On the Impossibility of Strong Encryption Over $\aleph_0$

  • Authors:
  • Raphael C. Phan;Serge Vaudenay

  • Affiliations:
  • Loughborough Uni, U.K.;EPFL, Switzerland

  • Venue:
  • IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
  • Year:
  • 2009

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Abstract

We give two impossibility results regarding strong encryption over an infinite enumerable domain. The first one relates to statistically secure one-time encryption. The second one relates to computationally secure encryption resisting adaptive chosen ciphertext attacks in streaming mode with bounded resources: memory, time delay or output length. Curiously, both impossibility results can be achieved with either finite or continuous domains. The latter result explains why known CCA-secure cryptosystem constructions require at least two passes to decrypt a message with bounded resources.