Homomorphic Encryption

Organizations and individuals have been moving to the cloud computing technology looking for effective and fast computing services. Confidential information is becoming more vulnerable to leak due to outsource computations to third-parties. The issue of data breaches could remove all the benefits organizations might get by moving to the cloud-based services. The main goal of securing information is to provide confidentiality, authenticity, integrity and data privacy. Data encryption is being widely employed to secure data. However, as users need to process data in the cloud, normal encryption schemes are practically inapplicable because they require the transmission of the secret keys to the server side to obtain the original data thus performing the required computation on the plaintext. Fully homomorphic encryption can be considered as an effective process that supports arbitrary computation on the ciphertext without requirement of decryption in the cloud. A genetic algorithm is a search operation based on natural genetic and natural selection. Applying the concept of Genetic Algorithms on cryptosystem provides strong randomness that hardens the attacking process for the ciphertext. In this paper, a method to use Genetic Algorithm to generate keys for the fully homomorphic encryption scheme is described and its effectiveness is examined. Moreover, some simple computations were performed on the encrypted data as well. Results showed that a GA generated key provides more randomness than other conventional methods used to generate public and private keys.

This article provides a general introduction to the subject of Cryptology, Crytography and Crytoanalysis and explains the terminology and the practical application of security techniques… In recorded History , technological innovations have revolutionized societies. The printing press is an often-cited example of the great impact one humble person’s invention can have on ruling dynasties, world religions, and personal life.. Quantum encryption could rival Guttenberg’s printing press in its impact. Cryptology has a fascinating History., In Warfare Cryptography is a broad, sticky, and mathematically complex, but interesting subject and an integral part of the evolution of warfare. So let’s get some definitions out of the way first. Cryptology is the study of codes, both creating and solving them. Cryptography is the art of creating codes. Cryptanalysis is the art of surreptitiously revealing the contents of coded messages, breaking codes, that were not intended for you as a recipient....

An Image Encryption and Decryption Using AES (Advance Encryption Standard) Algorithm is proposed in the project. Due to increasing use of image in various field, it is very important to protect the confidential image data from unauthorized access. The design uses the iterative approach with block size of 128 bit and key size of 128, 192 or 256 bit. The numbers of round for key size of 256 bits is 14 , for 128 bits is 10 and for 192 bits is 12. As secret key increases the security as well as complexity of the cryptography algorithms. In this paper , an algorithm in which the image is an input to AES Encryption to get the encrypted image and then input it to AES Decryption to get the original image is proposed and explained which will further be implemented by me. The paper shows the study in which a system could be used for effective image data encryption and key generation in diversified application areas, where sensitive and confidential data needs to be transmitted along with the image. I.

Questo lavoro è diviso in due parti. Nella prima vi è uno studio dei concetti di privacy by design e by default introdotti col GDPR. Viene presentato uno strumento (questionario) in grado di analizzare la compliance al regolamento  e vengono presentate le principali tecniche in tema di security.
Nella seconda parte viene analizzata da un punto di vista matematico la crittografia omomorfica, approfondendo gli schemi RSA, Paillier e Gentry.

The goal of this chapter is to present a survey of homomorphic encryption techniques and their applications. After a detailed discussion on the introduction and motivation of the chapter, we present some basic concepts of cryptography. The fundamental theories of homomorphic encryption are then discussed with suitable examples. The chapter then provides a survey of some of the classical homomorphic encryption schemes existing in the current literature. Various applications and salient properties of homomorphic encryption schemes are then discussed in detail. The chapter then introduces the most important and recent research direction in the filed - fully homomorphic encryption. A significant number of propositions on fully homomorphic encryption is then discussed. Finally, the chapter concludes by outlining some emerging research trends in this exciting field of cryptography.

