359 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
Cloud Computing in the Quantum Era
Cloud computing has become the prominent technology of this era. Its elasticity, dynamicity, availability, heterogeneity, and pay as you go pricing model has attracted several companies to migrate their businesses' services into the cloud. This gives them more time to focus solely on their businesses and reduces the management and backup overhead leveraging the flexibility of cloud computing. On the other hand, quantum technology is developing very rapidly. Experts are expecting to get an efficient quantum computer within the next decade. This has a significant impact on several sciences including cryptography, medical research, and other fields. This paper analyses the reciprocal impact of quantum technology on cloud computing and vice versa
Approximate common divisors via lattices
We analyze the multivariate generalization of Howgrave-Graham's algorithm for
the approximate common divisor problem. In the m-variable case with modulus N
and approximate common divisor of size N^beta, this improves the size of the
error tolerated from N^(beta^2) to N^(beta^((m+1)/m)), under a commonly used
heuristic assumption. This gives a more detailed analysis of the hardness
assumption underlying the recent fully homomorphic cryptosystem of van Dijk,
Gentry, Halevi, and Vaikuntanathan. While these results do not challenge the
suggested parameters, a 2^(n^epsilon) approximation algorithm with epsilon<2/3
for lattice basis reduction in n dimensions could be used to break these
parameters. We have implemented our algorithm, and it performs better in
practice than the theoretical analysis suggests.
Our results fit into a broader context of analogies between cryptanalysis and
coding theory. The multivariate approximate common divisor problem is the
number-theoretic analogue of multivariate polynomial reconstruction, and we
develop a corresponding lattice-based algorithm for the latter problem. In
particular, it specializes to a lattice-based list decoding algorithm for
Parvaresh-Vardy and Guruswami-Rudra codes, which are multivariate extensions of
Reed-Solomon codes. This yields a new proof of the list decoding radii for
these codes.Comment: 17 page
A Like ELGAMAL Cryptosystem But Resistant To Post-Quantum Attacks
The Modulo 1 Factoring Problem (M1FP) is an elegant mathematical problem which could be exploited to design safe cryptographic protocols and encryption schemes that resist to post quantum attacks. The ELGAMAL encryption scheme is a well-known and efficient public key algorithm designed by Taher ELGAMAL from discrete logarithm problem. It is always highly used in Internet security and many other applications after a large number of years. However, the imminent arrival of quantum computing threatens the security of ELGAMAL cryptosystem and impose to cryptologists to prepare a resilient algorithm to quantum computer-based attacks. In this paper we will present a like-ELGAMAL cryptosystem based on the M1FP NP-hard problem. This encryption scheme is very simple but efficient and supposed to be resistant to post quantum attacks
Attack on Fully Homomorphic Encryption over the Integers
This paper presents a heuristic attack on the fully homomorphic encryption
over the integers by using lattice reduction algorithm. Our result shows that
the FHE in [DGHV10] is not secure for some parameter settings. We also present
an improvement scheme to avoid the lattice attack in this paper.Comment: 24 page
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
SALSA: Attacking Lattice Cryptography with Transformers
Currently deployed public-key cryptosystems will be vulnerable to attacks by
full-scale quantum computers. Consequently, "quantum resistant" cryptosystems
are in high demand, and lattice-based cryptosystems, based on a hard problem
known as Learning With Errors (LWE), have emerged as strong contenders for
standardization. In this work, we train transformers to perform modular
arithmetic and combine half-trained models with statistical cryptanalysis
techniques to propose SALSA: a machine learning attack on LWE-based
cryptographic schemes. SALSA can fully recover secrets for small-to-mid size
LWE instances with sparse binary secrets, and may scale to attack real-world
LWE-based cryptosystems.Comment: Extended version of work published at NeurIPS 202
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