Non-malleable encryption of quantum information

Abstract

We introduce the notion of "non-malleability" 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.], 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.], 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(epsilon^{-2} d^4 log d) elements.

8 pages. Title changed in v2, a couple of mistakes corrected, the results are essentially unchanged; accepted for publication at J Math Phys

References in corpus (3)

• Evenly distributed unitaries: on the structure of unitary designs
• Randomizing quantum states: Constructions and applications
• Optimality of private quantum channels

Cited by in corpus (21)

• Security in Quantum Cryptography
• Local random quantum circuits are approximate polynomial-designs
• Multiqubit Clifford groups are unitary 3-designs
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Classical Shadows With Noise
• Recovering quantum gates from few average gate fidelities
• Efficient unitary designs with a system-size independent number of non-Clifford gates
• Unforgeable Quantum Encryption
• Composite parameterization and Haar measure for all unitary and special unitary groups
• Catalytic quantum randomness
• Quantum non-malleability and authentication
• Efficient Unitary T-designs from Random Sums
• Efficient unitary designs and pseudorandom unitaries from permutations
• Weak approximate unitary designs and applications to quantum encryption
• On the explicit constructions of certain unitary $t$-designs
• Clifford Group and Unitary Designs under Symmetry
• Quantum Codes from Twisted Unitary $t$-groups
• Blind Oracular Quantum Computation
• Quantum Codes and Irreducible Products of Characters
• Tamper Detection against Unitary Operators
• Quantum Private Broadcasting