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.
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Phan, R.C.W., Vaudenay, S. (2009). On the Impossibility of Strong Encryption Over \(\aleph_0\) . In: Chee, Y.M., Li, C., Ling, S., Wang, H., Xing, C. (eds) Coding and Cryptology. IWCC 2009. Lecture Notes in Computer Science, vol 5557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01877-0_17
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