550 research outputs found
Improved Fully Homomorphic Encryption with Composite Number Modulus
Gentry’s bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In previous work I proposed a fully homomorphic encryption without bootstrapping which has the weak point in the plaintext. I also proposed a fully homomorphic encryption with composite number modulus which avoids the weak point by adopting the plaintext including the random numbers in it. In this paper I propose another fully homomorphic encryption with composite number modulus where the complexity required for enciphering and deciphering is smaller than the same modulus RSA scheme. In the proposed scheme it is proved that if there exists the PPT algorithm that decrypts the plaintext from the any ciphertexts of the proposed scheme, there exists the PPT algorithm that factors the given composite number modulus. In addition it is said that the proposed fully homomorphic encryption scheme is immune from the “p and -p attack”. Since the scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. Because proposed fully homomorphic encryption scheme is based on multivariate algebraic equations with high degree or too many variables, it is against the Gröbner basis attack, the differential attack, rank attack and so on
Fully Homomorphic Encryption with Composite Number Modulus
Gentry’s bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In previous work I proposed a fully homomorphic encryption without bootstrapping which has the weak point in the plaintext. In this paper I propose the improved fully homomorphic encryption scheme on non-associative octonion ring over finite ring with composite number modulus where the plaintext p consists of three numbers u,v,w. The proposed fully homomorphic encryption scheme is immune from the “p and -p attack”. As the scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. Because proposed fully homomorphic encryption scheme is based on multivariate algebraic equations with high degree or too many variables, it is against the Gröbner basis attack, the differential attack, rank attack and so on.
It is proved that if there exists the PPT algorithm that decrypts the plaintext from the ciphertexts of the proposed scheme, there exists the PPT algorithm that factors the given composite number modulus
Fully Homomorphic Public-Key Encryption with Two Ciphertexts based on Discrete Logarithm Problem
In previous paper I proposed the fully homomorphic public-key encryption based on discrete logarithm problem which may be vulnerable to “m and -m attack”. In this paper I propose improved fully homomorphic public-key encryption (FHPKE) with composite number modulus based on the discrete logarithm assumption (DLA) and computational Diffie–Hellman assumption (CDH) of multivariate polynomials on octonion ring which is immune from “m and -m attack”. The scheme has two ciphertexts corresponding to one plaintext
A Survey on Homomorphic Encryption Schemes: Theory and Implementation
Legacy encryption systems depend on sharing a key (public or private) among
the peers involved in exchanging an encrypted message. However, this approach
poses privacy concerns. Especially with popular cloud services, the control
over the privacy of the sensitive data is lost. Even when the keys are not
shared, the encrypted material is shared with a third party that does not
necessarily need to access the content. Moreover, untrusted servers, providers,
and cloud operators can keep identifying elements of users long after users end
the relationship with the services. Indeed, Homomorphic Encryption (HE), a
special kind of encryption scheme, can address these concerns as it allows any
third party to operate on the encrypted data without decrypting it in advance.
Although this extremely useful feature of the HE scheme has been known for over
30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE)
scheme, which allows any computable function to perform on the encrypted data,
was introduced by Craig Gentry in 2009. Even though this was a major
achievement, different implementations so far demonstrated that FHE still needs
to be improved significantly to be practical on every platform. First, we
present the basics of HE and the details of the well-known Partially
Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which
are important pillars of achieving FHE. Then, the main FHE families, which have
become the base for the other follow-up FHE schemes are presented. Furthermore,
the implementations and recent improvements in Gentry-type FHE schemes are also
surveyed. Finally, further research directions are discussed. This survey is
intended to give a clear knowledge and foundation to researchers and
practitioners interested in knowing, applying, as well as extending the state
of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the
survey that is being submitted to ACM CSUR and has been uploaded to arXiv for
feedback from stakeholder
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
Privately Connecting Mobility to Infectious Diseases via Applied Cryptography
Human mobility is undisputedly one of the critical factors in infectious
disease dynamics. Until a few years ago, researchers had to rely on static data
to model human mobility, which was then combined with a transmission model of a
particular disease resulting in an epidemiological model. Recent works have
consistently been showing that substituting the static mobility data with
mobile phone data leads to significantly more accurate models. While prior
studies have exclusively relied on a mobile network operator's subscribers'
aggregated data, it may be preferable to contemplate aggregated mobility data
of infected individuals only. Clearly, naively linking mobile phone data with
infected individuals would massively intrude privacy. This research aims to
develop a solution that reports the aggregated mobile phone location data of
infected individuals while still maintaining compliance with privacy
expectations. To achieve privacy, we use homomorphic encryption, zero-knowledge
proof techniques, and differential privacy. Our protocol's open-source
implementation can process eight million subscribers in one and a half hours.
Additionally, we provide a legal analysis of our solution with regards to the
EU General Data Protection Regulation.Comment: Added differentlial privacy experiments and new benchmark
Towards the AlexNet Moment for Homomorphic Encryption: HCNN, theFirst Homomorphic CNN on Encrypted Data with GPUs
Deep Learning as a Service (DLaaS) stands as a promising solution for
cloud-based inference applications. In this setting, the cloud has a
pre-learned model whereas the user has samples on which she wants to run the
model. The biggest concern with DLaaS is user privacy if the input samples are
sensitive data. We provide here an efficient privacy-preserving system by
employing high-end technologies such as Fully Homomorphic Encryption (FHE),
Convolutional Neural Networks (CNNs) and Graphics Processing Units (GPUs). FHE,
with its widely-known feature of computing on encrypted data, empowers a wide
range of privacy-concerned applications. This comes at high cost as it requires
enormous computing power. In this paper, we show how to accelerate the
performance of running CNNs on encrypted data with GPUs. We evaluated two CNNs
to classify homomorphically the MNIST and CIFAR-10 datasets. Our solution
achieved a sufficient security level (> 80 bit) and reasonable classification
accuracy (99%) and (77.55%) for MNIST and CIFAR-10, respectively. In terms of
latency, we could classify an image in 5.16 seconds and 304.43 seconds for
MNIST and CIFAR-10, respectively. Our system can also classify a batch of
images (> 8,000) without extra overhead
SHE based Non Interactive Privacy Preserving Biometric Authentication Protocols
Being unique and immutable for each person, biometric signals are widely used in access control systems. While biometric recognition appeases concerns about password's theft or loss, at the same time it raises concerns about individual privacy. Central servers store several enrolled biometrics, hence security against theft must be provided during biometric transmission and against those who have access to the database. If a server's database is compromised, other systems using the same biometric templates could also be compromised as well. One solution is to encrypt the stored templates. Nonetheless, when using traditional cryptosystem, data must be decrypted before executing the protocol, leaving the database vulnerable. To overcame this problem and protect both the server and the client, biometrics should be processed while encrypted. This is possible by using secure two-party computation protocols, mainly based on Garbled Circuits (GC) and additive Homomorphic Encryption (HE). Both GC and HE based solutions are efficient yet interactive, meaning that the client takes part in the computation. Instead in this paper we propose a non-interactive protocol for privacy preserving biometric authentication based on a Somewhat Homomorphic Encryption (SHE) scheme, modified to handle integer values, and also suggest a blinding method to protect the system from spoofing attacks. Although our solution is not as efficient as the ones based on GC or HE, the protocol needs no interaction, moving the computation entirely on the server side and leaving only inputs encryption and outputs decryption to the client
- …