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Erschienen in:
Improved Security Proofs in Lattice-Based Cryptography: Using the Rényi Divergence Rather Than the Statistical Distance Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Adaptively Secure Puncturable Pseudorandom Functions in the Standard Model

verfasst von : Susan Hohenberger, Venkata Koppula, Brent Waters

Erschienen in: Advances in Cryptology -- ASIACRYPT 2015

Verlag: Springer Berlin Heidelberg

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Abstract

We study the adaptive security of constrained PRFs in the standard model. We initiate our exploration with puncturable PRFs. A puncturable PRF family is a special class of constrained PRFs, where the constrained key is associated with an element \(x'\) in the input domain. The key allows evaluation at all points \(x\ne x'\).
We show how to build puncturable PRFs with adaptive security proofs in the standard model that involve only polynomial loss to the underlying assumptions. Prior work had either super-polynomial loss or applied the random oracle heuristic. Our construction uses indistinguishability obfuscation and DDH-hard algebraic groups of composite order.
More generally, one can consider a t-puncturable PRF: PRFs that can be punctured at any set of inputs S, provided the size of S is less than a fixed polynomial. We additionally show how to transform any (single) puncturable PRF family to a t-puncturable PRF family, using indistinguishability obfuscation.

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Vorheriges Kapitel Multi-party Key Exchange for Unbounded Parties from Indistinguishability Obfuscation
Nächstes Kapitel Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security
Fußnoten
1
These were alternatively called functional PRFs [6] and delegatable PRFs [21].
 
2
This definition can be extended to handle multiple challenge points. See Sect. 3 for details.
 
3
The prefix construction of  [6, 21] were also selective.
 
4
In fact, the GGM PRF construction can be used to construct prefix-fixing constrained PRFs.
 
5
Looking ahead, in the proof of security, the program \(\mathsf {PuncturedKey}_{k,x'}\) will be replaced by \(\mathsf {PuncturedKey}'_{V,w,D,u,x'}\), \(\mathsf {PuncturedKeyAlt}_{u,k,k',x'}\) and \(\mathsf {PuncturedKeyAlt}'_{u,W,E,k,x'}\) in subsequent hybrids. Since this transformation relies on \(i\mathcal {O}\) being secure, we need that all programs have same size. Hence, all programs are padded appropriately to ensure that they have the same size.
 
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Metadaten
Titel
Adaptively Secure Puncturable Pseudorandom Functions in the Standard Model
verfasst von
Susan Hohenberger
Venkata Koppula
Brent Waters
Copyright-Jahr
2015
Verlag
Springer Berlin Heidelberg
Buch
Advances in Cryptology -- ASIACRYPT 2015

Print ISBN: 978-3-662-48796-9

Electronic ISBN: 978-3-662-48797-6

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-662-48797-6_4

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