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316
Computing arbitrary functions of encrypted data
 Commun. ACM
, 2010
"... 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 comput ..."
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Cited by 36 (0 self)
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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. 1.
Improved delegation of computation using fully homomorphic encryption
 CRYPTO 2010, LNCS 6223
, 2010
"... Following Gennaro, Gentry, and Parno (Cryptology ePrint Archive 2009/547), we use fully homomorphic encryption to design improved schemes for delegating computation. In such schemes, a delegator outsources the computation of a function F on many, dynamically chosen inputs xi to a worker in such a wa ..."
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Cited by 35 (2 self)
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Following Gennaro, Gentry, and Parno (Cryptology ePrint Archive 2009/547), we use fully homomorphic encryption to design improved schemes for delegating computation. In such schemes, a delegator outsources the computation of a function F on many, dynamically chosen inputs xi to a worker in such a way that it is infeasible for the worker to make the delegator accept a result other than F (xi). The “online stage ” of the Gennaro et al. scheme is very efficient: the parties exchange two messages, the delegator runs in time poly(log T), and the worker runs in time poly(T), where T is the time complexity of F. However, the “offline stage ” (which depends on the function F but not the inputs to be delegated) is inefficient: the delegator runs in time poly(T) and generates a public key of length poly(T) that needs to be accessed by the worker during the online stage. Our first construction eliminates the large public key from the Gennaro et al. scheme. The delegator still invests poly(T) time in the offline stage, but does not need to communicate or publish anything. Our second construction reduces the work of the delegator in the offline stage to poly(log T) at the price of a 4message (offline) interaction with a poly(T)time worker
Improved Garbled Circuit Building Blocks and Applications to Auctions and Computing Minima
 In Cryptology and Network Security (CANS
, 2009
"... Abstract. We consider generic Garbled Circuit (GC)based techniques for Secure Function Evaluation (SFE) in the semihonest model. We describe efficient GC constructions for addition, subtraction, multiplication, and comparison functions. Our circuits for subtraction and comparison are approximately ..."
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Cited by 32 (6 self)
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Abstract. We consider generic Garbled Circuit (GC)based techniques for Secure Function Evaluation (SFE) in the semihonest model. We describe efficient GC constructions for addition, subtraction, multiplication, and comparison functions. Our circuits for subtraction and comparison are approximately two times smaller (in terms of garbled tables) than previous constructions. This implies corresponding computation and communication improvements in SFE of functions using our efficient building blocks. The techniques rely on recently proposed “free XOR ” GC technique. Further, we present concrete and detailed improved GC protocols for the problem of secure integer comparison, and related problems of auctions, minimum selection, and minimal distance. Performance improvement comes both from building on our efficient basic blocks and several problemspecific GC optimizations. We provide precise cost evaluation of our constructions, which serves as a baseline for future protocols.
Fully Homomorphic Encryption from RingLWE and Security for Key Dependent Messages
 in Advances in Cryptology—CRYPTO 2011, Lect. Notes in Comp. Sci. 6841 (2011
"... Abstract. We present a somewhat homomorphic encryption scheme that is both very simple to describe and analyze, and whose security (quantumly) reduces to the worstcase hardness of problems on ideal lattices. We then transform it into a fully homomorphic encryption scheme using standard “squashing ” ..."
