Non-linear Residue Codes for Robust Public-Key Arithmetic
Non-linear Residue Codes for Robust Public-Key Arithmetic
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DOI：
10.1007/11889700_16
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发表时间：
2006-10
期刊：
影响因子：
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通讯作者：
G. Gaubatz;B. Sunar;M. Karpovsky
中科院分区：
文献类型：
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作者：
G. Gaubatz;B. Sunar;M. Karpovsky
本文提出了一种基于非线性算术剩余码的正整数鲁棒多精度算术保护方案。这些代码有一个非常高的概率检测任何重量的任意错误。我们的计划本身以及直接实现标准的模乘技术，即蒙哥马利或巴雷特乘法，对主动故障注入攻击的安全。由于代码的非线性，检测到错误的概率不仅取决于错误模式，而且还取决于数据。由于后者通常不为对手所知的先验，成功注入未检测到的错误是极不可能的。我们给这些代码的鲁棒性的证明，通过提供一个上限的不可检测的错误的数量。
We present a scheme for robust multi-precision arithmetic over the positive integers, protected by a novel family of non-linear arithmetic residue codes. These codes have a very high probability of detecting arbitrary errors of any weight. Our scheme lends itself well for straightforward implementation of standard modular multiplication techniques, i.e. Montgomery or Barrett Multiplication, secure against active fault injection attacks. Due to the non-linearity of the code the probability of detecting an error does not only depend on the error pattern, but also on the data. Since the latter is not usually known to the adversary a priori, a successful injection of an undetected error is highly unlikely. We give a proof of the robustness of these codes by providing an upper bound on the number of undetectable errors.