TY - JOUR
T1 - Nonmalleable encryption of quantum information
AU - Ambainis, Andris
AU - Bouda, Jan
AU - Winter, Andreas
N1 - Funding Information:
J.B. acknowledges support of the Hertha Firnberg ARC stipend program, and Grant Nos. GAČR 201/06/P338, GAČR 201/07/0603, and MSM0021622419. A.W. received support from the European Commission (project “QAP”), from the U.K. EPSRC through the “QIP IRC” and an Advanced Research Fellowship, and through a Wolfson Research Merit Award of the Royal Society. The Centre for Quantum Technologies is funded by the Singapore Ministry of Education and the National Research Foundation as part of the Research Centres of Excellence program.
PY - 2009
Y1 - 2009
N2 - 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, 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 (d2 -1) 2 +1 on the number of unitaries in a 2-design [Gross, 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 d5 elements, we show that there are always approximate 2-designs with O (-2 d4 log d) elements.
AB - 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, 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 (d2 -1) 2 +1 on the number of unitaries in a 2-design [Gross, 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 d5 elements, we show that there are always approximate 2-designs with O (-2 d4 log d) elements.
UR - https://www.scopus.com/pages/publications/65549101831
U2 - 10.1063/1.3094756
DO - 10.1063/1.3094756
M3 - Article
AN - SCOPUS:65549101831
SN - 0022-2488
VL - 50
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 4
M1 - 042106
ER -