Organizations and individuals have been shifting to the Internet-based cloud computing technology to obtain more efficient and faster computing services in recent years. However, moving to the cloud services has created new security challenges. Confidential information becomes more vulnerable to be leaked due to computation outsourcing to the third-parties. The issue of data breaches could eliminate all the benefits that an organization may get by utilizing the cloud-based computing services. The primary goal of securing information is to provide confidentiality, authenticity, integrity and data privacy. Data encryption has been widely used to protect data during the communication and storage process. However, as users need to process data in the cloud, traditional cryptographic schemes cannot work well because it requires passing the secret keys to the cloud servers so that the servers can obtain the original data and perform the needed computations on the plaintext. Once encrypted data are disclosed for calculations, it can't guarantee the data confidentiality in the cloud; which poses a significant challenge for applications of cloud computing. Homomorphic Encryption (HE) has been proposed to overcome this security issue, which enables mathematical computations directly on encrypted data without the requirement of decryption in the cloud and can provide the same result as obtained by using calculations on the plaintext. Many Fully Homomorphic Encryption (FHE) schemes are designed, which can perform an arbitrary number of additions and multiplications on the ciphertext. In this paper, a comprehensive survey of homomorphic encryption technology using public key algorithms is introduced, then, FHE schemes are reviewed and analyzed. As researchers believe the advancement in the FHE technology will continue, this paper guides the state-of-the-art definitions, properties, algorithms, and schemes of FHE.

In an age of explosive worldwide growth of electronic data storage and communications, effective protection of information has become a critical requirement. When used in coordination with other tools for ensuring information security, cryptography in all of its applications, including data confidentiality, data integrity, and user authentication, is a most powerful tool for protecting information. This book presents a collection of research work in the field of cryptography. It discusses some of the critical challenges that are being faced by the current computing world and also describes some mechanisms to defend against these challenges. It is a valuable source of knowledge for researchers, engineers, graduate and doctoral students working in the field of cryptography. It will also be useful for faculty members of graduate schools and universities.

Wireless networks are truly pervasive in the modern environment: from the workplace and the home, to implanted medical devices. Network security, therefore, is of paramount importance. This volume begins with an overview of the security vulnerabilities of wireless sensor networks, but also offers some means of defence against them. It goes on to propose ways of securing routing in wireless mesh networks. Two further chapters offer in-depth studies of secure and privacy-preserving data protocols for wireless sensor and mesh networks. The book concludes with an overview of the history of homomorphism encryption as a means of securing data, also covering some emerging trends in which this form of encryption offers exciting new possibilities.

This article provides a general introduction to the subject of Cryptology, Crytography and Crytoanalysis and explains the terminology and the practical application of security techniques… In recorded History , technological innovations have revolutionized societies. The printing press is an often-cited example of the great impact one humble person's invention can have on ruling dynasties, world religions, and personal life.. Quantum encryption could rival Guttenberg's printing press in its impact. Cryptology has a fascinating History., In Warfare Cryptography is a broad, sticky, and mathematically complex, but interesting subject and an integral part of the evolution of warfare. So let's get some definitions out of the way first. Cryptology is the study of codes, both creating and solving them. Cryptography is the art of creating codes. Cryptanalysis is the art of surreptitiously revealing the contents of coded messages, breaking codes, that were not intended for you as a recipient.. Secondly, there are nomenclators and enciphers. Nomenclators are letters or numbers that represent words or phrases, like 103A means "meet me at 4PM". Ciphers are alphabetical letters or numbers that are encrypted using some sequential coding process and a key. For this essay, we will refer to both as codes. Also, enciphered, encrypted and encoded mean the same thing….Additionally, there is plain text. This is the original message that is readable and understandable, uncoded or unencrypted. Once it goes through the coding process and is encrypted, the output is readable but not understandable. There are a bunch of other terms like steganography, homophones, polyphones, digraphs, bigrams, and polygrams, but they are just variations of coding and decoding techniques. KEYWORDS Network Protocols, Mathematical Cryptology, encryption, decription 1. CRYPTOLOGY The study of cryptography and cryptanalysis. Cryptology is the mathematics, such as number theory, and the application of formulas and algorithms, that underpin cryptography and cryptanalysis. Since the cryptanalysis concepts are highly specialized and complex, we concentrate here only on some of the key mathematical concepts behind cryptography. cryptology is made up of cryptography and cryptanalysis. 1) Crytography-The art and science of making ciphers. Which concerns with the design of the cryptosystems and cryptography, is the actual securing, control, and identification of digital data. 2) Crytoanalysis-The art and science of breaking ciphers. In other words, the extraction of mm given cc, EE, DD, and possibly keke. which aims at studies relating to breaking of cryptosystems. cryptanalysis, is made up of all the attempts one might develop to undermine, circumvent, and/or break what the first part, cryptography, is attempting to accomplish. 3) Cryptosystems:-A particular suite of algorithms and protocols for encryption, decryption, and key generation. Examples: Cramer-Shoup cryptosystem, Rabin cryptosystem, Benaloh cryptosystem, RSA cryptosystem.

