Abstract

Modern algorithms for symmetric and asymmetric encryptions are not suitable to provide security of data that needs data processing. They cannot perform calculations over encrypted data without first decrypting it when risks are high. Residue Number System (RNS) as a homomorphic encryption allows ensuring the confidentiality of the stored information and performing calculations over encrypted data without preliminary decoding but with unacceptable time and resource consumption. An important operation for encrypted data processing is a number comparison. In RNS, it consists of two steps: the computation of the positional characteristic of the number in RNS representation and comparison of its positional characteristics in the positional number system. In this paper, we propose a new efficient method to compute the positional characteristic based on the approximate method. The approximate method as a tool to compare numbers does not require resource-consuming non-modular operations that are replaced by fast bit right shift operations and taking the least significant bits. We prove that in case when the dynamic range of RNS is an odd number, the size of the operands is reduced by the size of the module. If one of the RNS moduli is a power of two, then the size of the operands is less than the dynamic range. We simulate proposed method in the ISE Design Suite environment on the FPGA Xilinx Spartan-6 SP605 and show that it gains 31% in time and 37% in the area on average with respect to the known approximate method. It makes our method efficient for hardware implementation of cryptographic primitives constructed over a prime finite field.

中文翻译：

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同态加密中有效数字比较的位置特征

摘要

用于对称和非对称加密的现代算法不适合提供需要数据处理的数据的安全性。当风险很高时，他们不能对加密数据执行计算，而无需先对其解密。残差号码系统（RNS）作为同态加密，可以确保所存储信息的机密性，并可以对加密数据进行计算，而无需进行初步解码，但是会浪费时间和资源。加密数据处理的重要操作是数字比较。在RNS中，它包括两个步骤：RNS表示中数字位置特征的计算以及位置数字系统中其位置特征的比较。在本文中，我们提出了一种基于近似方法来计算位置特征的新有效方法。近似方法作为比较数字的工具，不需要耗费资源的非模运算，该运算被快速的右移运算和占用最低有效位所代替。我们证明，当RNS的动态范围是奇数时，操作数的大小将减少模块的大小。如果RNS模之一是2的幂，则操作数的大小小于动态范围。我们在ISE Design Suite环境中的FPGA Xilinx Spartan-6 SP605上模拟了所提出的方法，并表明，相对于已知的近似方法，该方法在时间上平均获得31％的收益，在面积上平均获得37％的收益。