838 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
A Non-commutative Cryptosystem Based on Quaternion Algebras
We propose BQTRU, a non-commutative NTRU-like cryptosystem over quaternion
algebras. This cryptosystem uses bivariate polynomials as the underling ring.
The multiplication operation in our cryptosystem can be performed with high
speed using quaternions algebras over finite rings. As a consequence, the key
generation and encryption process of our cryptosystem is faster than NTRU in
comparable parameters. Typically using Strassen's method, the key generation
and encryption process is approximately times faster than NTRU for an
equivalent parameter set. Moreover, the BQTRU lattice has a hybrid structure
that makes inefficient standard lattice attacks on the private key. This
entails a higher computational complexity for attackers providing the
opportunity of having smaller key sizes. Consequently, in this sense, BQTRU is
more resistant than NTRU against known attacks at an equivalent parameter set.
Moreover, message protection is feasible through larger polynomials and this
allows us to obtain the same security level as other NTRU-like cryptosystems
but using lower dimensions.Comment: Submitted for possible publicatio
An analysis of key generation efficiency of RSA cryptosystem in distributed environments
Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2005Includes bibliographical references (leaves: 68)Text in English Abstract: Turkish and Englishix, 74 leavesAs the size of the communication through networks and especially through Internet grew, there became a huge need for securing these connections. The symmetric and asymmetric cryptosystems formed a good complementary approach for providing this security. While the asymmetric cryptosystems were a perfect solution for the distribution of the keys used by the communicating parties, they were very slow for the actual encryption and decryption of the data flowing between them. Therefore, the symmetric cryptosystems perfectly filled this space and were used for the encryption and decryption process once the session keys had been exchanged securely. Parallelism is a hot research topic area in many different fields and being used to deal with problems whose solutions take a considerable amount of time. Cryptography is no exception and, computer scientists have discovered that parallelism could certainly be used for making the algorithms for asymmetric cryptosystems go faster and the experimental results have shown a good promise so far. This thesis is based on the parallelization of a famous public-key algorithm, namely RSA
Formal Analysis of CRT-RSA Vigilant's Countermeasure Against the BellCoRe Attack: A Pledge for Formal Methods in the Field of Implementation Security
In our paper at PROOFS 2013, we formally studied a few known countermeasures
to protect CRT-RSA against the BellCoRe fault injection attack. However, we
left Vigilant's countermeasure and its alleged repaired version by Coron et al.
as future work, because the arithmetical framework of our tool was not
sufficiently powerful. In this paper we bridge this gap and then use the same
methodology to formally study both versions of the countermeasure. We obtain
surprising results, which we believe demonstrate the importance of formal
analysis in the field of implementation security. Indeed, the original version
of Vigilant's countermeasure is actually broken, but not as much as Coron et
al. thought it was. As a consequence, the repaired version they proposed can be
simplified. It can actually be simplified even further as two of the nine
modular verifications happen to be unnecessary. Fortunately, we could formally
prove the simplified repaired version to be resistant to the BellCoRe attack,
which was considered a "challenging issue" by the authors of the countermeasure
themselves.Comment: arXiv admin note: substantial text overlap with arXiv:1401.817
Hardware and Software Multi-precision Implementations of Cryptographic Algorithms
The software implementations of cryptographic algorithms are considered to be very slow, when there are requirements of multi-precision arithmetic operations on very long integers. These arithmetic operations may include addition, subtraction, multiplication, division and exponentiation. Several research papers have been published providing different solutions to make these operations faster. Digital Signature Algorithm (DSA) is a cryptographic application that requires multi-precision arithmetic operations. These arithmetic operations are mostly based upon modular multiplication and exponentiation on integers of the size of 1024 bits. The use of such numbers is an essential part of providing high security against the cryptanalytic attacks on the authenticated messages. When these operations are implemented in software, performance in terms of speed becomes very low. The major focus of the thesis is the study of various arithmetic operations for public key cryptography and selecting the fast multi-precision arithmetic algorithms for hardware implementation. These selected algorithms are implemented in hardware and software for performance comparison and they are used to implement Digital Signature Algorithm for performance analysis
The Interpolating Random Spline Cryptosystem and the Chaotic-Map Public-Key Cryptosystem
The feasibility of implementing the interpolating cubic spline function as encryption and decryption transformations is presented. The encryption method can be viewed as computing a transposed polynomial. The main characteristic of the spline cryptosystem is that the domain and range of encryption are defined over real numbers, instead of the traditional integer numbers. Moreover, the spline cryptosystem can be implemented in terms of inexpensive multiplications and additions.
Using spline functions, a series of discontiguous spline segments can execute the modular arithmetic of the RSA system. The similarity of the RSA and spline functions within the integer domain is demonstrated. Furthermore, we observe that such a reformulation of RSA cryptosystem can be characterized as polynomials with random offsets between ciphertext values and plaintext values. This contrasts with the spline cryptosystems, so that a random spline system has been developed. The random spline cryptosystem is an advanced structure of spline cryptosystem. Its mathematical indeterminacy on computing keys with interpolants no more than 4 and numerical sensitivity to the random offset t( increases its utility.
This article also presents a chaotic public-key cryptosystem employing a one-dimensional difference equation as well as a quadratic difference equation. This system makes use of the El Gamal’s scheme to accomplish the encryption process. We note that breaking this system requires the identical work factor that is needed in solving discrete logarithm with the same size of moduli
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