Zhao Yizhou, Sun Hua
Department of Electrical Engineering, University of North Texas, Denton, TX 76203, USA.
Entropy (Basel). 2021 Nov 4;23(11):1461. doi: 10.3390/e23111461.
We consider the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs. For this minimal secure computation problem, we propose a novel coding scheme built from two steps. First, the function to be computed is such that it can be recovered while additional information might be leaked. Second, a step is applied to the expanded function such that the leaked information is protected. We implement this expand-and-randomize coding scheme with two algebraic structures-the finite field and the modulo ring of integers, where the step is realized with the operation and the step is realized with the operation over the respective algebraic structures.
我们在一个最小模型中考虑安全计算问题，其中爱丽丝和鲍勃各自持有一个输入，并希望在不泄露关于输入的任何额外信息的情况下，在卡罗尔处安全地计算他们输入的函数。对于这个最小安全计算问题，我们提出了一种由两个步骤构建的新颖编码方案。首先，要计算的函数是这样的，即它可以在可能泄露额外信息的情况下被恢复。其次，对扩展后的函数应用一个步骤，使得泄露的信息得到保护。我们用两种代数结构——有限域和整数模环来实现这种扩展并随机化的编码方案，其中第一步通过相应代数结构上的 运算来实现，第二步通过 运算来实现。
