We propose a fully homomorphic encryption scheme -- i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result -- that, to construct an encryption scheme that permits evaluation of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable.Next, we describe a public key encryption scheme using ideal lattices that is almost bootstrappable.Lattice-based cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a public-key ideal in a polynomial ring that is represented as a lattice), as needed to evaluate general circuits.Unfortunately, our initial scheme is not quite bootstrappable -- i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than the former. In the final step, we show how to modify the scheme to reduce the depth of the decryption circuit, and thereby obtain a bootstrappable encryption scheme, without reducing the depth that the scheme can evaluate. Abstractly, we accomplish this by enabling the encrypter to start the decryption process, leaving less work for the decrypter, much like the server leaves less work for the decrypter in a server-aided cryptosystem.

/pdf/fully-homomorphic-encryption-using-ideal-lattices-3oirjo0huq.pdf

Fully homomorphic encryption using ideal lattices

Evolutionary psychology is one of many biologically informed approaches to the study of human behavior. Along with cognitive psychologists, evolutionary psychologists propose that much, if not all, of our behavior can be explained by appeal to internal psychological mechanisms. What distinguishes evolutionary psychologists from many cognitive psychologists is the proposal that the relevant internal mechanisms are adaptations—products of natural selection—that helped our ancestors get around the world, survive and reproduce. To understand the central claims of evolutionary psychology we require an understanding of some key concepts in evolutionary biology, cognitive psychology, philosophy of science and philosophy of mind. Philosophers are interested in evolutionary psychology for a number of reasons. For philosophers of science —mostly philosophers of biology—evolutionary psychology provides a critical target. There is a broad consensus among philosophers of science that evolutionary psychology is a deeply flawed enterprise. For philosophers of mind and cognitive science evolutionary psychology has been a source of empirical hypotheses about cognitive architecture and specific components of that architecture. Philosophers of mind are also critical of evolutionary psychology but their criticisms are not as all-encompassing as those presented by philosophers of biology. Evolutionary psychology is also invoked by philosophers interested in moral psychology both as a source of empirical hypotheses and as a critical target.

/pdf/stanford-encyclopedia-of-philosophy-1wqoykisq0.pdf

Stanford Encyclopedia of Philosophy

As more sensitive data is shared and stored by third-party sites on the Internet, there will be a need to encrypt data stored at these sites. One drawback of encrypting data, is that it can be selectively shared only at a coarse-grained level (i.e., giving another party your private key). We develop a new cryptosystem for fine-grained sharing of encrypted data that we call Key-Policy Attribute-Based Encryption (KP-ABE). In our cryptosystem, ciphertexts are labeled with sets of attributes and private keys are associated with access structures that control which ciphertexts a user is able to decrypt. We demonstrate the applicability of our construction to sharing of audit-log information and broadcast encryption. Our construction supports delegation of private keys which subsumesHierarchical Identity-Based Encryption (HIBE).

/pdf/attribute-based-encryption-for-fine-grained-access-control-3fjqefx4um.pdf

Attribute-based encryption for fine-grained access control of encrypted data

We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel.

/pdf/short-signatures-from-the-weil-pairing-5ajupg0cpi.pdf

Short Signatures from the Weil Pairing

Driven by the visions of Internet of Things and 5G communications, recent years have seen a paradigm shift in mobile computing, from the centralized mobile cloud computing toward mobile edge computing (MEC). The main feature of MEC is to push mobile computing, network control and storage to the network edges (e.g., base stations and access points) so as to enable computation-intensive and latency-critical applications at the resource-limited mobile devices. MEC promises dramatic reduction in latency and mobile energy consumption, tackling the key challenges for materializing 5G vision. The promised gains of MEC have motivated extensive efforts in both academia and industry on developing the technology. A main thrust of MEC research is to seamlessly merge the two disciplines of wireless communications and mobile computing, resulting in a wide-range of new designs ranging from techniques for computation offloading to network architectures. This paper provides a comprehensive survey of the state-of-the-art MEC research with a focus on joint radio-and-computational resource management. We also discuss a set of issues, challenges, and future research directions for MEC research, including MEC system deployment, cache-enabled MEC, mobility management for MEC, green MEC, as well as privacy-aware MEC. Advancements in these directions will facilitate the transformation of MEC from theory to practice. Finally, we introduce recent standardization efforts on MEC as well as some typical MEC application scenarios.

A Survey on Mobile Edge Computing: The Communication Perspective

We describe two new public key broadcast encryption systems for stateless receivers. Both systems are fully secure against any number of colluders. In our first construction both ciphertexts and private keys are of constant size (only two group elements), for any subset of receivers. The public key size in this system is linear in the total number of receivers. Our second system is a generalization of the first that provides a tradeoff between ciphertext size and public key size. For example, we achieve a collusion resistant broadcast system for n users where both ciphertexts and public keys are of size $O(\sqrt{N})$ for any subset of receivers. We discuss several applications of these systems.

