Tamper Detection Against Unitary Operators

Security of a storage device against a tampering adversary has been a well-studied topic in classical cryptography. Such models give black-box access to an adversary, and the aim is to protect the stored message or abort the protocol if there is any tampering. The study of these models has led to some important cryptographic and communication primitives, such as tamper detection codes and non-malleable codes. In this work, we extend the scope of the theory of tamper detection codes against an adversary with quantum capabilities. We consider encoding and decoding schemes that are used to encode a k-qubit quantum message |m > to obtain an n-qubit quantum codeword |psi(m)>. A quantum codeword |psi(m)> can be adversarially tampered via a unitary U from some known tampering unitary family U-Adv (acting on C-2n), resulting in U|psi(m)> | = |Tr(U)| <= phi 2(n), where phi is suitably chosen parameter. Quantum tamper detection codes that we construct can be considered to be quantum variants of classical tamper detection codes studied by Jafargholi and Wichs ['15], which are also known to exist under similar restrictions. Additionally, we show that when the message set M is classical, such a construction can be realized as a non-malleable code against an adversary having access to any U-Adv of size up to 2(2 alpha n).