On Split-State Quantum Tamper Detection and Non-Malleability
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911286811426816 |
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| author | Bergamaschi, Thiago Boddu, Naresh Goud |
| author_facet | Bergamaschi, Thiago Boddu, Naresh Goud |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16009 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Split-State Quantum Tamper Detection and Non-Malleability Bergamaschi, Thiago Boddu, Naresh Goud Quantum Physics 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. |
| title | On Split-State Quantum Tamper Detection and Non-Malleability |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2311.16009 |