论文标题
MDS变量生成和用户选择的安全总和
MDS Variable Generation and Secure Summation with User Selection
论文作者
论文摘要
$ K $随机变量的集合称为$（k，n）$ -MDS，如果$ k $变量的任何$ n $是独立的，并确定所有剩余变量。在MDS变量生成问题中，$ k $用户希望使用每个用户拥有的随机变量生成$（k，n）$ -MD的变量。我们表明，要生成$ 1 $（k，n）$ - mds变量的$ 1 $ n \ in \ {1,2，\ cdots，k \} $，每个用户的随机变量的最小尺寸为$ 1 + 1/2 + \ cdots + 1/k $。 一个密切相关的问题是用户选择的安全求和，服务器可以选择$ K $用户的任意子集并安全地计算所选用户的输入的总和。我们表明，要牢固地计算任意选择的$ 1 $位，每个用户持有的密钥的最小尺寸为$ 1 + 1/2 + \ cdots + 1/（k-1）$位，其可实现性使用$（k，n）$ -MDS的生成（k，n）$ -MDS变量，用于$ n \ in \ in \ in \ in \ {1,2，\ cdots k cdots，k-cdots，k-1 \} $}。
A collection of $K$ random variables are called $(K,n)$-MDS if any $n$ of the $K$ variables are independent and determine all remaining variables. In the MDS variable generation problem, $K$ users wish to generate variables that are $(K,n)$-MDS using a randomness variable owned by each user. We show that to generate $1$ bit of $(K,n)$-MDS variables for each $n \in \{1,2,\cdots, K\}$, the minimum size of the randomness variable at each user is $1 + 1/2 + \cdots + 1/K$ bits. An intimately related problem is secure summation with user selection, where a server may select an arbitrary subset of $K$ users and securely compute the sum of the inputs of the selected users. We show that to compute $1$ bit of an arbitrarily chosen sum securely, the minimum size of the key held by each user is $1 + 1/2 + \cdots + 1/(K-1)$ bits, whose achievability uses the generation of $(K,n)$-MDS variables for $n \in \{1,2,\cdots,K-1\}$.
