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HOMOMORPHIC ENCRYPTION
, 2009
"... Alice and Bob possess sequences ¡i¿x¡sup¿n¡/sup¿¡/i ¿ and ¡i¿y¡sup¿n¡/sup¿¡/i ¿ respectively and would like to compute ¡i¿d(x¡sup¿n¡/sup¿,y¡sup¿n¡/sup¿)¡/i ¿ where ¡i¿d(.,.)¡/i ¿ is a distortion measure. However, Alice and Bob do not trust each other and do not wish to reveal their data to each othe ..."
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other. This paper describes and analyzes a protocol that uses homomorphic encryption for secure calculation of some special distortion functions without revealing ¡i¿x¡sup¿n¡/sup¿¡/i¿ and ¡i¿y¡sup¿n¡/sup¿¡/i¿. The resulting distortion result is also in encrypted form. Two variants of the protocol
Fully homomorphic encryption using ideal lattices
 In Proc. STOC
, 2009
"... 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 arbitra ..."
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Cited by 642 (17 self)
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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
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 80 (6 self)
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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
FULLY HOMOMORPHIC ENCRYPTION FOR MATHEMATICIANS
"... Abstract. We give an introduction to Fully Homomorphic Encryption for mathematicians. Fully Homomorphic Encryption allows untrusted parties to take encrypted data Enc(m1),..., Enc(mt) and any efficiently computable function f, and compute an encryption of f(m1,..., mt), without knowing or learning t ..."
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Cited by 3 (0 self)
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Abstract. We give an introduction to Fully Homomorphic Encryption for mathematicians. Fully Homomorphic Encryption allows untrusted parties to take encrypted data Enc(m1),..., Enc(mt) and any efficiently computable function f, and compute an encryption of f(m1,..., mt), without knowing or learning
Encrypted Receipts for . . . Homomorphic Encryption
, 2005
"... Voters are now demanding the ability to verify that their votes are cast and counted as intended. Most existing cryptographic election protocols do not treat the voter as a computationallylimited entity separate from the voting booth, and therefore do not ensure that the voting booth records the co ..."
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the correct vote. David Chaum and Andrew Neff have proposed mixnet schemes that do provide this assurance, but little research has been done that combines voter verification with homomorphic encryption. This thesis proposes adding voter verification to an existing multicandidate election scheme (Baudron et
Fully Homomorphic Encryption
, 2014
"... A homomorphic encryption scheme allows specific types of computations to be carried out on ciphertext and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintext. In other words, the scheme encrypts data in such a way that computations can be ..."
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A homomorphic encryption scheme allows specific types of computations to be carried out on ciphertext and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintext. In other words, the scheme encrypts data in such a way that computations can
Faster Fully Homomorphic Encryption
"... Abstract. We describe two improvements to Gentry's fully homomorphic scheme based on ideal lattices and its analysis: we provide a re ned analysis of one of the hardness assumptions (the one related to the Sparse Subset Sum Problem) and we introduce a probabilistic decryption algorithm that can ..."
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Cited by 43 (0 self)
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homomorphic schemes of Smart and Vercauteren [PKC'2010] and van Dijk et al. [Eurocrypt'2010]. Keywords: fully homomorphic encryption, ideal lattices, SSSP. 1
Fully Homomorphic Encryption over the Integers
, 2009
"... We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry’s technique to construct fully homomorphic scheme from a “bootstrappable” somewhat homomorphic scheme. However, instead of using ideal lattices over a polynomial ring, our bootstrappabl ..."
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Cited by 138 (10 self)
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We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry’s technique to construct fully homomorphic scheme from a “bootstrappable” somewhat homomorphic scheme. However, instead of using ideal lattices over a polynomial ring, our
Accelerating Fully Homomorphic Encryption on
"... the first plausible construction of a fully homomorphic encryption (FHE) scheme. FHE allows the evaluation of arbitrary functions directly on encrypted data on untwisted servers. In 2010, Gentry and Halevi presented the first FHE implementation on an IBM x3500 server. However, this implementation re ..."
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the first plausible construction of a fully homomorphic encryption (FHE) scheme. FHE allows the evaluation of arbitrary functions directly on encrypted data on untwisted servers. In 2010, Gentry and Halevi presented the first FHE implementation on an IBM x3500 server. However, this implementation
Parallel Homomorphic Encryption
, 2011
"... Abstract. In the problem of private outsourced computation, a client wishes to delegate the evaluation of a function f on a private input x to an untrusted worker without the latter learning anything about x and f(x). This problem occurs in many applications and, most notably, in the setting of clou ..."
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Cited by 4 (0 self)
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. At such scales, computation is beyond the capabilities of any single machine so it is performed by largescale clusters of workers. To address this problem, we consider parallel homomorphic encryption (PHE) schemes, which are encryption schemes that support computation over encrypted data through the use
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