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

Distributed Sensor Networks (DSNs) are ad-hoc mobile networks that include sensor nodes with limited computation and communication capabilities. DSNs are dynamic in the sense that they allow addition and deletion of sensor nodes after deployment to grow the network or replace failing and unreliable nodes. DSNs may be deployed in hostile areas where communication is monitored and nodes are subject to capture and surreptitious use by an adversary. Hence DSNs require cryptographic protection of communications, sensor-capture detection, key revocation and sensor disabling. In this paper, we present a key-management scheme designed to satisfy both operational and security requirements of DSNs. The scheme includes selective distribution and revocation of keys to sensor nodes as well as node re-keying without substantial computation and communication capabilities. It relies on probabilistic key sharing among the nodes of a random graph and uses simple protocols for shared-key discovery and path-key establishment, and for key revocation, re-keying, and incremental addition of nodes. The security and network connectivity characteristics supported by the key-management scheme are discussed and simulation experiments presented.

/pdf/a-key-management-scheme-for-distributed-sensor-networks-2arngir92b.pdf

A key-management scheme for distributed sensor networks

This paper describes a new replication algorithm that is able to tolerate Byzantine faults. We believe that Byzantinefault-tolerant algorithms will be increasingly important in the future because malicious attacks and software errors are increasingly common and can cause faulty nodes to exhibit arbitrary behavior. Whereas previous algorithms assumed a synchronous system or were too slow to be used in practice, the algorithm described in this paper is practical: it works in asynchronous environments like the Internet and incorporates several important optimizations that improve the response time of previous algorithms by more than an order of magnitude. We implemented a Byzantine-fault-tolerant NFS service using our algorithm and measured its performance. The results show that our service is only 3% slower than a standard unreplicated NFS.

/pdf/practical-byzantine-fault-tolerance-58gb0de0hd.pdf

Practical Byzantine fault tolerance

National Institute of Standards and Technology における超伝導研究及び生活

We introduce a model for provable data possession (PDP) that allows a client that has stored data at an untrusted server to verify that the server possesses the original data without retrieving it. The model generates probabilistic proofs of possession by sampling random sets of blocks from the server, which drastically reduces I/O costs. The client maintains a constant amount of metadata to verify the proof. The challenge/response protocol transmits a small, constant amount of data, which minimizes network communication. Thus, the PDP model for remote data checking supports large data sets in widely-distributed storage system.We present two provably-secure PDP schemes that are more efficient than previous solutions, even when compared with schemes that achieve weaker guarantees. In particular, the overhead at the server is low (or even constant), as opposed to linear in the size of the data. Experiments using our implementation verify the practicality of PDP and reveal that the performance of PDP is bounded by disk I/O and not by cryptographic computation.

/pdf/provable-data-possession-at-untrusted-stores-2jbt1jxu32.pdf

Provable data possession at untrusted stores

We describe a parallelizable block-cipher mode of operation that simultaneously provides privacy and authenticity. OCB encrypts-and-authenticates a nonempty string M e {0,1} using \lceil |M|/n\rceil + 2 block-cipher invocations, where n is the block length of the underlying block cipher. Additional overhead is small. OCB refines a scheme, IAPM, suggested by Charanjit Jutla. Desirable properties of OCB include: the ability to encrypt a bit string of arbitrary length into a ciphertext of minimal length; cheap offset calculations; cheap session setup; a single underlying cryptographic key; no extended-precision addition; a nearly optimal number of block-cipher calls; and no requirement for a random IV. We prove OCB secure, quantifying the adversary's ability to violate the mode's privacy or authenticity in terms of the quality of its block cipher as a pseudorandom permutation (PRP) or as a strong PRP, respectively.

