Secret Sharing Schemes Using Modulo-2^{m} Arithmetic Operations
Secret Sharing Schemes Using Modulo-2^{m} Arithmetic Operations
复制标题
使用模 2^{m} 算术运算的秘密共享方案
DOI：
10.1109/desec.2018.8625126
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Hidenori Kuwakado
中科院分区：
文献类型：
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作者：
Yuichi Sei;Akihiko Ohsuga;東和幸，高橋仁，中川博之，土屋達弘;Hidenori Kuwakado
最近已经推出了使用秘密共享方案的云服务。由于秘密共享方案通常是在有限域上实现的，因此共享和重构秘密的吞吐量取决于有限域运算的实现。然而，几乎所有的CPU都不支持有限域操作作为主要指令。本文研究了基于Z2 m上线性变换的k-out-n秘密共享方案。线性变换优于Z2的优点是几乎所有的CPU都支持模2乘、模2减和模2乘作为主要指令。给出了基于Z2 m上线性变换的k-out-of-n秘密共享方案的编码矩阵的条件。这些条件表明Z2上的k-out-of-n秘密共享方案是非理想的。我们还显示了一个秘密的最大大小，如果范德蒙矩阵的所有元素是2的幂被用作编码矩阵。
Cloud services using secret sharing schemes have been launched recently. Since secret sharing schemes have been usually achieved over a finite field, the throughput for sharing and reconstructing a secret depends on the implementation of finitefield operations. However, almost all the CPUs do not support finite-field operations as primary instructions. We study k-outof-n secret sharing schemes using the linear transform over Z2m. The advantage of the linear transform over Z2mis that almost all the CPUs support a modulo-2maddition, a modulo-2msubtraction, and a modulo-2mmultiplication as primary instructions. We show the conditions of an encoding matrix to achieve the k-out-of-n secret sharing scheme based on the linear transform over Z2m. The conditions suggest that the k-out-of-n secret sharing scheme over Z2mis non-ideal. We also show the maximum size of a secret if the Vandermonde matrix whose all the elements are a power of two is used as the encoding matrix.