Dima Grigoriev, Ilia Ponomarenko
In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over an appropriate finitely generated group.
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We propose a new homomorphic public-key cryptosystem over arbitrary nonidentity finite group based on the difficulty of the membership problem for groups of integer matrices. Besides, a homomorphic cryptosystem is designed for the first time over finite commutative rings.
An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f:G --> H, where G, H are (publically known) groups and H is finite. A letter of a message to be encrypted is an element h element of H, while its encryption g element of G is such that f(g)=h. A homomorphic cryptosystem allows one to perform computations (operating in a group G) with encrypted information (without knowing the original message over H). In this paper certain homomorphic cryptosystems are constructed for t…
Oblivious data processing has been an on and off topic for the last decade or so. It provides great opportunities for secure data management and processing, especially in the cloud. At the same time, modern computing resources seem to be affordable enough to allow for practical use of homomorphic cryptography. Yet, the availability of products that offer practical homomorphic data processing is extremely scarce. As part of a project aimed at developing a practical homomorphic data management platform, we have conducted an extensive study of homomorphic cryptosystems' performance, the results o…
Homomorphic encryption and blockchain technology are regarded as two significant technologies for improving e-voting systems. In this paper, we suggest a novel e-voting system using homomorphic encryption and blockchain technology that is focused on encrypting voter data. By encrypting voter information rather than cast votes, the system enables various statistical analyses regarding the vote result while securing the credibility, privacy, and verifiability of overall e-voting system. We checked the efficiency of the overall system by comparing the speed of the proposed system with the speed o…
Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in the same way. 2. The computational aspects of lattice-based cryptosystem are usually simple to understand and fairly easy to implement in practice. 3. Lattice-based cryptosystems have lower encryption/decryption computational complexities compared to popular cryptosystems that are based on the integer factorisation or the discrete logarithm problems. 4. Lattic…
Machine learning (ML) classifiers are invaluable building blocks that have been used in many fields. High quality training dataset collected from multiple data providers is essential to train accurate classifiers. However, it raises concern about data privacy due to potential leakage of sensitive information in training dataset. Existing studies have proposed many solutions to privacy-preserving training of ML classifiers, but it remains a challenging task to strike a balance among accuracy, computational efficiency, and security. In this paper, we propose Heda, an efficient privacypreserving …
Bridging the Gap Between PHE and FHE: A Performance and Trade-off Analysis of The Somewhat Homomorphic BGN Cryptosystem
本文将半同态BGN密码系统集成到lightphe框架，对比PHE与FHE开展基准测试，揭示其计算与通信的权衡特性，确立其为带宽受限去中心化架构的实用隐私保护加密引擎。
Comprehensive Introduction to Fully Homomorphic Encryption for Dynamic Feedback Controller via LWE-based Cryptosystem
本文介绍了基于LWE问题的密码系统，该系统通过在密文注入随机错误来保证安全性，尽管这会限制同态运算的递归操作，但在动态反馈控制器中可以克服这一限制，从而构建安全的反馈控制系统。
Homomorphic encryption has largely been studied in context of public key cryptosystems. But there are applications which inherently would require symmetric keys. We propose a symmetric key encryption scheme with fully homomorphic evaluation capabilities. The operations are matrix based, that is the scheme consists of mapping the operations on integers to operations on matrix. We also include a protocol which uses the proposed scheme for private data processing in clouds.
Machine Learning as a Service (MLaaS), such as Microsoft Azure, Amazon AWS, offers an effective DNN model to complete the machine learning task for small businesses and individuals who are restricted to the lacking data and computing power. However, here comes an issue that user privacy is ex-posed to the MLaaS server, since users need to upload their sensitive data to the MLaaS server. In order to preserve their privacy, users can encrypt their data before uploading it. This makes it difficult to run the DNN model because it is not designed for running in ciphertext domain. In this paper, usi…
Privacy is one of the key issues addressed by information Security. Through cryptographic encryption methods, one can prevent a third party from understanding transmitted raw data over unsecured channel during signal transmission. The cryptographic methods for enhancing the security of digital contents have gained high significance in the current era. Breach of security and misuse of confidential information that has been intercepted by unauthorized parties are key problems that information security tries to solve. This paper sets out to contribute to the general body of knowledge in the area …
With the development of cloud computing, the storage and processing of massive visual media data has gradually transferred to the cloud server. For example, if the intelligent video monitoring system cannot process a large amount of data locally, the data will be uploaded to the cloud. Therefore, how to process data in the cloud without exposing the original data has become an important research topic. We propose a single-server version of somewhat homomorphic encryption cryptosystem based on confused modulo projection theorem named CMP-SWHE, which allows the server to complete blind data proc…
In this paper, a code-based public-key cryptosystem based on interleaved Goppa codes is presented. The scheme is based on encrypting several ciphertexts with the same Goppa code and adding a burst error to them. Possible attacks are outlined and the key size of several choices of parameters is compared to those of known schemes for the same security level. For example, for security level 128 bits, we obtain a key size of 696 Kbits whereas the classical McEliece scheme based on Goppa codes using list decoding requires a key size of 1935 Kbits.
