从2011年基于LWE的全同态加密方案被提出以来,基于LWE类型的方案已成为全同态加密方案的主流方法,并逐步从理论走向实际应用。文章首先介绍全同态加密的基础知识和应用,并对构造方案的数学理论进行详细分析;然后系统梳理了每一代同态加密方案,并给出了每一代方案的典型构造方式;最后探讨了当前基于LWE的全同态加密方案存在的问题以及未来的发展趋势,为后续研究者提供一些参考。

基于Zynq平台的BFV全同态加密算法高效实现

针对BFV全同态加密算法,在Zynq平台上设计了一种高效实现方案。该方案结合负包裹卷积与数论变换(NTT)算法,优化并加速了多项式乘法的过程。同时采用流水线设计思想和并行化硬件电路架构,加速BFV算法的RNS实现。系统采用AXI-DMA传输机制高效地实现了ARM和FPGA之间数据传输。在Zynq Ultra‐Scale+MPSoC ZCU102平台上测试,系统在200 MHz时钟频率下,执行一次同态加法的平均耗时为0.024 ms;执行一次同态乘法的平均耗时为5.779 ms,其中包括0.874 ms的密文传输时间。与SEAL库和OpenFHE库的实现相比,所提方案的同态加法实现了4.63倍和6.79倍的效率提升,同态乘法实现了4.43倍和2.95倍的效率提升,这为全同态加密算法的实际工程实现提供了重要参考。

环保大数据在区块链中的隐私计算

近年来,随着我国网络安全、医疗及环保相关政策的先后出台,环境数据的价值与日俱增。但我国对于环境数据的科学管理与安全共享仍处于起步阶段,具有隐私保护需求的环境数据数量急剧增加,但在数据共享上却面临数据孤岛化、泄露风险高等诸多难题。针对环境数据共享场景,为从根本上满足用户数据云存储和云计算的隐私保护需求,文章将区块链和隐私计算相结合,采用国密算法构建了一个基于全同态加密和可搜索加密技术的数据密态管理系统。依托区块链部署和云服务存储、隐私计算支持,系统可实现全同态加密机器学习和可搜索加密两种功能。文章基于全同态加密技术实现了神经网络预测模型,并完成了密态数据的云计算;同时,文章采用对称可搜索加密方案,支持数据在全程密态下的远程托管,能够实现密文检索并保护查询关键词的隐私。在保护隐私安全前提下,该方案有效打通了各方数据流通通道,保证数据可用不可见。