Enhanced fully homomorphic encryption scheme using modified key generation for cloud environment

Fully homomorphic encryption (FHE) is a special class of encryption that allows performing unlimited mathematical operations on encrypted data without decrypting it. There are symmetric and asymmetric FHE schemes. The symmetric schemes suffer from the semantically security property and need more performance improvements. While asymmetric schemes are semantically secure however, they pose two implicit problems. The first problem is related to the size of key and ciphertext and the second problem is the efficiency of the schemes. This study aims to reduce the execution time of the symmetric FHE scheme by enhancing the key generation algorithm using the Pick-Test method. As such, the Binary Learning with Error lattice is used to solve the key and ciphertext size problems of the asymmetric FHE scheme. The combination of enhanced symmetric and asymmetric algorithms is used to construct a multi-party protocol that allows many users to access and manipulate the data in the cloud environment. The Pick-Test method of the Sym-Key algorithm calculates the matrix inverse and determinant in one instance requires only n-1 extra multiplication for the calculation of determinant which takes 0(N3) as a total cost, while the Random method in the standard scheme takes 0(N3) to find matrix inverse and 0(N!) to calculate the determinant which results in 0(N4) as a total cost. Furthermore, the implementation results show that the proposed key generation algorithm based on the pick-test method could be used as an alternative to improve the performance of the standard FHE scheme. The secret key in the Binary-LWE FHE scheme is selected from {0,1}n to obtain a minimal key and ciphertext size, while the public key is based on learning with error problem. As a result, the secret key, public key and tensored ciphertext is enhanced from logq , 0(n2log2q) and ((n+1)n2log2q)2log q to n, (n+1)2log q and (n+1)2log q respectively. The Binary-LWE FHE scheme is a secured but noise-based scheme. Hence, the modulus switching technique is used as a noise management technique to scale down the noise from e and c to e/B and c/B respectively thus, the total cost for noise management is enhanced from 0(n3log2q) to 0(n2log q) . The Multi-party protocol is constructed to support the cloud computing on Sym-Key FHE scheme. The asymmetric Binary-LWE FHE scheme is used as a small part of the protocol to verify the access of users to any resource. Hence, the protocol combines both symmetric and asymmetric FHE schemes which have the advantages of efficiency and security. FHE is a new approach with a bright future in cloud computing

О нестойкости двух симметричных гомоморфных криптосистем, основанных на системе остаточных классов

Одной из наиболее актуальных задач, связанных с защитой облачных вычислений, является анализ криптостойкости гомоморфных шифров. Данная статья посвящена изучению вопроса о защищенности двух недавно предложенных гомоморфных криптосистем, которые, в связи с их высокой вычислительной эффективностью, могут быть использованы для шифрования данных на облачных серверах. Обе криптосистемы основаны на системах остаточных классов, что позволяет рассмотреть их с единых позиций. Именно использование систем остаточных классов делает применение этих криптосистем в реальных приложениях заманчивым с точки зрения эффективности по сравнению с другими гомоморфными шифрами, так как появляется возможность легко распараллелить вычисления. Однако их криптостойкость не была в достаточной мере изучена в литературе и нуждается в анализе. Отметим, что ранее предшественниками была рассмотрена криптосистема похожая на один из шифров, криптостойкость которого исследуется. Была предложена идея адаптивной атаки по выбранным открытым текстам на эту конструкцию и дана оценка необходимого для раскрытия ключа количества пар >. Здесь проводится анализ этой атаки и показываем, что иногда она может работать некорректно. Также описывается более общий алгоритм атаки с известными открытыми текстами. Приводятся теоретические оценки вероятности успешного раскрытия секретного ключа с его помощью и практические оценки этой вероятности, полученные в ходе вычислительного эксперимента. Защищенность второй криптосистемы не была исследована ранее в литературе. Изучена её стойкость к атаке с известными открытыми текстами. Проанализирована зависимость необходимого для взлома количества пар > от параметров криптосистемы и даны рекомендации, которые могут помочь улучшить криптостойкость. Итог проведенного анализа заключается в том, что обе криптосистемы являются уязвимыми к атаке с известными открытыми текстами. Поэтому использовать их для шифрования конфиденциальных данных может быть небезопасно. Основным алгоритмом, используемым в предложенных атаках на криптосистемы, является алгоритм поиска наибольшего общего делителя. Как следствие, время, необходимое для реализации атак, является полиномиальным от размера входных данных

