Towards Universal Quantum Tamper Detection

Abstract

Tamper-resilient cryptography studies how to protect data against adversaries who can physically manipulate codewords before they are decoded. The notion of tamper detection codes formalizes this goal, requiring that any unauthorized modification be detected with high probability. Classical results, starting from Jafargholi and Wichs (TCC 2015), established the existence of such codes against very large families of tampering functions, subject to structural restrictions ruling out identity and constant maps. Recent works of Boddu and Kapshikar (Quantum, 7) and Bergamaschi (Eurocrypt 2024) have extended these ideas to quantum adversaries, but only consider unitary tampering families. In this work, we give the first general treatment of tamper detection against arbitrary quantum maps. We show that Haar-random encoding schemes achieve exponentially small soundness error against any adversarial family whose size, Kraus rank, and entanglement fidelity obey natural constraints, which are direct quantum analogues of restrictions in the classical setting. Our results unify and extend previous works. Beyond this, we demonstrate a fundamental separation between classical and quantum tamper detection. Classically, relaxed tamper detection which allows either rejection or recovery of the original message cannot protect even against the family of constant functions. This family is of size $2^n$. In contrast, we show that quantum encodings can handle this obstruction, and we conjecture and provide evidence that they may in fact provide relaxed tamper detection and non-malleable security against any family of quantum maps of size up to $2^{2^{\alpha n}}$ for any constant $\alpha <\frac{1}{2}$, leading to a conjecture on the existence of universal quantum tamper detection. Our results provide the first evidence that quantum tamper detection is strictly more powerful than its classical counterpart.