Security has become one of the key features of data transmission on large database. RDBMS are used for storage purposes but with applications generating enormous amount of data, RDBMS is no longer efficient because RDBMS doesn't support quick data access and computations as it do not support processing of data in distributed manner. NoSQL databases are nowadays popular in handling the unstructured data that are available as open source databases such as MongoDB, Cassandra, etc. This paper make a detailed study on the encryption techniques of NoSQL databases especially MongoDB which becomes popular in data management. Since encryption features are not applied on handling the data in MongoDB, In this paper, security for users data is provided by using additive homomorphic asymmetric cryptosystem which encrypts the users data in MongoDB(CryptMDB) and achieve strong user's data privacy protection. This also supports the database operations over the encrypted data.

Although cloud computing continues to grow rapidly, shifting to Internet-based shared computing service has created new security challenge. Organizations move to the cloud technology looking for efficient and fast computing but data security remains their top concern. Confidential data are prone to leak because of modern trend to outsource computations to third-parties. Furthermore, the issue of data breaches can remove any benefits businesses make by moving to the cloud computing technology. Three important questions must be put into consideration: How to guarantee that the user's private data will always be kept safe and secure? Can the cloud service provider be reliable to store and process client's private data confidentially? Is it possible to ensure that even if the cloud provider have been attacked, client's confidential data will not be stolen or reused? To provide better data protection during the communication and storage process, many cryptographic algorithms have already been used, but these methods are practically inapplicable as they require that the data needs to be visible to the cloud provider, in order to do that, the private key has to be transmitted to the server to perform the operations required. In the past thirty years, privacy homomorphism has been used to solves this issue. Homomorphic encryption allows us to execute the arithmetical calculations directly on the ciphertext while keeping the secret key that is used to decrypt the result. In addition to preserve privacy, it provides the exact same result as if we perform the computations on the plaintext. So far, many fully homomorphic encryption (FHE) schemes which evaluate an arbitrary number of additions and multiplications are implemented but researches remains unable to design more secure and powerful schemes. In this paper, a detailed survey of homomorphic encryption using public key algorithms such as RSA, El-Gamal, and Paillier algorithms is given, then, FHE schemes are introduced as well. This work can be helpful as a guide of principles, properties of FHE as researchers believe in the possibility of advancement in the FHE area.

NTRU is being considered as part of the NIST quantum resistant cryptography standard. While NIST has received substantial attention in the literature, more analysis is needed. This current study uses a unique approach. The team of researchers divided into-sub-teams. Each is using a separate analysis technique on NTRU. Then the diverse-sub-teams' work was brought together into a single cohesive statistical analysis to provide well-founded conclusions regarding NTRU.

An encryption scheme is “homomorphic” if it is possible to perform implicit operation on the plaintext by
processing the ciphertext only. The scheme is said to be “fully homomorphic’’ when we can perform (a
sequence of operations) both addition and multiplication, whereas, it is “somewhat homomorphic’’ if it
supports a limited number of operations. We describe how Gentry’s transformation can be applied on
bootstrappable Somewhat Homomorphic Encryption (SHE) scheme to make it a fully homomorphic scheme
(FHE) by squashing the decryption circuit i.e. evaluating with a low-degree polynomial. The security of the
above scheme is based on the hardness of Approximate Integer Common Divisor Problem (ACDP) which
was introduced in 2001 by Howgrave–Graham. Among the two versions of ACDP, the general version
(GACDP) is apparently more secure than its partial version (PACDP).
We have implemented and analyzed Gentry’s scheme and have suggested some improvements to make it
more secure by selecting the Keys parameter in the permissible range.

This paper presents an application for an e-voting system on Android OS. Our study is about Elliptic Curve Cryptography (ECC) that has features of homomorphic encryption. This application is aimed to develop an electronic election application which people can use easily in Turkey.

With the rapid development of cloud computing, the privacy security incidents occur frequently, especially data security issues. Cloud users would like to upload their sensitive information to cloud service providers in encrypted form rather than the raw data, and to prevent the misuse of data. The main challenge is to securely process or analyze these encrypted data without disclosing any useful information, and to achieve the rights management efficiently. In this paper, we propose the encrypted data processing protocols for cloud computing by utilizing additively homomorphic encryption and proxy cryptography. For the traditional homomorphic encryption schemes with many limitations, which are not suitable for cloud computing applications. We simulate a cloud computing scenario with flexible access control and extend the original homomorphic cryptosystem to suit our scenario by supporting various arithmetical calculations. We also prove the correctness and security of our protocols, and analyze the advantages and performance by comparing with some latest works.

