Nonmalleable encryption of quantum information

We introduce the notion of nonmalleability of a quantum state encryption scheme (in dimension d ): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a sch...

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Bibliographic Details
Published in:Journal of mathematical physics 2009-04, Vol.50 (4), p.042106-042106-8
Main Authors: Ambainis, Andris, Bouda, Jan, Winter, Andreas
Format: Article
Language:English
Subjects:
Approximation
Data encryption
Exact sciences and technology
Information
Mathematical methods in physics
Mathematics
Physics
Quantum physics
Sciences and techniques of general use
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Summary:We introduce the notion of nonmalleability of a quantum state encryption scheme (in dimension d ): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a unitary 2-design [Dankert, et al. , e-print arXiv:quant-ph/0606161 ], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of ( d 2 − 1 ) 2 + 1 on the number of unitaries in a 2-design [Gross, et al. , J. Math. Phys. 48, 052104 (2007)], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with ≤ d 5 elements, we show that there are always approximate 2-designs with O ( ϵ − 2 d 4   log   d ) elements.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3094756