Positional Characteristics for Efficient Number Comparison over the Homomorphic Encryption
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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.
The work is partially supported by Russian Foundation for Basic Research (RFBR) 18-07-00109, 18-07-01224, and 19-07-00856, State task nos. 2.6035.2017 and 2019-1105, Russian Federation President Grant MK-341.2019.9, and SP-2236.2018.5.
- 4.Chervyakov, N., Babenko, M., Tchernykh, A., Kucherov, N., Miranda-López, V., and Cortés-Mendoza, J.M., AR-RRNS: configurable reliable distributed data storage systems for Internet of things to ensure security, Future Gener. Comput. Syst., 2019, vol. 92, pp. 1080–1092. https://doi.org/10.1016/j.future.2017.09.061 CrossRefGoogle Scholar
- 9.Miranda-López, V., Tchernykh, A., Cortés-Mendoza, J.M., Babenko, M., G. Radchenko, Nesmachnow, S., and Du, Z., Experimental analysis of secret sharing schemes for cloud storage based on RNS, Proc. Latin American High Performance Computing Conf., Buenos Aires, 2017, pp. 370–383.Google Scholar
- 10.Tchernykh, A., Babenko, M., Chervyakov, N., Cortés-Mendoza, J.M., Kucherov, N., Miranda-López, V., Deryabin, M., Dvoryaninova, I., and Radchenko, G., Towards mitigating uncertainty of data security breaches and collusion in cloud computing, Proc. 28th Int. Workshop on Database and Expert Systems Applications (DEXA), Lyon, 2017, pp. 137–141.Google Scholar
- 11.Babenko, M., Chervyakov, N., Tchernykh, A., Kucherov, N., Shabalina, M., Vashchenko, I., Radchenko, G., and Murga, D., Unfairness correction in P2P grids based on residue number system of a special form, Proc. 28th Int. Workshop on Database and Expert Systems Applications (DEXA), Lyon, 2017, pp. 147–151.Google Scholar
- 16.Burgess, N., Scaling an RNS number using the core function, Proc. 16th IEEE Symp. on Computer Arithmetic, Santiago de Compostela, 2003, pp. 262–269.Google Scholar
- 18.Pirlo, G. and Impedovo, D., A new class of monotone functions of the residue number system, Int. J. Math. Models Methods Appl. Sci., 2013, vol. 7, no. 9, pp. 803–809.Google Scholar
- 22.Akushskii, I.Ya. and Yuditskii, D.I., Mashinnaya arifmetika v ostatochnykh protsessakh (Machine Arithmetic in Residual Classes), Moscow: Sovetskoe Radio, 1968.Google Scholar
- 27.Tchernykh, A., Babenko, M., Chervyakov, N., Miranda-López, V., Kuchukov, V., Cortés-Mendoza, J.M., Deryabin, M., Kucherov, N., Radchenko, G., and Avetisyan, A., AC-RRNS: anti-collusion secured data sharing scheme for cloud storage, Int. J. Approx. Reason., 2018, vol. 102, pp. 60–73.MathSciNetCrossRefGoogle Scholar