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Cryptographic Agents: Towards a Unified Theory of Computing on Encrypted Data

  • Shashank Agrawal
  • Shweta Agrawal
  • Manoj Prabhakaran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9057)

Abstract

We provide a new framework of cryptographic agents that unifies various modern “cryptographic objects” — identity-based encryption, fully-homomorphic encryption, functional encryption, and various forms of obfuscation – similar to how the Universal Composition framework unifies various multi-party computation tasks like commitment, coin-tossing and zero-knowledge proofs. These cryptographic objects can all be cleanly modeled as “schemata” in our framework.

Highlights of our framework include the following:
  • We use a new indistinguishability preserving (IND-PRE) definition of security that interpolates indistinguishability and simulation style definitions, which (often) sidesteps the known impossibilities for the latter. IND-PRE-security is parameterized by the choice of the “test” family, such that by choosing different test families, one can obtain different levels of security for the same primitive (including various standard definitions in the literature).

  • We present a notion of reduction from one schema to another and a powerful composition theorem with respect to \(\mathsf{IND-PRE }\) security. We show that obfuscation is a “complete” schema under this notion, under standard cryptographic assumptions. We also provide a stricter notion of reduction (\(\varDelta \)-reduction) that composes even when security is only with respect to certain restricted test families of importance.

  • Last but not the least, our framework can be used to model abstractions like the generic group model and the random oracle model, letting one translate a general class of constructions in these heuristic models to constructions based on standard model assumptions.

We also illustrate how our framework can be applied to specific primitives like obfuscation and functional encryption. We relate our definitions to existing definitions and also give new constructions and reductions between different primitives.

Keywords

Random Oracle Homomorphic Encryption Random Oracle Model Composition Theorem Probabilistic Polynomial Time 
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.

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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  • Shashank Agrawal
    • 1
  • Shweta Agrawal
    • 2
  • Manoj Prabhakaran
    • 1
  1. 1.University of Illinois Urbana-ChampaignChampaignUSA
  2. 2.Indian Institute of Technology DelhiDelhiIndia

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