О нестойкости двух симметричных гомоморфных криптосистем, основанных на системе остаточных классов

The security of two recently proposed symmetric homomorphic encryption schemes based on residue system is analyzed. Both schemes have a high computational efficiency since using residue system naturally allows parallelizing computations. So they could be good candidates to protect the data in clouds. But to the best of our knowledge there is a lack of security analysis for these encryption schemes. It should be noted that the first cryptosystem under our consideration was already considered in literature. The sketch of adaptive chosen-plaintext attack was proposed and estimation of its success was given. In this paper the attack is analyzed and it is shown that in some cases it may work incorrectly. Also more general algorithm of known-plaintext attack is presented.  Theoretical estimations of probability to recover the key using it and practical estimations of this probability obtained during the experiments are provided. The security of the second cryptosystem has not been analyzed yet and we fill this gap for known-plaintext attack.  The dependency between the number of «plaintext, ciphertext» pairs required to recover the key and parameters of the cryptosystem is analyzed. Also some recommendations for increasing the security level are provided. The final conclusion of our analysis is that both cryptosystems are vulnerable to known-plaintext attack. And it may be dangerous to encrypt private data using them. Finally it should be noted that the key element of the proposed attacks is the algorithm of computing the greatest common divisor. So their computational complexity depends polynomially on the size of input data.Одной из наиболее актуальных задач, связанных с защитой облачных вычислений, является анализ криптостойкости гомоморфных шифров. Данная статья посвящена изучению вопроса о защищенности двух недавно предложенных гомоморфных криптосистем, которые, в связи с их высокой вычислительной эффективностью, могут быть использованы для шифрования данных на облачных серверах. Обе криптосистемы основаны на системах остаточных классов, что позволяет рассмотреть их с единых позиций. Именно использование систем остаточных классов делает применение этих криптосистем в реальных приложениях заманчивым с точки зрения эффективности по сравнению с другими гомоморфными шифрами, так как появляется возможность легко распараллелить вычисления. Однако их криптостойкость не была в достаточной мере изучена в литературе и нуждается в анализе. Отметим, что ранее предшественниками была рассмотрена криптосистема похожая на один из шифров, криптостойкость которого исследуется. Была предложена идея адаптивной атаки по выбранным открытым текстам на эту конструкцию и дана оценка необходимого для раскрытия ключа количества пар <<открытый текст, шифртекст>>. Здесь проводится анализ этой атаки и показываем, что иногда она может работать некорректно. Также описывается более общий алгоритм атаки с известными открытыми текстами. Приводятся теоретические оценки вероятности успешного раскрытия секретного ключа с его помощью и практические оценки этой вероятности, полученные в ходе вычислительного эксперимента. Защищенность второй криптосистемы не была исследована ранее в литературе. Изучена её стойкость к атаке с известными открытыми текстами. Проанализирована зависимость необходимого для взлома количества пар <<открытый текст, шифртекст>> от параметров криптосистемы и даны рекомендации, которые могут помочь улучшить криптостойкость. Итог проведенного анализа заключается в том, что обе криптосистемы являются уязвимыми к атаке с известными открытыми текстами. Поэтому использовать их для шифрования конфиденциальных данных может быть небезопасно. Основным алгоритмом, используемым в предложенных атаках на криптосистемы, является алгоритм поиска наибольшего общего делителя. Как следствие, время, необходимое для реализации атак, является полиномиальным от размера входных данных

Modern Cryptography Volume 2

This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature of this book is to use probability distribution to carry out rigorous mathematical definition and mathematical demonstration for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattice, ideal lattice and generalized NTRU cryptography. This book is used as a professional book for graduate students majoring in mathematics and cryptography, as well as a reference book for scientific and technological personnel engaged in cryptography research

Modern Cryptography Volume 2

This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature of this book is to use probability distribution to carry out rigorous mathematical definition and mathematical demonstration for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattice, ideal lattice and generalized NTRU cryptography. This book is used as a professional book for graduate students majoring in mathematics and cryptography, as well as a reference book for scientific and technological personnel engaged in cryptography research