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Cited by 31 (1 self)
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Abstract. We present a somewhat homomorphic encryption scheme that is both very simple to describe and analyze, and whose security (quantumly) reduces to the worstcase hardness of problems on ideal lattices. We then transform it into a fully homomorphic encryption scheme using standard “squashing ” and “bootstrapping ” techniques introduced by Gentry (STOC 2009). One of the obstacles in going from “somewhat ” to full homomorphism is the requirement that the somewhat homomorphic scheme be circular secure, namely, the scheme can be used to securely encrypt its own secret key. For all known somewhat homomorphic encryption schemes, this requirement was not known to be achievable under any cryptographic assumption, and had to be explicitly assumed. We take a step forward towards removing this additional assumption by proving that our scheme is in fact secure when encrypting polynomial functions of the secret key. Our scheme is based on the ring learning with errors (RLWE) assumption that was recently introduced by Lyubashevsky, Peikert and Regev (Eurocrypt 2010). The RLWE assumption is reducible to worstcase problems on ideal lattices, and allows us to completely abstract out the lattice interpretation, resulting in an extremely simple scheme. For example, our secret key is s, and our public key is (a, b = as + 2e), where s, a, e are all degree (n − 1) integer polynomials whose coefficients are independently drawn from easy to sample distributions. 1
Efficient privacypreserving face recognition
, 2009
"... Automatic recognition of human faces is becoming increasingly popular in civilian and law enforcement applications that require reliable recognition of humans. However, the rapid improvement and widespread deployment of this technology raises strong concerns regarding the violation of individuals ’ ..."
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Cited by 31 (4 self)
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Automatic recognition of human faces is becoming increasingly popular in civilian and law enforcement applications that require reliable recognition of humans. However, the rapid improvement and widespread deployment of this technology raises strong concerns regarding the violation of individuals ’ privacy. A typical application scenario for privacypreserving face recognition concerns a client who privately searches for a specific face image in the face image database of a server. In this paper we present a privacypreserving face recognition scheme that substantially improves over previous work in terms of communicationand computation efficiency: the most recent proposal of Erkin et al. (PETS’09) requires O(log M) rounds and computationally expensive operations on homomorphically encrypted data to recognize a face in a database of M faces. Our improved scheme requires only O(1) rounds and has a substantially smaller online communication complexity (by a factor of 15 for each database entry) and less computation complexity. Our solution is based on known cryptographic building blocks combining homomorphic encryption with garbled circuits. Our implementation results show the practicality of our scheme also for large databases (e.g., for M = 1000 we need less than 13 seconds and less than 4 MByte online communication on two 2.4GHz PCs connected via Gigabit Ethernet).
Can Homomorphic Encryption be Practical?
"... Abstract. The prospect of outsourcing an increasing amount of data storage and management to cloud services raises many new privacy concerns for individuals and businesses alike. The privacy concerns can be satisfactorily addressed if users encrypt the data they send to the cloud. If the encryption ..."
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Cited by 30 (2 self)
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Abstract. The prospect of outsourcing an increasing amount of data storage and management to cloud services raises many new privacy concerns for individuals and businesses alike. The privacy concerns can be satisfactorily addressed if users encrypt the data they send to the cloud. If the encryption scheme is homomorphic, the cloud can still perform meaningful computations on the data, even though it is encrypted. In fact, we now know a number of constructions of fully homomorphic encryption schemes that allow arbitrary computation on encrypted data. In the last two years, solutions for fully homomorphic encryption have been proposed and improved upon, but it is hard to ignore the elephant in the room, namely efficiency – can homomorphic encryption ever be efficient enough to be practical? Certainly, it seems that all known fully homomorphic encryption schemes have a long way to go before they can be used in practice. Given this state of affairs, our contribution is twofold. First, we exhibit a number of realworld applications, in the medical, financial, and the advertising domains, which require only that the encryption scheme is “somewhat ” homomorphic. Somewhat homomorphic encryption schemes, which support a limited number of homomorphic operations, can be much faster, and more compact than fully homomorphic encryption schemes. Secondly, we show a proofofconcept implementation of the recent somewhat homomorphic encryption scheme of Brakerski and Vaikuntanathan, whose security relies on the “ring learning with errors ” (Ring LWE) problem. The system is very efficient, and has reasonably short ciphertexts. Our unoptimized implementation in magma enjoys comparable efficiency to even optimized pairingbased schemes with the same level of security and homomorphic capacity. We also show a number of applicationspecific optimizations to the encryption scheme, most notably the ability to convert between different message encodings in a ciphertext.
