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.

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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.

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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).

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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.

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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

Suppose that you want to delegate the ability to process your data, without giving away access to it. We show that this separation is possible: we describe a "fully homomorphic" encryption scheme that keeps data private, but that allows a worker that does not have the secret decryption key to compute any (still encrypted) result of the data, even when the function of the data is very complex. In short, a third party can perform complicated processing of data without being able to see it. Among other things, this helps make cloud computing compatible with privacy.

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Computing arbitrary functions of encrypted data

We introduce a new characterization of the NP complexity class, called Quadratic Span Programs (QSPs), which is a natural extension of span programs defined by Karchmer and Wigderson. Our main motivation is the quick construction of succinct, easily verified arguments for NP statements.

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Quadratic Span Programs and Succinct NIZKs without PCPs

An argument system for NP is succinct, if its communication complexity is polylogarithmic the instance and witness sizes. The seminal works of Kilian '92 and Micali '94 show that such arguments can be constructed under standard cryptographic hardness assumptions with four rounds of interaction, and that they be made non-interactive in the random-oracle model. However, we currently do not have any construction of succinct non-interactive arguments (SNARGs) in the standard model with a proof of security under any simple cryptographic assumption.In this work, we give a broad black-box separation result, showing that black-box reductions cannot be used to prove the security of any SNARG construction based on any falsifiable cryptographic assumption. This includes essentially all common assumptions used in cryptography (one-way functions, trapdoor permutations, DDH, RSA, LWE etc.). More generally, we say that an assumption is falsifiable if it can be modeled as an interactive game between an adversary and an efficient challenger that can efficiently decide if the adversary won the game. This is similar, in spirit, to the notion of falsifiability of Naor '03, and captures the fact that we can efficiently check if an adversarial strategy breaks the assumption.Our separation result also extends to designated verifier SNARGs, where the verifier needs a trapdoor associated with the CRS to verify arguments, and slightly succinct SNARGs, whose size is only required to be sublinear in the statement and witness size.

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Separating succinct non-interactive arguments from all falsifiable assumptions

We show that homomorphic evaluation of (wide enough) arithmetic circuits can be accomplished with only polylogarithmic overhead. Namely, we present a construction of fully homomorphic encryption (FHE) schemes that for security parameter λ can evaluate any width-Ω(λ) circuit with t gates in time t· polylog(λ).

To get low overhead, we use the recent batch homomorphic evaluation techniques of Smart-Vercauteren and Brakerski-Gentry-Vaikuntanathan, who showed that homomorphic operations can be applied to "packed" ciphertexts that encrypt vectors of plaintext elements. In this work, we introduce permuting/routing techniques to move plaintext elements across these vectors efficiently. Hence, we are able to implement general arithmetic circuit in a batched fashion without ever needing to "unpack" the plaintext vectors.

We also introduce some other optimizations that can speed up homomorphic evaluation in certain cases. For example, we show how to use the Frobenius map to raise plaintext elements to powers of p at the "cost" of a linear operation.

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Fully homomorphic encryption with polylog overhead

We introduce the notion of certificate-based encryption. In this model, a certificate – or, more generally, a signature – acts not only as a certificate but also as a decryption key. To decrypt a message, a keyholder needs both its secret key and an up-to-date certificate from its CA (or a signature from an authorizer). Certificate-based encryption combines the best aspects of identity-based encryption (implicit certification) and public key encryption (no escrow). We demonstrate how certificate-based encryption can be used to construct an efficient PKI requiring less infrastructure than previous proposals, including Micali’s Novomodo, Naor-Nissim and Aiello-Lodha-Ostrovsky. Comment: This is a version of the Eurocrypt 2003 paper, identical except for this comment and a correction in Section 3.2. I’m posting it online to make it more widely available, particularly since a couple of recent works propose essentially the same idea.

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Craig Gentry

Papers

Computing arbitrary functions of encrypted data

Quadratic Span Programs and Succinct NIZKs without PCPs

Separating succinct non-interactive arguments from all falsifiable assumptions

Fully homomorphic encryption with polylog overhead

Certificate-Based Encryption and the Certificate Revocation Problem.