Smart and Secure Augmented Reality for Assisted Living

Augmented reality (AR) is one of the biggest technology trends which enables people to see the real-life surrounding environment with a layer of virtual information overlaid on it. Assistive devices use this match of information to help people better understand the environment and consequently be more efficient. Specially, AR has been extremely useful in the area of Ambient Assisted Living (AAL). AR-based AAL solutions are designed to support people in maintaining their autonomy and compensate for slight physical and mental restrictions by instructing them on everyday tasks. The discovery of visual attention for assistive aims is a big challenge since in dynamic cluttered environments objects are constantly overlapped and partial object occlusion is also frequent. Current solutions use egocentric object recognition techniques. However, the lack of accuracy affects the system's ability to predict users’ needs and consequently provide them with the proper support. Another issue is the manner that sensitive data is treated. This highly private information is crucial for improving the quality of healthcare services. However, current blockchain approaches are used only as a permission management system, while the data is still stored locally. As a result, there is a potential risk of security breaches. Privacy risk in the blockchain domain is also a concern. As major investigation tackles privacy issues based on off-chain approaches, there is a lack of effective solutions for providing on-chain data privacy. Finally, the Blockchain size has been shown to be a limiting factor even for chains that store simple transactional data, much less the massive blocks that would be required for storing medical imaging studies. To tackle the aforementioned major issues, this research proposes a framework to provide a smarter and more secure AR-based solution for AAL. Firstly, a combination of head-worn eye-trackers cameras with egocentric video is designed to improve the accuracy of visual attention object recognition in free-living settings. A heuristic function is designed to generate a probability estimation of visual attention over objects within an egocentric video. Secondly, a novel methodology for the storage of large sensitive AR-based AAL data is introduced in a decentralized fashion. By leveraging the power of the IPFS (InterPlanetary File System) protocol to tackle the lack of storage issue in the Blockchain. Meanwhile, a blockchain solution on the Secret Network blockchain is developed to tackle the existent lack of privacy on smart contracts, which provides data privacy at both transactional and computational levels. In addition, is included a new off-chain solution encapsulates a governing body for permission management purposes to solve the problem of the lost or eventual theft of private keys. Based on the research findings, that visual attention-object detection approach is applicable to cluttered environments which presents a transcend performance compared to the current methods. This study also produced an egocentric indoor dataset annotated with human fixation during natural exploration in a cluttered environment. Comparing to previous works, this dataset is more realistic because it was recorded in real settings with variations in terms of objects overlapping regions and object sizes. With respect to the novel decentralized storage methodology, results indicate that sensitive data can be stored and queried efficiently using the Secret Network blockchain. The proposed approach achieves both computational and transactional privacy with significantly less cost. Additionally, this approach mitigates the risk of permanent loss of access to the patient on-chain data records. The proposed framework can be applied as an assistive technology in a wide range of sectors that requires AR-based solution with high-precision visual-attention object detection, efficient data access, high-integrity data storage and full data privacy and security

Privacy preserving computation in cloud using noise-free fully homomorphic encryption (FHE) schemes

With the wide adoption of cloud computing paradigm, it is important to develop appropriate techniques to protect client data privacy in the cloud. Encryption is one of the major techniques that could be used to achieve this goal. However, data encryption at the rest alone is insufficient for secure cloud computation environments. There is also the need for efficient techniques to carry out computation over encrypted data. Fully homomorphic encryption (FHE) and garbled circuits are naturally used to process encrypted data without leaking any information about the data. However, existing FHE schemes are inefficient for processing large amount of data in cloud and garbled circuits are one time programs and cannot be reused. Based on quaternion/octonion algebra and Jordan algebra over finite rings ?q, this paper designs efficient fully homomorphic symmetric key encryption (FHE) schemes without bootstrapping (that is, noise-free FHE schemes) that are secure in the weak ciphertext-only security model assuming the hardness of solving multivariate quadratic equation systems and solving univariate high degree polynomial equation systems in ?q. The FHE scheme designed in this paper is sufficient for privacy preserving computation in cloud. Springer International Publishing Switzerland 2016.The work reported in this paper is supported by Qatar Foundation Grants NPRP8-2158-1-423 and NPRP X-063-1-014.Scopu