Fully homomorphic encryption without modulus switching from classical GapSVP
 In Advances in Cryptology  Crypto 2012, volume 7417 of Lecture
"... We present a new tensoring technique for LWEbased fully homomorphic encryption. While in all previous works, the ciphertext noise grows quadratically (B → B 2 · poly(n)) with every multiplication (before “refreshing”), our noise only grows linearly (B → B · poly(n)). We use this technique to constr ..."
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Cited by 29 (4 self)
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We present a new tensoring technique for LWEbased fully homomorphic encryption. While in all previous works, the ciphertext noise grows quadratically (B → B 2 · poly(n)) with every multiplication (before “refreshing”), our noise only grows linearly (B → B · poly(n)). We use this technique to construct a scaleinvariant fully homomorphic encryption scheme, whose properties only depend on the ratio between the modulus q and the initial noise level B, and not on their absolute values. Our scheme has a number of advantages over previous candidates: It uses the same modulus throughout the evaluation process (no need for “modulus switching”), and this modulus can take arbitrary form. In addition, security can be classically reduced from the worstcase hardness of the GapSVP problem (with quasipolynomial approximation factor), whereas previous constructions could only exhibit a quantum reduction from GapSVP. Fully homomorphic encryption has been the focus of extensive study since the first candidate scheme was introduced by Gentry [Gen09b]. In a nutshell, fully homomorphic encryption allows to
Better key sizes (and attacks) for LWEbased encryption
 In CTRSA
, 2011
"... We analyze the concrete security and key sizes of theoretically sound latticebased encryption schemes based on the “learning with errors ” (LWE) problem. Our main contributions are: (1) a new lattice attack on LWE that combines basis reduction with an enumeration algorithm admitting a time/success ..."
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Cited by 27 (5 self)
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We analyze the concrete security and key sizes of theoretically sound latticebased encryption schemes based on the “learning with errors ” (LWE) problem. Our main contributions are: (1) a new lattice attack on LWE that combines basis reduction with an enumeration algorithm admitting a time/success tradeoff, which performs better than the simple distinguishing attack considered in prior analyses; (2) concrete parameters and security estimates for an LWEbased cryptosystem that is more compact and efficient than the wellknown schemes from the literature. Our new key sizes are up to 10 times smaller than prior examples, while providing even stronger concrete security levels.
Candidate indistinguishability obfuscation and functional encryption for all circuits
 In FOCS
, 2013
"... 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 ..."
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Cited by 27 (9 self)
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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, ciphertexts encrypt inputs x and keys are issued for circuits C. Using the key SKC to decrypt a ciphertext 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 polynomialsize circuits. We accomplish this goal in three steps: • We describe a candidate construction for indistinguishability obfuscation for NC 1 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. • We show how to use indistinguishability obfuscation for NC 1 together with Fully Homomorphic Encryption (with decryption in NC 1) to achieve indistinguishability obfuscation for all circuits.
Progressionfree sets and sublinear pairingbased noninteractive zeroknowledge arguments
 In TCC
, 2012
"... Abstract. In 2010, Groth constructed the only previously known sublinearcommunication NIZK circuit satisfiability argument in the common reference string model. We optimize Groth’s argument by, in particular, reducing both the CRS length and the prover’s computational complexity from quadratic to q ..."
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Cited by 26 (2 self)
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Abstract. In 2010, Groth constructed the only previously known sublinearcommunication NIZK circuit satisfiability argument in the common reference string model. We optimize Groth’s argument by, in particular, reducing both the CRS length and the prover’s computational complexity from quadratic to quasilinear in the circuit size. We also use a (presumably) weaker security assumption, and have tighter security reductions. Our main contribution is to show that the complexity of Groth’s basic arguments is dominated by the quadratic number of monomials in certain polynomials. We collapse the number of monomials to quasilinear by using a recent construction of progressionfree sets.