International Association
for Cryptologic Research

Tamper-detection codes (TDCs) are fundamental objects at the intersection of cryptography and coding theory. A TDC encodes messages in such a manner that tampering the codeword causes the decoder to either output the original message, or reject it. In this work, we study quantum analogs of one of the most well-studied adversarial tampering models: the so-called $t$-split-state tampering model, where the codeword is divided into $t$ shares, and each share is tampered with ``locally". It is impossible to achieve tamper detection in the split-state model using classical codewords. Nevertheless, we demonstrate that the situation changes significantly if the message can be encoded into a multipartite quantum state, entangled across the $t$ shares. Concretely, we define a family of quantum TDCs defined on any $t\geq 3$ shares, which can detect arbitrary split-state tampering so long as the adversaries are unentangled, or even limited to a finite amount of pre-shared entanglement. Previously, this was only known in the limit of asymptotically large $t$. As our flagship application, we show how to augment threshold secret sharing schemes with similar tamper-detecting guarantees. We complement our results by establishing connections between quantum TDCs and quantum encryption schemes.

Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. One of the strongest and most well-studied adversarial tampering models is 2-split-state tampering. Here, a codeword is split into two parts which are stored in physically distant servers, and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of classical messages. Furthermore, until recent work by Aggarwal, Boddu, and Jain (IEEE Trans. Inf. Theory 2024 & arXiv 2022), adversaries with quantum capabilities and shared entanglement had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. Then, we present explicit constructions of such schemes that achieve low-error non-malleability. More precisely, for some constant c>0, we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length n, any message length at most n^c, and error \eps=2^{-{n^{c}}}. In the easier setting of average-case non-malleability, we achieve efficient non-malleable coding with rate close to 1/11.