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Fine-Grained Cryptography

  • Akshay Degwekar
  • Vinod Vaikuntanathan
  • Prashant Nalini Vasudevan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9816)

Abstract

Fine-grained cryptographic primitives are ones that are secure against adversaries with an a-priori bounded polynomial amount of resources (time, space or parallel-time), where the honest algorithms use less resources than the adversaries they are designed to fool. Such primitives were previously studied in the context of time-bounded adversaries (Merkle, CACM 1978), space-bounded adversaries (Cachin and Maurer, CRYPTO 1997) and parallel-time-bounded adversaries (Håstad, IPL 1987). Our goal is come up with fine-grained primitives (in the setting of parallel-time-bounded adversaries) and to show unconditional security of these constructions when possible, or base security on widely believed separation of worst-case complexity classes. We show:
  1. 1.

    \({\textsf {NC}^{1}}\)-cryptography: Under the assumption that Open image in new window , we construct one-way functions, pseudo-random generators (with sub-linear stretch), collision-resistant hash functions and most importantly, public-key encryption schemes, all computable in \({\textsf {NC}^{1}}\) and secure against all \({\textsf {NC}^{1}}\) circuits. Our results rely heavily on the notion of randomized encodings pioneered by Applebaum, Ishai and Kushilevitz, and crucially, make non-black-box use of randomized encodings for logspace classes.

     
  2. 2.

    \({\textsf {AC}^{0}}\)-cryptography: We construct (unconditionally secure) pseudo-random generators with arbitrary polynomial stretch, weak pseudo-random functions, secret-key encryption and perhaps most interestingly, collision-resistant hash functions, computable in \({\textsf {AC}^{0}}\) and secure against all \({\textsf {AC}^{0}}\) circuits. Previously, one-way permutations and pseudo-random generators (with linear stretch) computable in \({\textsf {AC}^{0}}\) and secure against \({\textsf {AC}^{0}}\) circuits were known from the works of Håstad and Braverman.

     

Keywords

Hash Function Encryption Scheme Homomorphic Encryption Cryptographic Primitive Semantic Security 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We thank Prabhanjan Ananth for several useful discussions towards the beginning of the project. We would also like to thank the anonymous reviewers for their careful comments.

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Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Akshay Degwekar
    • 1
  • Vinod Vaikuntanathan
    • 1
  • Prashant Nalini Vasudevan
    • 1
  1. 1.MIT, CSAILCambridgeUSA

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