论文标题
访问结构隐藏了新型设定系统和向量家庭的秘密共享
Access Structure Hiding Secret Sharing from Novel Set Systems and Vector Families
论文作者
论文摘要
秘密共享提供了一种分配秘密股份的方法，以便可以将访问结构指定的任何授权子集汇总在一起以重新计算秘密。标准的秘密共享模型需要公共访问结构，这侵犯了隐私并通过揭示高价值目标来促进对手。在本文中，我们通过引入\ emph {隐藏的访问结构}来解决这一缺点，直到某人的某些授权子集协作为止。这项工作的中心部分是构建设定系统$ \ mathcal {h} $，严格大于$ \ exp \ left（c \ dfrac {1.5（\ log h）^2} {\ log \ log \ log h} \ h} \ h} \ right）$ h $ elements的$ subset。我们的设定系统$ \ MATHCAL {H} $在$ \ Mathbb {z} _M $上定义，其中$ m $是一个非prime-PRIME功率，因此，$ \ Mathcal {H h} $中的每个集合的大小都是$ m $的，但除非$ M $ M $ clies $ M $ M $ M $ M $ M，除非一个设置$ M，否则一个设置了A ATER ANET ANET ANET ANET ANET ANET ANET AN NET ANET A ANET A NET AT SET A AN设置为A A A A A A A A A A A A A A A A A a A AN设置。我们从$ \ mathcal {h} $中得出一个vector family $ \ mathcal {v} $，以使$ \ mathcal {h} $中的超集 - subset关系由$ \ mathcal {v} $中的内部产品表示。我们使用$ \ MATHCAL {V} $来“编码”访问结构，从而开发第一个\ emph {访问结构隐藏}秘密共享方案。对于带有$ \ ell $派对的设置，我们的方案支持$ 2^{\ binom {\ ell} {\ ell/2+ 1}} $中的$ 2^{2^{2^{\ ell -o（\ log \ ell）o（\ log \ ell）}} $总单调访问结构，以及其最大访问结构的最大访问型结构$（1+ o（1） \ dfrac {2^{\ ell+1}}} {\ sqrt {π\ ell/2}} $。该方案假定半honest多项式时间各方，其安全性依赖于广义的差异 - 赫尔曼假设。
Secret sharing provides a means to distribute shares of a secret such that any authorized subset of shares, specified by an access structure, can be pooled together to recompute the secret. The standard secret sharing model requires public access structures, which violates privacy and facilitates the adversary by revealing high-value targets. In this paper, we address this shortcoming by introducing \emph{hidden access structures}, which remain secret until some authorized subset of parties collaborate. The central piece of this work is the construction of a set-system $\mathcal{H}$ with strictly greater than $\exp\left(c \dfrac{1.5 (\log h)^2}{\log \log h}\right)$ subsets of a set of $h$ elements. Our set-system $\mathcal{H}$ is defined over $\mathbb{Z}_m$, where $m$ is a non-prime-power, such that the size of each set in $\mathcal{H}$ is divisible by $m$ but the sizes of their pairwise intersections are not divisible by $m$, unless one set is a subset of another. We derive a vector family $\mathcal{V}$ from $\mathcal{H}$ such that superset-subset relationships in $\mathcal{H}$ are represented by inner products in $\mathcal{V}$. We use $\mathcal{V}$ to "encode" the access structures and thereby develop the first \emph{access structure hiding} secret sharing scheme. For a setting with $\ell$ parties, our scheme supports $2^{\binom{\ell}{\ell/2+1}}$ out of the $2^{2^{\ell - O(\log \ell)}}$ total monotone access structures, and its maximum share size for any access structures is $(1+ o(1)) \dfrac{2^{\ell+1}}{\sqrt{π\ell/2}}$. The scheme assumes semi-honest polynomial-time parties, and its security relies on the Generalized Diffie-Hellman assumption.
