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- Craig Gentry, Chris Peikert, Vinod Vaikuntanathan
- Electronic Colloquium on Computational Complexity
- 2007

We show how to construct a variety of "trapdoor" cryptographic tools assuming the worst-case 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 trapdoor function with <i>preimage sampling</i>, simple and efficient… (More)

- Vadim Lyubashevsky, Chris Peikert, Oded Regev
- EUROCRYPT
- 2010

The “learning with errors” (LWE) problem is to distinguish random linear equations, which have been perturbed by a small amount of noise, from truly uniform ones. The problem has been shown to be as hard as worst-case lattice problems, and in recent years it has served as the foundation for a plethora of cryptographic applications.… (More)

- Richard Lindner, Chris Peikert
- CT-RSA
- 2010

We analyze the concrete security and key sizes of theoretically sound lattice-based encryption schemes based on the “learning with errors” (LWE) problem. Our main contributions are: (1) a new lattice attack on LWE that combines basis reduction with an enumeration algorithm admitting a time/success tradeoff, which performs better than the simple… (More)

- Chris Peikert, Brent Waters
- Electronic Colloquium on Computational Complexity
- 2007

We propose a new general primitive called lossy trapdoor functions (lossy TDFs), and realize it under a variety of different number theoretic assumptions, including hardness of the decisional Diffie-Hellman (DDH) problem and the worst-case hardness of lattice problems.
Using lossy TDFs, we develop a new approach for constructing several important… (More)

- Daniele Micciancio, Chris Peikert
- IACR Cryptology ePrint Archive
- 2011

We give new methods for generating and using “strong trapdoors” in cryptographic lattices, which are simultaneously simple, efficient, easy to implement (even in parallel), and asymptotically optimal with very small hidden constants. Our methods involve a new kind of trapdoor, and include specialized algorithms for inverting LWE, randomly sampling SIS… (More)

- Chris Peikert
- Theoretical Foundations of Practical Information…
- 2008

We construct public-key cryptosystems that are secure assuming the<i>worst-case</i> hardness of approximating the minimum distance on n-dimensional lattices to within small Poly(n) factors. Prior cryptosystems with worst-case connections were based either on the shortest vector problem for a <i>special class</i> of lattices (Ajtai and Dwork, STOC 1997;… (More)

- David Cash, Dennis Hofheinz, Eike Kiltz, Chris Peikert
- Journal of Cryptology
- 2010

We introduce a new lattice-based 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 ‘hash-and-sign’ signature scheme in the standard model (i.e., no random oracles), and the first hierarchical identity-based encryption (HIBE) scheme (also… (More)

- Joël Alwen, Chris Peikert
- Theory of Computing Systems
- 2008

We revisit the problem of generating a ‘hard’ random lattice together with a basis of relatively short vectors. This problem has gained in importance lately due to new cryptographic schemes that use such a procedure to generate public/secret key pairs. In these applications, a shorter basis corresponds to milder underlying complexity assumptions and smaller… (More)

- Benny Applebaum, David Cash, Chris Peikert, Amit Sahai
- CRYPTO
- 2009

The well-studied task of learning a linear function with errors is a seemingly hard problem and the basis for several cryptographic schemes. Here we demonstrate additional applications that enjoy strong security properties and a high level of efficiency. Namely, we construct: 1. Public-key and symmetric-key cryptosystems that provide security for… (More)

- Chris Peikert, Vinod Vaikuntanathan, Brent Waters
- CRYPTO
- 2007

We propose a simple and general framework for constructing oblivious transfer (OT) protocols that are efficient, universally composable, and generally realizable from a variety of standard number-theoretic assumptions, including the decisional Diffie-Hellman assumption, the quadratic residuosity assumption, and worst-case lattice assumptions. Our OT… (More)