25 research outputs found
Noise-Free Symmetric Fully Homomorphic Encryption Based on Non-Commutative Rings
A framework of noise-free symmetric fully homomorphic encryption
(FHE) is proposed in this work. Dierent from the frameworks that are dened over non-commutative groups, our framework is constructed from matrices over noncommutative rings. The scheme is one-way secure against
chosen plaintext attacks (OW-CPA) based on the factorization
problem of matrices over noncommutative rings as well as the hardness of an overdened system of multivariate polynomial equations over the given non-commutative algebraic structure. On the basis of this framework, a verifiable FHE is proposed, where the receiver can check the validity of ciphertexts
A Verifiable Fully Homomorphic Encryption Scheme for Cloud Computing Security
Performing smart computations in a context of cloud computing and big data is
highly appreciated today. Fully homomorphic encryption (FHE) is a smart
category of encryption schemes that allows working with the data in its
encrypted form. It permits us to preserve confidentiality of our sensible data
and to benefit from cloud computing powers. Currently, it has been demonstrated
by many existing schemes that the theory is feasible but the efficiency needs
to be dramatically improved in order to make it usable for real applications.
One subtle difficulty is how to efficiently handle the noise. This paper aims
to introduce an efficient and verifiable FHE based on a new mathematic
structure that is noise free
Can there be efficient and natural FHE schemes?
In 1978, Rivest, Adleman and Dertouzos asked for algebraic systems for which useful privacy homomorphisms exist. To date, the only acknownledged result is noise based encryption combined with bootstrapping. Before that, there were several failed attempts.
We prove that fully homomorphic schemes are impossible for several algebraic structures. Then we develop a characterisation of all fully homomorphic schemes and use it to analyse three examples. Finally, we propose a conjecture stating that secure FHE schemes must either have a significant ciphertext expansion or use unusual algebraic structures
An improved Framework for Biometric Database’s privacy
Security and privacy are huge challenges in biometric systems. Biometrics are sensitive data that should be protected from any attacker and especially attackers targeting the confidentiality and integrity of biometric data. In this paper an extensive review of different physiological biometric techniques is provided. A comparative analysis of the various sus mentioned biometrics, including characteristics and properties is conducted. Qualitative and quantitative evaluation of the most relevant physiological biometrics is achieved. Furthermore, we propose a new framework for biometric database privacy. Our approach is based on the use of the promising fully homomorphic encryption technology. As a proof of concept, we establish an initial implementation of our security module using JAVA programming language
International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022
Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022.
Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress.
The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library
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
Homomorphic encryption in algebraic settings
PhD ThesisCryptography methods have been around for a long time to protect sensitive data. With
data sets becoming increasingly large we wish to not only store sensitive data in public
clouds but in fact, analyse and compute there too. The idea behind homomorphic encryption
is that encryption preserves the structure and allows us to perform the same
operations on ciphertext as we would on the plaintext. A lot of the work so far restricts
the operations that can be performed correctly on ciphertexts. The goal of this thesis is
to explore methods for encryption which should greatly increase the amount of analysis
and computation that can be performed on ciphertexts.
First of all, we will consider the implications of quantum computers on cryptography.
There has already been research conducted into quantum-resistant encryption methods.
The particular method we will be interested in is still classical. We are assuming these
schemes are going to be used in a post-quantum world anyway, we look at how we can use
the quantum properties to improve the cryptosystem. More speci cally, we aim to remove
a restriction that naturally comes with the scheme restricting how many operations we
can perform on ciphertexts.
Secondly, we propose a key exchange protocol that works in a polynomial ideal setting.
We do this so that the key can be used for a homomorphic cryptography protocol. The
advantage of using key exchange over a public key system is that a large proportion of the
process needs to be carried out only once instead of needing a more complicated encryption
function to use for each piece of data. Polynomial rings are an appropriate choice of
structure for this particular type of scheme as they allow us to do everything we need. We
will examine how we can perform computation correctly on ciphertexts and address some
of the potential weaknesses of such a process.
Finally after establishing a fully homomorphic encryption system we will take a more
in-depth look at complexity. Measuring the complexity of mathematical problems is, of
course, crucial in cryptography, but the choice of measure is something we need to consider
seriously. In the nal chapter we will look at generic complexity as its gives us a good feel
for how di cult the typical instances of a problem are to solve.Engineering and Physical Sciences Research Council, Centre
for Doctoral Training in Cloud Computing for Big Dat
Compressible FHE with Applications to PIR
Homomorphic encryption (HE) is often viewed as impractical, both in communication and computation. Here we provide an additively homomorphic encryption scheme based on (ring) LWE with nearly optimal rate ( for any ). Moreover, we describe how to compress many FHE ciphertexts that may have come from a homomorphic evaluation (e.g., of the Gentry-Sahai-Waters (GSW) scheme), into fewer high-rate ciphertexts.
Using our high-rate HE scheme, we are able for the first time to describe a single-server private information retrieval (PIR) scheme with sufficiently low computational overhead so as to be practical for large databases. Single-server PIR inherently requires the server to perform at least one bit operation per database bit, and we describe a rate-(4/9) scheme with computation which is not so much worse than this inherent lower bound. In fact it is probably faster than whole-database AES encryption -- specifically under 1.8 mod- multiplication per database byte, where is about 50 to 60 bits.
Asymptotically, the computational overhead of our PIR scheme is \tilde{O}(\log \log \secparam + \log \log \log N), where \secparam is the security parameter and is the number of database files, which are assumed to be sufficiently large
Applying Secure Multi-party Computation in Practice
In this work, we present solutions for technical difficulties in deploying secure multi-party computation in real-world applications. We will first give a brief overview of the current state of the art, bring out several shortcomings and address them.
The main contribution of this work is an end-to-end process description of deploying secure multi-party computation for the first large-scale registry-based statistical study on linked databases. Involving large stakeholders like government institutions introduces also some non-technical requirements like signing contracts and negotiating with the Data Protection Agency