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221
Trapdoors for Hard Lattices and New Cryptographic Constructions
, 2007
"... We show how to construct a variety of “trapdoor ” cryptographic tools assuming the worstcase hardness of standard lattice problems (such as approximating the shortest nonzero vector to within small factors). The applications include trapdoor functions with preimage sampling, simple and efficient “ha ..."
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Cited by 191 (26 self)
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We show how to construct a variety of “trapdoor ” cryptographic tools assuming the worstcase hardness of standard lattice problems (such as approximating the shortest nonzero vector to within small factors). The applications include trapdoor functions with preimage sampling, simple and efficient “hashandsign ” digital signature schemes, universally composable oblivious transfer, and identitybased encryption. A core technical component of our constructions is an efficient algorithm that, given a basis of an arbitrary lattice, samples lattice points from a Gaussianlike probability distribution whose standard deviation is essentially the length of the longest vector in the basis. In particular, the crucial security property is that the output distribution of the algorithm is oblivious to the particular geometry of the given basis. ∗ Supported by the Herbert Kunzel Stanford Graduate Fellowship. † This material is based upon work supported by the National Science Foundation under Grants CNS0716786 and CNS0749931. Any opinions, findings, and conclusions or recommedations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. ‡ The majority of this work was performed while at SRI International. 1 1
Predicate Encryption Supporting Disjunctions, Polynomial Equations, and Inner Products
"... Abstract. Predicate encryption is a new paradigm generalizing, among other things, identitybased encryption. In a predicate encryption scheme, secret keys correspond to predicates and ciphertexts are associated with attributes; the secret key SKf corresponding to a predicate f can be used to decryp ..."
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Cited by 173 (23 self)
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Abstract. Predicate encryption is a new paradigm generalizing, among other things, identitybased encryption. In a predicate encryption scheme, secret keys correspond to predicates and ciphertexts are associated with attributes; the secret key SKf corresponding to a predicate f can be used to decrypt a ciphertext associated with attribute I if and only if f(I) = 1. Constructions of such schemes are currently known for relatively few classes of predicates. We construct such a scheme for predicates corresponding to the evaluation of inner products over ZN (for some large integer N). This, in turn, enables constructions in which predicates correspond to the evaluation of disjunctions, polynomials, CNF/DNF formulae, or threshold predicates (among others). Besides serving as a significant step forward in the theory of predicate encryption, our results lead to a number of applications that are interesting in their own right. 1
CiphertextPolicy AttributeBased Encryption: An Expressive, Efficient, and Provably Secure Realization
, 2008
"... We present new techniques for realizing CiphertextPolicy Attribute Encryption (CPABE) under concrete and noninteractive cryptographic assumptions. Our solutions allow any encryptor to specify access control in terms of an LSSS matrix, M, over the attributes in the system. We present three differen ..."
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Cited by 134 (9 self)
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We present new techniques for realizing CiphertextPolicy Attribute Encryption (CPABE) under concrete and noninteractive cryptographic assumptions. Our solutions allow any encryptor to specify access control in terms of an LSSS matrix, M, over the attributes in the system. We present three different constructions that allow different tradeoffs between the systems efficiency and the complexity of the assumptions used. All three constructions use a common methodology of “directly” solving the CPABE problem that enable us to get much better efficiency than prior approaches.
Bonsai Trees, or How to Delegate a Lattice Basis
, 2010
"... We introduce a new latticebased cryptographic structure called a bonsai tree, and use it to resolve some important open problems in the area. Applications of bonsai trees include: • An efficient, stateless ‘hashandsign ’ signature scheme in the standard model (i.e., no random oracles), and • The ..."
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Cited by 123 (7 self)
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We introduce a new latticebased cryptographic structure called a bonsai tree, and use it to resolve some important open problems in the area. Applications of bonsai trees include: • An efficient, stateless ‘hashandsign ’ signature scheme in the standard model (i.e., no random oracles), and • The first hierarchical identitybased encryption (HIBE) scheme (also in the standard model) that does not rely on bilinear pairings. Interestingly, the abstract properties of bonsai trees seem to have no known realization in conventional numbertheoretic cryptography. 1
Multidimension range query over encrypted data
 In IEEE Symposium on Security and Privacy
, 2007
"... encryption We design an encryption scheme called Multidimensional Range Query over Encrypted Data (MRQED), to address the privacy concerns related to the sharing of network audit logs and various other applications. Our scheme allows a network gateway to encrypt summaries of network flows before su ..."
