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arXiv 2105.04487cs.CRcs.ITmath.ITquant-ph
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针对酉算子的篡改检测

Tamper Detection against Unitary Operators

Naresh Goud Boddu, Upendra S. Kapshikar

AI总结:

本研究将篡改检测码扩展到量子对手场景,证明在酉算子族规模小于2^{2^{αn}}且不过于接近恒等算子的条件下,量子篡改检测码存在,并可为经典消息集实现非可延展码。

摘要:

存储设备对抗篡改对手的安全性一直是经典密码学中研究充分的话题。此类模型给予对手黑盒访问权限,目标是保护存储的消息,或在发生任何篡改时中止协议。在本工作中,我们将篡改检测码理论的范围扩展到具有量子能力的对手。我们考虑用于编码k量子比特量子消息|m>以获得n量子比特量子码字|ψ_m>的编码和解码方案。量子码字|ψ_m>可能通过某个来自已知篡改酉族U_Adv(作用于C^{2^n})的酉算子U被对手篡改。首先,我们启动了量子篡改检测码的一般性研究,该码检测是否存在由酉算子作用引起的任何篡改。若没有篡改,我们希望输出原始消息。我们证明,对于任何酉算子族U_Adv,只要|U_Adv| < 2^{2^{αn}}(其中α∈(0,1/6)为某常数),且酉算子不过于接近恒等算子,量子篡改检测码就存在。我们构造的量子篡改检测码可视为Jafargholi和Wichs['15]研究的经典篡改检测码的量子变体,后者在类似限制下也被证明存在。此外,我们表明当消息集M是经典时,该构造可实现为针对任何大小至多2^{2^{αn}}的U_Adv的非可延展码。

英文摘要:

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. 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 $\vert m\rangle$ to obtain an $n$-qubit quantum codeword $\vert {ψ_m} \rangle$. A quantum codeword $\vert {ψ_m} \rangle$ can be adversarially tampered via a unitary $U$ from some known tampering unitary family $\mathcal{U}_{\mathsf{Adv}}$ (acting on $\mathbb{C}^{2^n}$). Firstly, we initiate the general study of \emph{quantum tamper detection codes}, which detect if there is any tampering caused by the action of a unitary operator. In case there was no tampering, we would like to output the original message. We show that quantum tamper detection codes exist for any family of unitary operators $\mathcal{U}_{\mathsf{Adv}}$, such that $\vert\mathcal{U}_{\mathsf{Adv}} \vert < 2^{2^{αn}}$ for some constant $α\in (0,1/6)$; provided that unitary operators are not too close to the identity operator. Quantum tamper detection codes that we construct can be considered to be quantum variants of \emph{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 $\mathcal{M}$ is classical, such a construction can be realized as a \emph{non-malleable code} against any $\mathcal{U}_{\mathsf{Adv}}$ of size up to $2^{2^{αn}}$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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