613 research outputs found
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
Why you cannot even hope to use Gr\uf6bner bases in cryptography: an eternal golden braid of failures
In 1994, Moss Sweedler\u2019s dog proposed a cryptosystem, known as Barkee\u2019s Cryptosystem, and the related cryptanalysis. Its explicit aim was to dispel the proposal of using the urban legend that \u201cGr\uf6bner bases are hard to compute\u201d, in order to devise a public key cryptography scheme. Therefore he claimed that \u201cno scheme using Gr\uf6bner bases will ever work\u201d. Later, further variations of Barkee\u2019s Cryptosystem were proposed on the basis of another urban legend, related to the infiniteness (and consequent uncomputability) of non-commutative Gr\uf6bner bases; unfortunately Pritchard\u2019s algorithm for computing (finite) non-commutative Gr\uf6bner bases was already available at that time and was sufficient to crash the system proposed by Ackermann and Kreuzer. The proposal by Rai, where the private key is a principal ideal and the public key is a bunch of polynomials within this principal ideal, is surely immune to Pritchard\u2019s attack but not to Davenport\u2019s factorization algorithm. It was recently adapted specializing and extending Stickel\u2019s Diffie\u2013Hellman protocols in the setting of Ore extension. We here propose a further generalization and show that such protocols can be broken simply via polynomial division and Buchberger reduction
Oracle-supported drawing of the Groebner {\em escalier}
The aim of this note is to discuss the following quite queer Problem:
\noindent GIVEN \noindent i) the free non-commutative polynomial ring, {\Cal
P} := {\Bbb F}\langle X_1,\ldots,X_n\rangle {\em (public)}, \noindent ii) a
bilateral ideal {\em
(private)}, \noindent iii) a finite set
of elements of the ideal {\em (public)}, \noindent a noetherian
semigroup term-ordering {\rm (private)}, on the word semigroup {\Cal
T} := , \noindent COMPUTE \noindent --a finite subset
of the Gr\"obner basis of
w.r.t. s.t., for each its {\em normal form}
w.r.t. is zero, \noindent "by means of a finite number of queries to an
oracle", which, \noindent given a term \tau\in{\Cal T} returns its {\em
canonical form} \Can(\tau,{\sf I},\prec) w.r.t. the ideal and the
term-ordering . \qed This queer problem has been suggested to us by
Bulygin (2005) where a similar problem, but with stronger assumptions, is faced
in order to set up a chosen-cyphertext attack against the cryptographic system
proposed in Rai (2004)
Why Children Should Attend Summer Camp: The Benefits of Residential Summer Camp and Outdoor Education
Summer camp has been a long tradition for many families across the United States. It is a favorite summer activity and an important time of social and developmental growth for many children. The purpose of this project was to dive into the history of summer camps and outdoor education in the United States as well as the many benefits attending summer camp can provide to children. Children attend summer camp to have a great experience, make friends, and learn to have some independence from their families. Camp counselors work at summer camp to care for children and show them that a week full of fun can also be educational and beneficial to their growth. This project will walk the reader through a quick history of summer camp and outdoor education and their purpose in society and then provide a detailed explanation of the benefits and challenges of summer camp
On FHE without bootstrapping
We investigate the use of multivariate polynomials in constructing a fully homomorphic encryption. In this work we come up with two fully homomorphic schemes. First, we propose an IND-CPA secure symmetric key homomorphic encryption scheme using multivariate polynomial ring over finite fields. This scheme gives a method of constructing a CPA secure homomorphic encryption scheme from another symmetric deterministic CPA secure scheme. We base the security of the scheme on pseudo random functions and also construct an information theoretically secure variant, rather than basing security on hard problems like Ideal Membership and Gröbner basis as seen in most polly cracker based schemes which also use multivariate polynomial rings. This scheme is not compact but has many interesting properties- It can evaluate circuits of arbitrary depths without bootstrapping for bounded length input to the algorithm. Second what follows naturally is, an attempt to make it compact we propose some changes to the scheme and analyse the scheme in (Albrecht et. al. Asiacrypt-2011). We try to make it compact but fail and realise that this could give us a Multi Party Computation protocol. Realising that polynomials leads us to non compact schemes we move propose schemes based on matrices. We then propose our candidate for a fully homomorphic encryption without bootstrapping
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