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119
An Uninstantiable RandomOracleModel Scheme for a HybridEncryption Problem,” Full version of this paper. Available at http://wwwcse.ucsd.edu/users/mihir
"... Abstract. We present a simple, natural randomoracle (RO) model scheme, for a practical goal, that is uninstantiable, meaning is proven in the RO model to meet its goal yet admits no standardmodel instantiation that meets this goal. The goal in question is INDCCApreserving asymmetric encryption w ..."
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Cited by 96 (5 self)
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Abstract. We present a simple, natural randomoracle (RO) model scheme, for a practical goal, that is uninstantiable, meaning is proven in the RO model to meet its goal yet admits no standardmodel instantiation that meets this goal. The goal in question is INDCCApreserving asymmetric encryption which formally captures security of the most common practical usage of asymmetric encryption, namely to transport a symmetric key in such a way that symmetric encryption under the latter remains secure. The scheme is an ElGamal variant, called Hash ElGamal, that resembles numerous existing ROmodel schemes, and on the surface shows no evidence of its anomalous properties. These results extend our understanding of the gap between the standard and RO models, and bring concerns raised by previous work closer to practice by indicating that the problem of ROmodel schemes admitting no secure instantiation can arise in domains where RO schemes are commonly designed. 1
Robust PCPs of Proximity, Shorter PCPs and Applications to Coding
 in Proc. 36th ACM Symp. on Theory of Computing
, 2004
"... We continue the study of the tradeo between the length of PCPs and their query complexity, establishing the following main results (which refer to proofs of satis ability of circuits of size n): 1. We present PCPs of length exp( ~ O(log log n) ) n that can be veri ed by making o(log log n) ..."
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Cited by 95 (27 self)
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We continue the study of the tradeo between the length of PCPs and their query complexity, establishing the following main results (which refer to proofs of satis ability of circuits of size n): 1. We present PCPs of length exp( ~ O(log log n) ) n that can be veri ed by making o(log log n) Boolean queries.
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 71 (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
Pinocchio: Nearly practical verifiable computation
 In Proceedings of the IEEE Symposium on Security and Privacy
, 2013
"... To instill greater confidence in computations outsourced to the cloud, clients should be able to verify the correctness of the results returned. To this end, we introduce Pinocchio, a built system for efficiently verifying general computations while relying only on cryptographic assumptions. With Pi ..."
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Cited by 64 (6 self)
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To instill greater confidence in computations outsourced to the cloud, clients should be able to verify the correctness of the results returned. To this end, we introduce Pinocchio, a built system for efficiently verifying general computations while relying only on cryptographic assumptions. With Pinocchio, the client creates a public evaluation key to describe her computation; this setup is proportional to evaluating the computation once. The worker then evaluates the computation on a particular input and uses the evaluation key to produce a proof of correctness. The proof is only 288 bytes, regardless of the computation performed or the size of the inputs and outputs. Anyone can use a public verification key to check the proof. Crucially, our evaluation on seven applications demonstrates that Pinocchio is efficient in practice too. Pinocchio’s verification time is typically 10ms: 57 orders of magnitude less than previous work; indeed Pinocchio is the first generalpurpose system to demonstrate verification cheaper than native execution (for some apps). Pinocchio also reduces the worker’s proof effort by an additional 1960×. As an additional feature, Pinocchio generalizes to zeroknowledge proofs at a negligible cost over the base protocol. Finally, to aid development, Pinocchio provides an endtoend toolchain that compiles a subset of C into programs that implement the verifiable computation protocol. 1
From extractable collision resistance to succinct noninteractive arguments of knowledge, and back again
 In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, ITCS '12
, 2012
"... The existence of noninteractive succinct arguments (namely, noninteractive computationallysound proof systems where the verifier’s time complexity is only polylogarithmically related to the complexity of deciding the language) has been an intriguing question for the past two decades. The question ..."
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Cited by 63 (18 self)
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The existence of noninteractive succinct arguments (namely, noninteractive computationallysound proof systems where the verifier’s time complexity is only polylogarithmically related to the complexity of deciding the language) has been an intriguing question for the past two decades. The question has gained renewed importance in light of the recent interest in delegating computation to untrusted workers. Still, other than Micali’s CS proofs in the Random Oracle Model, the only existing candidate construction is based on an elaborate assumption that is tailored to the specific proposal [Di Crescenzo and Lipmaa, CiE ’08]. We modify and reanalyze that construction: • We formulate a general and relatively mild notion of extractable collisionresistant hash functions (ECRHs), and show that if ECRHs exist then the modified construction is a noninteractive succinct argument (SNARG) for NP. Furthermore, we show that (a) this construction is a proof of knowledge, and (b) it remains secure against adaptively chosen instances. These two properties are arguably essential for using the construction as a delegation of computation scheme. • We show that existence of SNARGs of knowledge (SNARKs) for NP implies existence of ECRHs, as well as extractable variants of some other cryptographic primitives. This provides further evi
ZeroKnowledge Sets
, 2003
"... We show how a polynomialtime prover can commit to an arbitrary finite set S of strings so that, later on, he can, for any string x, reveal with a proof whetherÜËorÜ�Ë, without revealing any knowledge beyond the verity of these membership assertions. Our method is non interactive. Given a public ran ..."
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Cited by 58 (0 self)
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We show how a polynomialtime prover can commit to an arbitrary finite set S of strings so that, later on, he can, for any string x, reveal with a proof whetherÜËorÜ�Ë, without revealing any knowledge beyond the verity of these membership assertions. Our method is non interactive. Given a public random string, the prover commits to a set by simply posting a short and easily computable message. After that, each time it wants to prove whether a given element is in the set, it simply posts another short and easily computable proof, whose correctness can be verified by any one against the public random string. Our scheme is very efficient; no reasonable prior way to achieve our desiderata existed. Our new primitive immediately extends to providing zeroknowledge “databases.”
Homomorphic signatures for polynomial functions
, 2010
"... We construct the first homomorphic signature scheme that is capable of evaluating multivariate polynomials on signed data. Given the public key and a signed data set, there is an efficient algorithm to produce a signature on the mean, standard deviation, and other statistics of the signed data. Prev ..."
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Cited by 56 (4 self)
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We construct the first homomorphic signature scheme that is capable of evaluating multivariate polynomials on signed data. Given the public key and a signed data set, there is an efficient algorithm to produce a signature on the mean, standard deviation, and other statistics of the signed data. Previous systems for computing on signed data could only handle linear operations. For polynomials of constant degree, the length of a derived signature only depends logarithmically on the size of the data set. Our system uses ideal lattices in a way that is a “signature analogue” of Gentry’s fully homomorphic encryption. Security is based on hard problems on ideal lattices similar to those in Gentry’s system.
On the (In)security of the FiatShamir Paradigm
 In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
, 2003
"... In 1986, Fiat and Shamir suggested a general method for transforming secure 3round publiccoin identification schemes into digital signature schemes. The significant contribution of this method is a means for designing efficient digital signatures, while hopefully achieving security against chosen ..."
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Cited by 55 (2 self)
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In 1986, Fiat and Shamir suggested a general method for transforming secure 3round publiccoin identification schemes into digital signature schemes. The significant contribution of this method is a means for designing efficient digital signatures, while hopefully achieving security against chosen message attacks. All other known constructions which achieve such security are substantially more inefficient and complicated in design. In 1996...