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SIAM Journal on Computing
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Non-Malleable Non-Interactive Zero Knowledge and Adaptive Chosen-Ciphertext Security
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Journal of Cryptology
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Multiple non-interactive zero knowledge proofs based on a single random string
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CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Relations among notions of non-malleability for encryption
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
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A fully homomorphic encryption scheme
A fully homomorphic encryption scheme
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i-hop homomorphic encryption and rerandomizable Yao circuits
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Fully homomorphic encryption with relatively small key and ciphertext sizes
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
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Malleable proof systems and applications
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Succinct malleable NIZKs and an application to compact shuffles
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Succinct non-interactive arguments via linear interactive proofs
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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MyCloud: supporting user-configured privacy protection in cloud computing
Proceedings of the 29th Annual Computer Security Applications Conference
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We put forward the notion of targeted malleability: given a homomorphic encryption scheme, in various scenarios we would like to restrict the homomorphic computations one can perform on encrypted data. We introduce a precise framework, generalizing the foundational notion of non-malleability introduced by Dolev, Dwork, and Naor (SICOMP '00), ensuring that the malleability of a scheme is targeted only at a specific set of "allowable" functions. In this setting we are mainly interested in the efficiency of such schemes as a function of the number of repeated homomorphic operations. Whereas constructing a scheme whose ciphertext grows linearly with the number of such operations is straightforward, obtaining more realistic (or merely non-trivial) length guarantees is significantly more challenging. We present two constructions that transform any homomorphic encryption scheme into one that offers targeted malleability. Our constructions rely on standard cryptographic tools and on succinct non-interactive arguments, which are currently known to exist in the standard model based on variants of the knowledge-of-exponent assumption. The two constructions offer somewhat different efficiency guarantees, each of which may be preferable depending on the underlying building blocks.