Data Mining has gained attention nowadays in the field of sales, marketing, insurance and healthcare applications to name a few. Organizations aspire to perform mining operations on their joint datasets for gaining trade benefits while hiding own sensitive information. Owing to huge resource consumption and less computational power, they often prefer to outsource their data on the cloud platform for entire computation. As there is a risk of exposing the organization's sensitive data from various mistrusted parties involves in it, privacy becomes one of the major challenging issues in cloud computing. Authors have proposed an algorithm were cloud server applies k means clustering on encrypted data sets. A Trusted Party is assumed for key distribution and management. Computations between each party are either performed mutually or via Trusted Authority which involving exchange of sensitive data transfer of each participating parties. Complexity of the algorithm has been analyzed and compared with the existing approach and found that it is linearly depends upon various parameters settings and hence is a better approach while maintaining authenticity and data confidentiality between various participating parties during the mining process.

The biggest advantage of building “intelligence” into a sensor is that the sensor can process data before sending them to a data consumer. The kind of processing that is often needed is to aggregate the data into a more compact representation called an aggregate, and send the aggregate to the data consumer instead. The main security challenges to such a process are (1) to prevent Byzantine-corrupted data from rendering the final aggregate totally meaningless and (2) to provide end-to-end confidentiality between the data providers and the data consumer. This chapter surveys the state of the art in techniques for addressing these challenges.

An encryption scheme is “homomorphic” if it is possible to perform implicit operation on the plaintext by
processing the ciphertext only. The scheme is said to be “fully homomorphic’’ when we can perform (a
sequence of operations) both addition and multiplication, whereas, it is “somewhat homomorphic’’ if it
supports a limited number of operations. We describe how Gentry’s transformation can be applied on
bootstrappable Somewhat Homomorphic Encryption (SHE) scheme to make it a fully homomorphic scheme
(FHE) by squashing the decryption circuit i.e. evaluating with a low-degree polynomial. The security of the
above scheme is based on the hardness of Approximate Integer Common Divisor Problem (ACDP) which
was introduced in 2001 by Howgrave–Graham. Among the two versions of ACDP, the general version
(GACDP) is apparently more secure than its partial version (PACDP).
We have implemented and analyzed Gentry’s scheme and have suggested some improvements to make it
more secure by selecting the Keys parameter in the permissible range.

Organizations and individuals have been shifting to the Internet-based cloud computing technology to obtain more efficient and faster computing services in recent years. However, moving to the cloud services has created new security challenges. Confidential information becomes more vulnerable to be leaked due to computation outsourcing to the third-parties. The issue of data breaches could eliminate all the benefits that an organization may get by utilizing the cloud-based computing services. The primary goal of securing information is to provide confidentiality, authenticity, integrity and data privacy. Data encryption has been widely used to protect data during the communication and storage process. However, as users need to process data in the cloud, traditional cryptographic schemes cannot work well because it requires passing the secret keys to the cloud servers so that the servers can obtain the original data and perform the needed computations on the plaintext. Once encrypted...

Recently there has been a huge interest in secure and private cloud computing. In particular; to perform signal processing and machine learning tasks in the encrypted domain. Homomorphic encryption offers provably secure, asymmetric encryption solution to this problem, however, it comes with a high storage and computation cost. Compressed sensing (CS) and random projection (RP) approaches are much lighter; however, they lack privacy since the encryption uses a symmetric key which is the random projection matrix. A multi-key, compressed sensing encryption approach is proposed in this paper for performing basic generic computations. The computing architecture consists of a User, a Cloud (which stores encrypted data from an Owner), and a Trusted Third Party (TTP) which is responsible for distributing the random CS keys. The TTP also trains two machine learning modules; ML1 and ML2. ML1, used at the cloud, takes as input the multi-key encrypted data and produces an intermediate encrypted result. ML2, available at the user side, decrypts the results. This novel approach is much cheaper than homomorphic encryption in terms of data expansion, storage as well as encryption time. Also, it offers the privacy of the multi-keys. The proposed approach is applied on 2 generic computing tasks; namely, squared Euclidean distance and dot product. The developed approach is tested on the COREL image classification task using the squared Euclidean distance and on an autoregressive (AR) stock prediction task using the dot product.

