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Encryption with weakly random keys using quantum ciphertext

Basic information
Original title:Encryption with weakly random keys using quantum ciphertext
Authors:Jan Bouda, Matej Pivoluska, Martin Plesch
Further information
Citation:BOUDA, Jan, Matej PIVOLUSKA a Martin PLESCH. Encryption with weakly random keys using quantum ciphertext. Quantum Information and Computing, Princeton, USA: Rinton, 2012, roč. 12, 5-6, s. 395-403. ISSN 1533-7146.Export BibTeX
@article{977098,
author = {Bouda, Jan and Pivoluska, Matej and Plesch, Martin},
article_location = {Princeton, USA},
article_number = {5-6},
keywords = {quantum cryptography weak randomness encryption},
language = {eng},
issn = {1533-7146},
journal = {Quantum Information and Computing},
title = {Encryption with weakly random keys using quantum ciphertext},
volume = {12},
year = {2012}
}
Original language:English
Field:Informatics
Type:Article in Periodical
Keywords:quantum cryptography weak randomness encryption

The lack of perfect randomness can cause significant problems in securing communication between two parties. McInnes and Pinkas proved that unconditionally secure encryption is impossible when the key is sampled from a weak random source. The adversary can always gain some information about the plaintext, regardless of the cryptosystem design. Most notably, the adversary can obtain full information about the plaintext if he has access to just two bits of information about the source (irrespective on length of the key). In this paper we show that for every weak random source there is a cryptosystem with a classical plaintext, a classical key, and a quantum ciphertext that bounds the adversary's probability $p$ to guess correctly the plaintext strictly under the McInnes-Pinkas bound, except for a single case, where it coincides with the bound. In addition, regardless of the source of randomness, the adversary's probability $p$ is strictly smaller than $1$ as long as there is some uncertainty in the key (Shannon/min-entropy is non-zero). These results are another demonstration that quantum information processing can solve cryptographic tasks with strictly higher security than classical information processing.

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