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Pseudorandom Functions and Lattices (2011)

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by Abhishek Banerjee , Chris Peikert , Alon Rosen
Citations:35 - 10 self
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BibTeX

@MISC{Banerjee11pseudorandomfunctions,
    author = {Abhishek Banerjee and Chris Peikert and Alon Rosen},
    title = {Pseudorandom Functions and Lattices},
    year = {2011}
}

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Abstract

We give direct constructions of pseudorandom function (PRF) families based on conjectured hard lattice problems and learning problems. Our constructions are asymptotically efficient and highly parallelizable in a practical sense, i.e., they can be computed by simple, relatively small low-depth arithmetic or boolean circuits (e.g., in NC 1 or even TC 0). In addition, they are the first low-depth PRFs that have no known attack by efficient quantum algorithms. Central to our results is a new “derandomization ” technique for the learning with errors (LWE) problem which, in effect, generates the error terms deterministically. 1 Introduction and Main Results The past few years have seen significant progress in constructing public-key, identity-based, and homomorphic cryptographic schemes using lattices, e.g., [Reg05, PW08, GPV08, Gen09, CHKP10, ABB10a] and many more. Part of their appeal stems from provable worst-case hardness guarantees (starting with the seminal work of Ajtai [Ajt96]), good asymptotic efficiency and parallelism, and apparent resistance to quantum

Keyphrases

pseudorandom function    provable worst-case hardness guarantee    seminal work    apparent resistance    significant progress    practical sense    good asymptotic efficiency    ajtai ajt96    direct construction    past year    new derandomization technique    homomorphic cryptographic scheme    main result    error term    efficient quantum algorithm    first low-depth prfs    boolean circuit    conjectured hard lattice problem   

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