Trapdoors for Hard Lattices and New Cryptographic Constructions

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Trapdoors for Hard Lattices and New Cryptographic Constructions (2007)

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by Craig Gentry , Chris Peikert , Vinod Vaikuntanathan

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@MISC{Gentry07trapdoorsfor,
    author = {Craig Gentry and Chris Peikert and Vinod Vaikuntanathan},
    title = {Trapdoors for Hard Lattices and New Cryptographic Constructions},
    year = {2007}
}

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Abstract

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 “hash-and-sign ” digital signature schemes, universally composable oblivious transfer, and identity-based 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 Gaussian-like 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 CNS-0716786 and CNS-0749931. 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

Keyphrases

hard lattice new cryptographic construction national science foundation arbitrary lattice core technical component sri international worstcase hardness output distribution efficient algorithm standard lattice problem herbert kunzel stanford graduate fellowship particular geometry composable oblivious transfer crucial security property trapdoor cryptographic tool nonzero vector trapdoor function gaussian-like probability distribution identity-based encryption efficient hash-and-sign digital signature scheme grant cns-0716786 small factor preimage sampling standard deviation

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