/pdf/collusion-resistant-broadcast-encryption-with-short-31dhzqvvof.pdf

Collusion resistant broadcast encryption with short ciphertexts and private keys

We introduce and formalize the notion of Verifiable Computation, which enables a computationally weak client to "outsource" the computation of a function F on various dynamically-chosen inputs x1, ...,xk to one or more workers. The workers return the result of the function evaluation, e.g., yi = F(xi), as well as a proof that the computation of F was carried out correctly on the given value xi. The primary constraint is that the verification of the proof should require substantially less computational effort than computing F(i) from scratch.

We present a protocol that allows the worker to return a computationally-sound, non-interactive proof that can be verified in O(mċpoly(λ)) time, where m is the bit-length of the output of F, and λ is a security parameter. The protocol requires a one-time pre-processing stage by the client which takes O(|C|ċpoly(λ)) time, where C is the smallest known Boolean circuit computing F. Unlike previous work in this area, our scheme also provides (at no additional cost) input and output privacy for the client, meaning that the workers do not learn any information about the xi or yi values.

https://link.springer.com/content/pdf/10.1007%2F978-3-642-14623-7_25.pdf

Non-interactive verifiable computing: outsourcing computation to untrusted workers

In this work, we study indistinguishability obfuscation and functional encryption for general circuits: Indistinguishability obfuscation requires that given any two equivalent circuits C0 and C1 of similar size, the obfuscations of C0 and C1 should be computationally indistinguishable. In functional encryption, cipher texts encrypt inputs x and keys are issued for circuits C. Using the key SKC to decrypt a cipher text CTx = Enc(x), yields the value C(x) but does not reveal anything else about x. Furthermore, no collusion of secret key holders should be able to learn anything more than the union of what they can each learn individually. We give constructions for indistinguishability obfuscation and functional encryption that supports all polynomial-size circuits. We accomplish this goal in three steps: - (1) We describe a candidate construction for indistinguishability obfuscation for NC1 circuits. The security of this construction is based on a new algebraic hardness assumption. The candidate and assumption use a simplified variant of multilinear maps, which we call Multilinear Jigsaw Puzzles. (2) We show how to use indistinguishability obfuscation for NC1 together with Fully Homomorphic Encryption (with decryption in NC1) to achieve indistinguishability obfuscation for all circuits. (3) Finally, we show how to use indistinguishability obfuscation for circuits, public-key encryption, and non-interactive zero knowledge to achieve functional encryption for all circuits. The functional encryption scheme we construct also enjoys succinct cipher texts, which enables several other applications.

/pdf/candidate-indistinguishability-obfuscation-and-functional-1pg05ss4tz.pdf

Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits

We describe plausible lattice-based constructions with properties that approximate the sought-after multilinear maps in hard-discrete-logarithm groups, and show an example application of such multi-linear maps that can be realized using our approximation. The security of our constructions relies on seemingly hard problems in ideal lattices, which can be viewed as extensions of the assumed hardness of the NTRU function.

/pdf/candidate-multilinear-maps-from-ideal-lattices-iubgttyi7z.pdf

Candidate Multilinear Maps from Ideal Lattices

We describe a working implementation of leveled homomorphic encryption without bootstrapping that can evaluate the AES-128 circuit in three different ways. One variant takes under over 36 hours to evaluate an entire AES encryption operation, using NTL over GMP as our underlying software platform, and running on a large-memory machine. Using SIMD techniques, we can process over 54 blocks in each evaluation, yielding an amortized rate of just under 40 minutes per block. Another implementation takes just over two and a half days to evaluate the AES operation, but can process 720 blocks in each evaluation, yielding an amortized rate of just over five minutes per block. We also detail a third implementation, which theoretically could yield even better amortized complexity, but in practice turns out to be less competitive.

For our implementations we develop both AES-specific optimizations as well as several "generic" tools for FHE evaluation. These last tools include among others a different variant of the Brakerski-Vaikuntanathan key-switching technique that does not require reducing the norm of the ciphertext vector, and a method of implementing the Brakerski-Gentry-Vaikuntanathan modulus-switching transformation on ciphertexts in CRT representation.

/pdf/homomorphic-evaluation-of-the-aes-circuit-1oeujlbrxz.pdf

Craig Gentry

Papers

Collusion resistant broadcast encryption with short ciphertexts and private keys

Non-interactive verifiable computing: outsourcing computation to untrusted workers

Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits

Candidate Multilinear Maps from Ideal Lattices

Homomorphic Evaluation of the AES Circuit