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292
Delegating computation: interactive proofs for muggles
 In Proceedings of the ACM Symposium on the Theory of Computing (STOC
, 2008
"... In this work we study interactive proofs for tractable languages. The (honest) prover should be efficient and run in polynomial time, or in other words a “muggle”. 1 The verifier should be superefficient and run in nearlylinear time. These proof systems can be used for delegating computation: a se ..."
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Cited by 113 (6 self)
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In this work we study interactive proofs for tractable languages. The (honest) prover should be efficient and run in polynomial time, or in other words a “muggle”. 1 The verifier should be superefficient and run in nearlylinear time. These proof systems can be used for delegating computation: a server can run a computation for a client and interactively prove the correctness of the result. The client can verify the result’s correctness in nearlylinear time (instead of running the entire computation itself). Previously, related questions were considered in the Holographic Proof setting by Babai, Fortnow, Levin and Szegedy, in the argument setting under computational assumptions by Kilian, and in the random oracle model by Micali. Our focus, however, is on the original interactive proof model where no assumptions are made on the computational power or adaptiveness of dishonest provers. Our main technical theorem gives a public coin interactive proof for any language computable by a logspace uniform boolean circuit with depth d and input length n. The verifier runs in time (n+d)·polylog(n) and space O(log(n)), the communication complexity is d · polylog(n), and the prover runs in time poly(n). In particular, for languages computable by logspace uniform N C (circuits of polylog(n) depth), the prover is efficient, the verifier runs in time n · polylog(n) and space O(log(n)), and the communication complexity is polylog(n).
Indifferentiability, impossibility results on reductions, and applications to the random oracle methodology
 Theory of Cryptography  TCC 2004, Lecture Notes in Computer Science
, 2004
"... Abstract. The goals of this paper are threefold. First we introduce and motivate a generalization of the fundamental concept of the indistinguishability of two systems, called indifferentiability. This immediately leads to a generalization of the related notion of reducibility of one system to anot ..."
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Cited by 96 (2 self)
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Abstract. The goals of this paper are threefold. First we introduce and motivate a generalization of the fundamental concept of the indistinguishability of two systems, called indifferentiability. This immediately leads to a generalization of the related notion of reducibility of one system to another. Second, we prove that indifferentiability is the necessary and sufficient condition on two systems S and T such that the security of any cryptosystem using T as a component is not affected when T is substituted by S. In contrast to indistinguishability, indifferentiability is applicable in settings where a possible adversary is assumed to have access to additional information about the internal state of the involved systems, for instance the public parameter selecting a member from a family of hash functions. Third, we state an easily verifiable criterion for a system U not to be reducible (according to our generalized definition) to another system V and, as an application, prove that a random oracle is not reducible to a weaker primitive, called asynchronous beacon, and also that an asynchronous beacon is not reducible to a finitelength random string. Each of these irreducibility results alone implies the main theorem of Canetti, Goldreich and Halevi stating that there exist cryptosystems that are secure in the random oracle model but for which replacing the random oracle by any implementation leads to an insecure cryptosystem. Key words. Indistinguishability, reductions, indifferentiability, security proofs, random oracle methodology, hash functions.
An Uninstantiable RandomOracleModel Scheme for a HybridEncryption Problem
"... 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 for ..."
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Cited by 95 (4 self)
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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.
How to Enhance the Security of PublicKey Encryption at Minimum Cost
, 1999
"... This paper presents a simple and generic conversion from a publickey encryption scheme which is indistinguishable against chosenplaintext attacks into a publickey encryption scheme which is indistinguishable against adaptive chosenciphertext attacks in the random oracle model. The scheme obtained ..."
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Cited by 92 (8 self)
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This paper presents a simple and generic conversion from a publickey encryption scheme which is indistinguishable against chosenplaintext attacks into a publickey encryption scheme which is indistinguishable against adaptive chosenciphertext attacks in the random oracle model. The scheme obtained by the conversion is as efficient as the original encryption scheme and the security reduction is very tight in the exact security manner.
Authenticated DiffieHellman Key Agreement Protocols
, 1998
"... This paper surveys recent work on the design and analysis of key agreement protocols that are based on the intractability of the DiffieHellman problem. The focus is on protocols that have been standardized, or are in the process of being standardized, by organizations such as ANSI, IEEE, ISO/IEC, a ..."