/pdf/ocb-a-block-cipher-mode-of-operation-for-efficient-6z81aboaqg.pdf

OCB: a block-cipher mode of operation for efficient authenticated encryption

We describe a message authentication algorithm, UMAC, which can authenticate messages (in software, on contemporary machines) roughly an order of magnitude faster than current practice (e.g., HMAC-SHA1), and about twice as fast as times previously reported for the universal hash-function family MMH. To achieve such speeds, UMAC uses a new universal hash-function family, NH, and a design which allows effective exploitation of SIMD parallelism. The "cryptographic" work of UMAC is done using standard primitives of the user's choice, such as a block cipher or cryptographic hash function; no new heuristic primitives are developed here. Instead, the security of UMAC is rigorously proven, in the sense of giving exact and quantitatively strong results which demonstrate an inability to forge UMAC-authenticated messages assuming an inability to break the underlying cryptographic primitive. Unlike conventional, inherently serial MACs, UMAC is parallelizable, and will have ever-faster implementation speeds as machines offer up increasing amounts of parallelism. We envision UMAC as a practical algorithm for next-generation message authentication.

/pdf/umac-fast-and-secure-message-authentication-3algbmjwnk.pdf

UMAC: Fast and Secure Message Authentication

Preneel, Govaerts, and Vandewalle [6] considered the 64 most basic ways to construct a hash function H: {0, 1}* ? {0, 1}n from a block cipher E: {0, 1}n × {0, 1}n ? {0, 1}n. They regarded 12 of these 64 schemes as secure, though no proofs or formal claims were given. The remaining 52 schemes were shown to be subject to various attacks. Here we provide a formal and quantitative treatment of the 64 constructions considered by PGV. We prove that, in a black-box model, the 12 schemes that PGV singled out as secure really are secure: we give tight upper and lower bounds on their collision resistance. Furthermore, by stepping outside of the Merkle-Damgard approach to analysis, we show that an additional 8 of the 64 schemes are just as collision resistant (up to a small constant) as the first group of schemes. Nonetheless, we are able to differentiate among the 20 collision-resistant schemes by bounding their security as one-way functions. We suggest that proving black-box bounds, of the style given here, is a feasible and useful step for understanding the security of any block-cipher-based hash-function construction.

/pdf/black-box-analysis-of-the-block-cipher-based-hash-function-42lh72da94.pdf

Black-Box Analysis of the Block-Cipher-Based Hash-Function Constructions from PGV

We describe a message authentication algorithm, UMAC, which can authenticate messages (in software, on contemporary machines) roughly an order of magnitude faster than current practice (e.g., HMAC-SHA1), and about twice as fast as times previously reported for the universal hash-function family MMH. To achieve such speeds, UMAC uses a new universal hash-function family, NH, and a design which allows effective exploitation of SIMD parallelism The cryptographic work of UMAC is done using standard primitives of the user's choice, such as a block cipher or cryptographic hash function; no new heuristic primitives are developed here. Instead, the security of UMAC is rigorously proven, in the sense of giving exact and quantitatively strong results which demonstrate an inability to forge UMAC-authenticated messages assuming an inability to break the underlying cryptographic primitive. Unlike conventional, inherently serial MACs, UMAC is parallelizable, and will have ever-faster implementation speeds as machines offer up increasing amounts of parallelism. We envision UMAC as a practical algorithm for next-generation message authentication.

UMAC : Fast and secure message authentication

We describe a parallelizable block-cipher mode of operation that simultaneously provides privacy and authenticity. OCB encrypts-and-authenticates a nonempty string M ∈ {0, 1}* using ⌈|M|/n⌉ + 2 block-cipher invocations, where n is the block length of the underlying block cipher. Additional overhead is small. OCB refines a scheme, IAPM, suggested by Charanjit Jutla. Desirable properties of OCB include the ability to encrypt a bit string of arbitrary length into a ciphertext of minimal length, cheap offset calculations, cheap key setup, a single underlying cryptographic key, no extended-precision addition, a nearly optimal number of block-cipher calls, and no requirement for a random IV. We prove OCB secure, quantifying the adversary's ability to violate the mode's privacy or authenticity in terms of the quality of its block cipher as a pseudorandom permutation (PRP) or as a strong PRP, respectively.

John Black

Papers

OCB: a block-cipher mode of operation for efficient authenticated encryption

UMAC: Fast and Secure Message Authentication

Black-Box Analysis of the Block-Cipher-Based Hash-Function Constructions from PGV

UMAC : Fast and secure message authentication

OCB: A block-cipher mode of operation for efficient authenticated encryption