MORE (Matrix Operation for Randomization or Encryption) is a free-noise fully homomorphic encryption scheme [8]. It is a symmetric scheme invented in 2012 by Kipnis and Hibshoush. The homomorphy of this cryptosystem is obtained via matrix operations. Although the authors said that the security of the algorithm is based on the hardness of factoring big integers, it suffers from new vulnerabilities. The Brenner et al, homomorphic encryption scheme's [11] is a simple algebraic somewhat homomorphic cryptosystem that is supposed to became fully homomorphic after using a new refreshment procedure introduced by Iti Sharma in [10], but unfortunately this refresh method fails in general. In this paper we will provide a cryptanalysis of the MORE cryptosystem based on a single known plaintext and we will show the fail of the Iti Sharma's refreshment procedure.

One of the most widespread computer applications used for person-to-person or organization-to-organization communication is the electronic mail (email or e-mail). The main objective for this study is to develop an emailing solution that is accessible without internet. Kannel works as an SMS gateway for GSM (Global System for Mobile communication) networks. Almost all GSM phones can send and receive SMS messages, so this is a way to serve many more clients than just those using a new WAP phone. The Agile Method is a particular approach to project management that is utilized in software development. This method assists teams in responding to the unpredictability of constructing software.

This paper details Implementation of the Encryption algorithm AES under VHDL language In FPGA by using different architecture of mixcolumn. We then review this research investigates the AES algorithm in FPGA and the Very High Speed Integrated Circuit Hardware Description language (VHDL). Altera Quartus II software is used for simulation and optimization of the synthesizable VHDL code. The set of transformations of both Encryptions and decryption are simulated using an iterative design approach in order to optimize the hardware consumption. Altera Cyclone III Family devices are utilized for hardware evaluation.

In this paper, the notion α -anti fuzzy new-ideal of a PU-algebra are defined and discussed. The homomorphic images (pre images) ofα -anti fuzzy new-ideal under homomorphism of a PU-algebras has been obtained. Some related result have been derived.

In recent years, the trend has increased for the use of cloud computing, which provides broad capabilities with the sharing of resources, and thus it is possible to store and process data in the cloud remotely, but this (cloud) is untrusted because some parties can connect to the network such as the internet and read or change data because it is not protected, therefore, protecting data security and privacy is one of the challenges that must be addressed when using cloud computing. Encryption is interested in the field of security, confidentiality and integrity of information that sent by a secure connection between individuals or institutions regardless of the method used to prepare this connection. But using the traditional encryption methods to encrypt the data before sending it will force the data provider to send his private key to the server to decrypt the data to perform computations on it. In this paper we present a proposal to secure banking data transmission through the cloud by using partially homomorphic encryption algorithms such as (paillier, RSA algorithm) that allow performing mathematical operations on encrypted data without needing to decryption. A proxy server will also use for performing re-encryption process to enhance security.

Wireless sensor networks are now in widespread use to monitor regions, detect events and acquire information. Since the deployed nodes are separated, they need to cooperatively communicate sensed data to the base station. Hence, transmissions are a very energy-consuming operation. To reduce the amount of sending data, an aggregation approach can be applied along the path from sensors to the sink. However, usually the carried information contains confidential data. Therefore, an end-to-end secure aggregation approach is required to ensure a healthy data reception. End-to-end encryption schemes that support operations over cypher-text have been proved important for private party sensor network implementations. These schemes offer two main advantages: end-to-end concealment of data and ability to operate on cipher text, then no more decryption is required for aggregation. Unfortunately, nowadays these methods are very complex and not suitable for sensor nodes having limited resources. In this paper, we propose a secure end-to-end encrypted-data aggregation scheme. It is based on elliptic curve cryptography that exploits a smaller key size. Additionally, it allows the use of higher number of operations on cypher-texts and prevents the distinction between two identical texts from their cryptograms. These properties permit to our approach to achieve higher security levels than existing cryptosystems in sensor networks. Our experiments show that our proposed secure aggregation method significantly reduces computation and communication overhead and can be practically implemented in on-the-shelf sensor platforms. By using homomorphic encryption on elliptic curves, we thus have realized an efficient and secure data aggregation in sensor networks. Lastly, to enlarge the aggregation functions that can be used in a secure wireless sensor network, a watermarking-based authentication scheme is finally proposed.