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Cited by 83 (1 self)
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This paper surveys recent work on the design and analysis of key agreement protocols that are based on the intractability of the DiffieHellman problem. The focus is on protocols that have been standardized, or are in the process of being standardized, by organizations such as ANSI, IEEE, ISO/IEC, and NIST. The practical and provable security aspects of these protocols are discussed.
A Framework for PasswordBased Authenticated Key Exchange
 in Cryptology — Eurocrypt 2003, LNCS
, 2003
"... In this paper we present a general framework for passwordbased authenticated key exchange protocols, in the common reference string model. Our protocol is actually an abstraction of the key exchange protocol of Katz et al. and is based on the recently introduced notion of smooth projective hashi ..."
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Cited by 81 (2 self)
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In this paper we present a general framework for passwordbased authenticated key exchange protocols, in the common reference string model. Our protocol is actually an abstraction of the key exchange protocol of Katz et al. and is based on the recently introduced notion of smooth projective hashing by Cramer and Shoup. We gain a number of benefits from this abstraction. First, we obtain a modular protocol that can be described using just three highlevel cryptographic tools. This allows a simple and intuitive understanding of its security.
Magic Functions
, 1999
"... We consider three apparently unrelated fundamental problems in distributed computing, cryptography and complexity theory and prove that they are essentially the same problem. ..."
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Cited by 76 (1 self)
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We consider three apparently unrelated fundamental problems in distributed computing, cryptography and complexity theory and prove that they are essentially the same problem.
On Obfuscating Point Functions
, 2005
"... We study the problem of obfuscation in the context of point functions (also known as delta functions). ..."
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Cited by 74 (2 self)
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We study the problem of obfuscation in the context of point functions (also known as delta functions).
Quadratic Span Programs and Succinct NIZKs without PCPs
"... We introduce a new characterization of the NP complexity class, called Quadratic Span Programs (QSPs), which is a natural extension of span programs defined by Karchmer and Wigderson. Our main motivation is the construction of succinct arguments of NPstatements that are quick to construct and verif ..."
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Cited by 72 (8 self)
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We introduce a new characterization of the NP complexity class, called Quadratic Span Programs (QSPs), which is a natural extension of span programs defined by Karchmer and Wigderson. Our main motivation is the construction of succinct arguments of NPstatements that are quick to construct and verify. QSPs seem wellsuited for this task, perhaps even better than Probabilistically Checkable Proofs (PCPs). In 2010, Groth constructed a NIZK argument in the common reference string (CRS) model for CircuitSAT consisting of only 42 elements in a bilinear group. Interestingly, his argument does not (explicitly) use PCPs. But his scheme has some disadvantages – namely, the CRS size and prover computation are both quadratic in the circuit size. In 2011, Lipmaa reduced the CRS size to quasilinear, but with prover computation still quadratic. Using QSPs we construct a NIZK argument in the CRS model for CircuitSAT consisting of just 7 group elements. The CRS size is linear in the circuit size, and prover computation is quasilinear, making our scheme seemingly quite practical. (The prover only needs to do a linear number of group operations; the quasilinear computation is a multipoint evaluation and interpolation.) Our results are complementary to those of Valiant (TCC 2008) and Bitansky et al. (2012), who use “bootstrapping ” (recursive composition) of arguments to reduce CRS size and prover and verifier computation. QSPs also provide a crisp mathematical abstraction of some of the techniques underlying Groth’s and Lipmaa’s constructions.
Symmetric Encryption in a Simulatable DolevYao Style Cryptographic Library
 In Proc. 17th IEEE Computer Security Foundations Workshop (CSFW
, 2004
"... Recently we solved the longstanding open problem of justifying a DolevYao type model of cryptography as used in virtually all automated protocol provers under active attacks. The justification was done by defining an ideal system handling DolevYaostyle terms and a cryptographic realization wi ..."
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Cited by 72 (20 self)
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Recently we solved the longstanding open problem of justifying a DolevYao type model of cryptography as used in virtually all automated protocol provers under active attacks. The justification was done by defining an ideal system handling DolevYaostyle terms and a cryptographic realization with the same user interface, and by showing that the realization is as secure as the ideal system in the sense of reactive simulatability. This definition encompasses arbitrary active attacks and enjoys general composition and propertypreservation properties. Security holds in the standard model of cryptography and under standard assumptions of adaptively secure primitives.