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Cited by 112 (5 self)
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encryption We design an encryption scheme called Multidimensional Range Query over Encrypted Data (MRQED), to address the privacy concerns related to the sharing of network audit logs and various other applications. Our scheme allows a network gateway to encrypt summaries of network flows before submitting them to an untrusted repository. When network intrusions are suspected, an authority can release a key to an auditor, allowing the auditor to decrypt flows whose attributes (e.g., source and destination addresses, port numbers, etc.) fall within specific ranges. However, the privacy of all irrelevant flows are still preserved. We formally define the security for MRQED and prove the security of our construction under the decision bilinear DiffieHellman and decision linear assumptions in certain bilinear groups. We study the practical performance of our construction in the context of network audit logs. Apart from network audit logs, our scheme also has interesting applications for financial audit logs, medical privacy, untrusted remote storage, etc. In particular, we show that MRQED implies a solution to its dual problem, which enables investors to trade stocks through a broker in a privacypreserving manner. 1
Functional Encryption: Definitions and Challenges
"... We initiate the formal study of functional encryption by giving precise definitions of the concept and its security. Roughly speaking, functional encryption supports restricted secret keys that enable a key holder to learn a specific function of encrypted data, but learn nothing else about the data. ..."
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Cited by 109 (17 self)
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We initiate the formal study of functional encryption by giving precise definitions of the concept and its security. Roughly speaking, functional encryption supports restricted secret keys that enable a key holder to learn a specific function of encrypted data, but learn nothing else about the data. For example, given an encrypted program the secret key may enable the key holder to learn the output of the program on a specific input without learning anything else about the program. We show that defining security for functional encryption is nontrivial. First, we show that a natural gamebased definition is inadequate for some functionalities. We then present a natural simulationbased definition and show that it (provably) cannot be satisfied in the standard model, but can be satisfied in the random oracle model. We show how to map many existing concepts to our formalization of functional encryption and conclude with several interesting open problems in this young area.
Pairings for Cryptographers
 IN PREPARATION
, 2006
"... Many research papers in pairing based cryptography treat pairings as a "black box". These papers build cryptographic schemes making use of various properties of pairings. If this approach is taken, then it is easy for authors to make invalid assumptions concerning the properties of pai ..."
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Cited by 104 (7 self)
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Many research papers in pairing based cryptography treat pairings as a "black box". These papers build cryptographic schemes making use of various properties of pairings. If this approach is taken, then it is easy for authors to make invalid assumptions concerning the properties of pairings. The cryptographic schemes developed may not be realizable in practice, or may not be as e#cient as the authors assume.
Efficient lattice (H)IBE in the standard model
 In EUROCRYPT 2010, LNCS
, 2010
"... Abstract. We construct an efficient identity based encryption system based on the standard learning with errors (LWE) problem. Our security proof holds in the standard model. The key step in the construction is a family of lattices for which there are two distinct trapdoors for finding short vectors ..."
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Cited by 98 (15 self)
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Abstract. We construct an efficient identity based encryption system based on the standard learning with errors (LWE) problem. Our security proof holds in the standard model. The key step in the construction is a family of lattices for which there are two distinct trapdoors for finding short vectors. One trapdoor enables the real system to generate short vectors in all lattices in the family. The other trapdoor enables the simulator to generate short vectors for all lattices in the family except for one. We extend this basic technique to an adaptivelysecure IBE and a Hierarchical IBE. 1
Identitybased Encryption with Efficient Revocation
, 2008
"... Identitybased encryption (IBE) is an exciting alternative to publickey encryption, as IBE eliminates the need for a Public Key Infrastructure (PKI). Any setting, PKI or identitybased, must provide a means to revoke users from the system. Efficient revocation is a wellstudied problem in the trad ..."
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Cited by 87 (3 self)
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Identitybased encryption (IBE) is an exciting alternative to publickey encryption, as IBE eliminates the need for a Public Key Infrastructure (PKI). Any setting, PKI or identitybased, must provide a means to revoke users from the system. Efficient revocation is a wellstudied problem in the traditional PKI setting. However in the setting of IBE, there has been little work on studying the revocation mechanisms. The most practical solution requires the senders to also use time periods when encrypting, and all the receivers (regardless of whether their keys have been compromised or not) to update their private keys regularly by contacting the trusted authority. We note that this solution does not scale well – as the number of users increases, the work on key updates becomes a bottleneck. We propose an IBE scheme that significantly improves keyupdate efficiency on the side of the trusted party (from linear to logarithmic in the number of users), while staying efficient for the users. Our scheme builds on the ideas of the Fuzzy IBE primitive and binary tree data structure, and is provably secure.