At Eurocrypt'99, Paillier presented a public-key cryptosystem based on a novel computational problem. It has interested many researchers because it was additively homomorphic. In this paper, we show that there is a big difference between the original Paillier's encryption and some variants. The Paillier's encryption can be naturally transformed into a signature scheme but these variants miss the feature. In particular, we simplify the alternative decryption procedure of Bresson-Catalano-Pointcheval encryption scheme proposed at Asiacrypt'03. The new version is more applicable to cloud computin…
Towards Provably Secure Encrypted Control Using Homomorphic Encryption
针对加密控制系统缺乏安全性证明及未考虑特定攻击的问题，提出基于可证明安全概念的新型安全定义，并证明采用安全同态加密可增强系统安全性。
Permutational-key quantum homomorphic encryption with homomorphic quantum error-correction
本文提出将置换密钥量子同态加密与同态量子纠错相结合，使客户端和服务器无需置换密钥即可执行纠错编解码，保持信息论安全性。
The autonomous flying agents in a Network-centric environment and brings out various security threats and various techniques of Cryptography. Primary Focus is on study and implementation of how cryptographic algorithms can be effectively be used in a warfare scenario. The data security is the utmost key factor for the protection of data in such environments. The paper proposes mechanisms secured data transmission from the command center (which can be the sending flying agent) to shooter target. The command center and shooter target have a unique set of encryption and decryption key which are c…
Encrypted Dynamic Control exploiting Limited Number of Multiplications and a Method using RLWE-based Cryptosystem
本文提出一种基于RLWE加密系统的加密动态控制方法，通过有限乘法次数和并行运算降低计算与通信开销，实现长期稳定性能。
On homomorphic encryption using abelian groups: Classical security analysis
本文分析Leonardi-Ruiz-Lopez加法同态加密方案在有限阿贝尔群下的经典安全性，并研究可解群实例化面临的量子攻击。
The trend towards delegating data processing to a remote party raises major concerns related to privacy violations for both end-users and service providers. These concerns have attracted the attention of the research community, and several techniques have been proposed to protect against malicious parties by providing secure communication protocols. Most of the proposed techniques, however, require the involvement of a third party, and this by itself can be viewed as another security concern. These security breaches can be avoided by following a new approach that depends on data sorted, manage…
Homomorphic Encryption (HE) is a set of powerful properties of certain cryptosystems that allow for privacy-preserving operation over the encrypted text. Still, HE is not widespread due to limitations in terms of efficiency and usability. Among the challenges of HE, scheme parametrization (i.e., the selection of appropriate parameters within the algorithms) is a relevant multi-faced problem. First, the parametrization needs to comply with a set of properties to guarantee the security of the underlying scheme. Second, parametrization requires a deep understanding of the low-level primitives sin…
This paper proposes a new homomorphic functional encryption using modular multiplications over a hidden ring. Unlike traditional homomorphic encryption where users can only passively perform ciphertext addition or multiplication, the homomorphic functional encryption retains homomorphic addition and scalar multiplication properties, but also allows for the user's inputs through polynomial variables. The proposed homomorphic encryption can be applied to any polynomials over a finite field, with their coefficients considered as their privacy. We denote the polynomials before homomorphic encrypti…
Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation. Unfortunately, recent advances in quantum computation show that many of the existing schemes completely break down once quantum computers reach maturity (mainly due to Shor's algorithm). This leads to the challenge of constructing quantum-resistant group homomorphic cryptosystems. In this work, we prove the general impossibility of (abelian) group homomorphic e…
Homomorphic encryption enables arbitrary computation over data while it remains encrypted. This privacy-preserving feature is attractive for machine learning, but requires significant computational time due to the large overhead of the encryption scheme. We present Faster CryptoNets, a method for efficient encrypted inference using neural networks. We develop a pruning and quantization approach that leverages sparse representations in the underlying cryptosystem to accelerate inference. We derive an optimal approximation for popular activation functions that achieves maximally-sparse encodings…
Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink proposed a variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed-Solomon code. More recently, new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee, and a variation o…
LINE: Public-key encryption
提出一种基于欠定线性方程组多解性的公钥加密密码系统，通过同态矩阵变换补全输入参数实现加解密，兼具高安全性与低计算开销。
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new homomorphic public-key cryptosystem. They rely on difficulty of the conjugacy and membership problems for subgroups of a given group. To support these and other known cryptographic schemes we present a general technique to produce a family of instances being matrix groups (over finite commutative rings) which play a role for these schemes similar to the groups $Z\_n^*…
Stability Buys Time: A Re-Keying Game for Encrypted Multi-Agent Control
研究加密多智能体控制中CKKS方案密钥恢复漏洞问题，将循环安全性建模为两阶段博弈，通过重新密钥生成防御主动操纵，确定了FHE精度等三方张力范围及有效安全点，揭示反馈回路中密码系统安全性是动态博弈。
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