716 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
Ring-LWE Ciphertext Compression and Error Correction: Tools for Lightweight Post-Quantum Cryptography
Some lattice-based public key cryptosystems allow one to transform
ciphertext from one lattice or ring representation to another efficiently
and without knowledge of public and private keys. In this work we explore
this lattice transformation property from cryptographic engineering
viewpoint.
We apply ciphertext transformation to compress Ring-LWE ciphertexts and to
enable efficient decryption on an ultra-lightweight implementation targets
such as Internet of Things, Smart Cards, and RFID applications.
Significantly, this can be done without modifying the original
encryption procedure or its security parameters.
Such flexibility is unique to lattice-based cryptography and may find
additional, unique real-life applications.
Ciphertext compression can significantly increase the probability
of decryption errors. We show that the frequency of such errors can be
analyzed, measured and used to derive precise failure bounds for
-bit error correction. We introduce XECC, a fast multi-error correcting
code that allows constant time implementation in software.
We use these tools to construct and explore TRUNC8, a concrete
Ring-LWE encryption and authentication system. We analyze its
implementation, security, and performance. We show that our lattice
compression technique reduces ciphertext size by more
than 40% at equivalent security level, while also enabling public key
cryptography on previously unreachable ultra-lightweight platforms.
The experimental public key encryption and authentication system has been
implemented on an 8-bit AVR target, where it easily outperforms elliptic
curve and RSA-based proposals at similar security level. Similar results
have been obtained with a Cortex M0 implementation. The new
decryption code requires only a fraction of the software footprint of
previous Ring-LWE implementations with the same encryption parameters,
and is well suited for hardware implementation
Learning with Errors is easy with quantum samples
Learning with Errors is one of the fundamental problems in computational
learning theory and has in the last years become the cornerstone of
post-quantum cryptography. In this work, we study the quantum sample complexity
of Learning with Errors and show that there exists an efficient quantum
learning algorithm (with polynomial sample and time complexity) for the
Learning with Errors problem where the error distribution is the one used in
cryptography. While our quantum learning algorithm does not break the LWE-based
encryption schemes proposed in the cryptography literature, it does have some
interesting implications for cryptography: first, when building an LWE-based
scheme, one needs to be careful about the access to the public-key generation
algorithm that is given to the adversary; second, our algorithm shows a
possible way for attacking LWE-based encryption by using classical samples to
approximate the quantum sample state, since then using our quantum learning
algorithm would solve LWE
Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory
The present survey reports on the state of the art of the different
cryptographic functionalities built upon the ring learning with errors problem
and its interplay with several classical problems in algebraic number theory.
The survey is based to a certain extent on an invited course given by the
author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other
authors/ comment of the author: quotation has been added to Theorem 5.
Ring-LWE:applications to cryptography and their efficient realization
© Springer International Publishing AG 2016. The persistent progress of quantum computing with algorithms of Shor and Proos and Zalka has put our present RSA and ECC based public key cryptosystems at peril. There is a flurry of activity in cryptographic research community to replace classical cryptography schemes with their post-quantum counterparts. The learning with errors problem introduced by Oded Regev offers a way to design secure cryptography schemes in the post-quantum world. Later for efficiency LWE was adapted for ring polynomials known as Ring-LWE. In this paper we discuss some of these ring-LWE based schemes that have been designed. We have also drawn comparisons of different implementations of those schemes to illustrate their evolution from theoretical proposals to practically feasible schemes
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