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1,158
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
Pseudorandom Generator Based on Hard Lattice Problem
"... This paper studies how to construct a pseudorandom generator using hard lattice problems. We use a variation of the classical hard problem Inhomogeneous Small Integer Solution ISIS of lattice, say Inhomogeneous Subset Sum Solution ISSS. ISSS itself is a hash function. Proving the preimage sizes ISS ..."
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This paper studies how to construct a pseudorandom generator using hard lattice problems. We use a variation of the classical hard problem Inhomogeneous Small Integer Solution ISIS of lattice, say Inhomogeneous Subset Sum Solution ISSS. ISSS itself is a hash function. Proving the preimage sizes
Solving Hard Lattice Problems and the Security of Latticebased Cryptosystems
, 2012
"... This paper is a tutorial introduction to the present stateoftheart in the field of security of latticebased cryptosystems. After a short introduction to lattices, we describe the main hard problems in lattice theory that cryptosystems base their security on, and we present the main methods of att ..."
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Cited by 4 (3 self)
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This paper is a tutorial introduction to the present stateoftheart in the field of security of latticebased cryptosystems. After a short introduction to lattices, we describe the main hard problems in lattice theory that cryptosystems base their security on, and we present the main methods
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
 In STOC
, 2005
"... Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear co ..."
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Cited by 364 (6 self)
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(classical) publickey cryptosystem whose security is based on the hardness of the learning problem. By the main result, its security is also based on the worstcase quantum hardness of SVP and SIVP. Previous latticebased publickey cryptosystems such as the one by Ajtai and Dwork were based only on unique
How to Use a Short Basis: Trapdoors for Hard Lattices and New Cryptographic Constructions
, 2008
"... We show how to construct a variety of “trapdoor ” cryptographic tools assuming the worstcase hardness of standard lattice problems (such as approximating the length of the shortest nonzero vector to within certain polynomial factors). Our contributions include a new notion of preimage sampleable fu ..."
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Cited by 1 (0 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 length of the shortest nonzero vector to within certain polynomial factors). Our contributions include a new notion of preimage sampleable
Electronic Colloquium on Computational Complexity, Report No. 133 (2007) 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 ..."
Abstract
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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
Generating Hard Instances of Lattice Problems (Extended Abstract)
 In Proceedings of the TwentyEighth Annual ACM Symposium on the Theory of Computing
, 1996
"... . We give a random class of lattices in Z n so that, if there is a probabilistic polynomial time algorithm which finds a short vector in a random lattice with a probability of at least 1 2 then there is also a probabilistic polynomial time algorithm which solves the following three lattice probl ..."
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Cited by 143 (0 self)
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. We give a random class of lattices in Z n so that, if there is a probabilistic polynomial time algorithm which finds a short vector in a random lattice with a probability of at least 1 2 then there is also a probabilistic polynomial time algorithm which solves the following three lattice
The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations
, 1993
"... We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2. If for some ..."
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Cited by 170 (7 self)
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We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2
Estimation of effective interresidue contact energies from protein crystal structures: quasichemical approximation
 Macromolecules
, 1985
"... ABSTRACT: Effective interresidue contact energies for proteins in solution are estimated from the numbers of residueresidue contacts observed in crystal structures of globular proteins by means of the quasichemical approximation with an approximate treatment of the effects of chain connectivity. E ..."
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Cited by 269 (11 self)
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. Employing a lattice model, each residue of a protein is assumed to occupy a site in a lattice and vacant sites are regarded to be occupied by an effective solvent molecule whose size is equal to the average size of a residue. A basic assumption is that the average characteristics of residueresidue contacts
Results 1  10
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