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Signature schemes and anonymous credentials from bilinear maps
, 2004
"... We propose a new and efficient signature scheme that is provably secure in the plain model. The security of our scheme is based on a discretelogarithmbased assumption put forth by Lysyanskaya, Rivest, Sahai, and Wolf (LRSW) who also showed that it holds for generic groups and is independent of th ..."
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Cited by 235 (25 self)
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We propose a new and efficient signature scheme that is provably secure in the plain model. The security of our scheme is based on a discretelogarithmbased assumption put forth by Lysyanskaya, Rivest, Sahai, and Wolf (LRSW) who also showed that it holds for generic groups and is independent of the decisional DiffieHellman assumption. We prove security of our scheme under the LRSW assumption for groups with bilinear maps. We then show how our scheme can be used to construct efficient anonymous credential systems as well as group signature and identity escrow schemes. To this end, we provide efficient protocols that allow one to prove in zeroknowledge the knowledge of a signature on a committed (or encrypted) message and to obtain a signature on a committed message.
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 115 (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).
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
MerkleDamg˚ard Revisited: How to Construct a Hash Function
 Advances in Cryptology, Crypto 2005
"... The most common way of constructing a hash function (e.g., SHA1) is to iterate a compression function on the input message. The compression function is usually designed from scratch or made out of a blockcipher. In this paper, we introduce a new security notion for hashfunctions, stronger than col ..."
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Cited by 94 (8 self)
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The most common way of constructing a hash function (e.g., SHA1) is to iterate a compression function on the input message. The compression function is usually designed from scratch or made out of a blockcipher. In this paper, we introduce a new security notion for hashfunctions, stronger than collisionresistance. Under this notion, the arbitrary length hash function H must behave as a random oracle when the fixedlength building block is viewed as a random oracle or an ideal blockcipher. The key property is that if a particular construction meets this definition, then any cryptosystem proven secure assuming H is a random oracle remains secure if one plugs in this construction (still assuming that the underlying fixedlength primitive is ideal). In this paper, we show that the current design principle behind hash functions such as SHA1 and MD5 — the (strengthened) MerkleDamg˚ard transformation — does not satisfy this security notion. We provide several constructions that provably satisfy this notion; those new constructions introduce minimal changes to the plain MerkleDamg˚ard construction and are easily implementable in practice.
Another Look at “Provable Security"
, 2004
"... We give an informal analysis and critique of several typical “provable security” results. In some cases there are intuitive but convincing arguments for rejecting the conclusions suggested by the formal terminology and “proofs,” whereas in other cases the formalism seems to be consistent with common ..."
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Cited by 73 (13 self)
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We give an informal analysis and critique of several typical “provable security” results. In some cases there are intuitive but convincing arguments for rejecting the conclusions suggested by the formal terminology and “proofs,” whereas in other cases the formalism seems to be consistent with common sense. We discuss the reasons why the search for mathematically convincing theoretical evidence to support the security of publickey systems has been an important theme of researchers. But we argue that the theoremproof paradigm of theoretical mathematics is often of limited relevance here and frequently leads to papers that are confusing and misleading. Because our paper is aimed at the general mathematical public, it is selfcontained and as jargonfree as possible.
Towards plaintextaware publickey encryption without random oracles
 Advances in Cryptology – Asiacrypt 2004, volume 3329 of Lecture Notes in Computer Science
, 2004
"... Abstract. We consider the problem of defining and achieving plaintextaware encryption without random oracles in the classical publickey model. We provide definitions for a hierarchy of notions of increasing strength: PA0, PA1 and PA2, chosen so that PA1+INDCPA → INDCCA1 and PA2+INDCPA → INDCCA2 ..."
