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(Batch) Fully Homomorphic Encryption over Integers for NonBinary Message Spaces
"... In this paper, we construct a fully homomorphic encryption (FHE) scheme over integers with the message space ZQ for any prime Q. Even for the binary case Q = 2, our decryption circuit has a smaller degree than that of the previous scheme; the multiplicative degree is reduced from O((log )2) to O(), ..."
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In this paper, we construct a fully homomorphic encryption (FHE) scheme over integers with the message space ZQ for any prime Q. Even for the binary case Q = 2, our decryption circuit has a smaller degree than that of the previous scheme; the multiplicative degree is reduced from O((log )2) to O
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
IdentityBased Encryption from the Weil Pairing
, 2001
"... We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic ..."
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Cited by 1699 (29 self)
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We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing
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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that can be implemented with an algebraic circuit of low multiplicative degree. Combined together, these improvements lead to a faster fully homomorphic scheme, with a e O(λ 3) bit complexity per elementary binary add/mult gate, where λ is the security parameter. These improvements also apply to the fully
Convergent Treereweighted Message Passing for Energy Minimization
 ACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI), 2006. ABSTRACTACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI)
, 2006
"... Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy ..."
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Cited by 491 (16 self)
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Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound
A Digital Signature Scheme Secure Against Adaptive ChosenMessage Attacks
, 1995
"... We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a ..."
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Cited by 985 (43 self)
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We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen
CRTbased Fully Homomorphic Encryption over the Integers ⋆
"... Abstract. In 1978, Rivest, Adleman and Dertouzos introduced the basic concept of privacy homomorphism that allows computation on encrypted data without decryption. It was elegant work that precedes the recent development of fully homomorphic encryption schemes although there were found some security ..."
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Cited by 5 (2 self)
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plaintext/ciphertext can break this scheme. However, by exploiting the standard technique to insert an error to a message before encryption, we can cope with this problem. We present a secure modification of their proposal by showing that the proposed scheme is fully homomorphic and secure against
Fully homomorphic encryption with polylog overhead
"... 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 widthΩ(λ) circuit with t gates in time t · ..."
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Cited by 63 (4 self)
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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 widthΩ(λ) circuit with t gates in time
ScaleInvariant Fully Homomorphic Encryption over the Integers ⋆
"... Abstract. At Crypto 2012, Brakerski constructed a scaleinvariant fully homomorphic encryption scheme based on the LWE problem, in which the same modulus is used throughout the evaluation process, instead of a ladder of moduli when doing “modulus switching”. In this paper we describe a variant of th ..."
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Cited by 7 (0 self)
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of the van Dijk et al. FHE scheme over the integers with the same scaleinvariant property. Our scheme has a single secret modulus whose size is linear in the multiplicative depth of the circuit to be homomorphically evaluated, instead of exponential; we therefore construct a leveled fully homomorphic
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