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Cited by 50 (0 self)
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Abstract. We consider the problem of defining and achieving plaintextaware encryption without random oracles in the classical publickey model. We provide definitions for a hierarchy of notions of increasing strength: PA0, PA1 and PA2, chosen so that PA1+INDCPA → INDCCA1 and PA2+INDCPA → INDCCA2. Towards achieving the new notions of plaintext awareness, we show that a scheme due to Damg˚ard [12], denoted DEG, and the “lite ” version of the CramerShoup scheme [11], denoted CSlite, are both PA0 under the DHK0 assumption of [12], and PA1 under an extension of this assumption called DHK1. As a result, DEG is the most efficient proven INDCCA1 scheme known. 1
On the compressibility of NP instances and cryptographic applications
 In Electronic Colloquium on Computational Complexity (ECCC
, 2006
"... We initiate the study of compression that preserves the solution to an instance of a problem rather than preserving the instance itself. Our focus is on the compressibility of NP decision problems. We consider NP problems that have long instances but relatively short witnesses. The question is, can ..."
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Cited by 41 (1 self)
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We initiate the study of compression that preserves the solution to an instance of a problem rather than preserving the instance itself. Our focus is on the compressibility of NP decision problems. We consider NP problems that have long instances but relatively short witnesses. The question is, can one efficiently compress an instance and store a shorter representation that maintains the information of whether the original input is in the language or not. We want the length of the compressed instance to be polynomial in the length of the witness rather than the length of original input. Such compression enables to succinctly store instances until a future setting will allow solving them, either via a technological or algorithmic breakthrough or simply until enough time has elapsed. We give a new classification of NP with respect to compression. This classification forms a stratification of NP that we call the VC hierarchy. The hierarchy is based on a new type of reduction called Wreduction and there are compressioncomplete problems for each class. Our motivation for studying this issue stems from the vast cryptographic implications compressibility has. For example, we say that SAT is compressible if there exists a polynomial p(·, ·) so that given a formula consisting of m clauses over n variables it is possible to come up with an equivalent (w.r.t satisfiability) formula of size at most p(n, logm). Then given a compression algorithm for SAT we provide a construction of collision resistant hash functions from any oneway function. This task was shown to be impossible via blackbox reductions [57], and indeed the construction presented is inherently nonblackbox. Another application of SAT compressibility is a cryptanalytic result concerning the limitation of everlasting security in the bounded storage model when mixed with (time) complexity based cryptography. In addition, we study an approach to constructing an Oblivious Transfer Protocol from any oneway function. This approach is based on compression for SAT that also has a property that we call witness retrievability. However, we mange to prove severe limitations on the ability to achieve witness retrievable compression of SAT. 1
Discretelogbased signatures may not be equivalent to discrete log
 ASIACRYPT 2005, LNCS 3788
, 2005
"... Abstract. We provide evidence that the unforgeability of several discretelog based signatures like Schnorr signatures cannot be equivalent to the discrete log problem in the standard model. This contradicts in nature wellknown proofs standing in weakened proof methodologies, in particular proofs e ..."
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Cited by 28 (2 self)
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Abstract. We provide evidence that the unforgeability of several discretelog based signatures like Schnorr signatures cannot be equivalent to the discrete log problem in the standard model. This contradicts in nature wellknown proofs standing in weakened proof methodologies, in particular proofs employing various formulations of the Forking Lemma in the random oracle Model. Our impossibility proofs apply to many discretelogbased signatures like ElGamal signatures and their extensions, DSA, ECDSA and KCDSA as well as standard generalizations of these, and even RSAbased signatures like GQ. We stress that our work sheds more light on the provable (in)security of popular signature schemes but does not explicitly lead to actual attacks on these. 1
Efficient Consistency Proofs for Generalized Queries on Committed Database
, 2004
"... A consistent query protocol (CQP) allows a database owner to publish a very short string c which commits her and everybody else to a particular database D, so that any copy of the database can later be used to answer queries and give short proofs that the answers are consistent with the commitmen ..."
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Cited by 28 (2 self)
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A consistent query protocol (CQP) allows a database owner to publish a very short string c which commits her and everybody else to a particular database D, so that any copy of the database can later be used to answer queries and give short proofs that the answers are consistent with the commitment c.
Communicationefficient noninteractive proofs of knowledge with online extractors
 In CRYPTO 2005
, 2005
"... marc.fischlin @ inf.ethz.ch ..."
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