Skip to main content

Cryptographic Primitives Optimization Based on the Concepts of the Residue Number System and Finite Ring Neural Network

  • 335 Accesses

Part of the Communications in Computer and Information Science book series (CCIS,volume 1443)

Abstract

Data encryption has become a vital mechanism for data protection. One of the main challenges and an important target for optimization is the encryption/decryption speed. In this paper, we propose techniques for speeding up the software performance of several important cryptographic primitives based on the Residue Number System (RNS) and Finite Ring Neural Network (FRNN). RNS&FRNN reduces the computational complexity of operations with arbitrary-length integers such as addition, subtraction, multiplication, division by constant, Euclid division, and sign detection. To validate practical significance, we compare LLVM library implementations with state-of-the-art, high-performance, portable C++ NTL library implementations. The experimental analysis shows the superiority of the proposed optimization approach compared to the available approaches. For the NIST FIPS 186-5 digital signature algorithm, the proposed solution is 85% faster, even though the sign detection has low efficiency.

Keywords

  • Residue number system
  • Finite ring neural network
  • Encryption
  • High-performance
  • Cryptographic primitives

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-85672-4_18
  • Chapter length: 13 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-85672-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   109.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.

References

  1. Krasnobayev, V.A., Yanko, A.S., Koshman, S.A.: A Method for arithmetic comparison of data represented in a residue number system. Cybern. Syst. Anal. 52(1), 145–150 (2016). https://doi.org/10.1007/s10559-016-9809-2

    CrossRef  MATH  Google Scholar 

  2. Ruchkin, V., Romanchuk, V., Sulitsa, R.: Clustering, restorability and designing of embedded computer systems based on neuroprocessors. In: 2013 2nd Mediterranean Conference on Embedded Computing (MECO), pp. 58–61 (2013). https://doi.org/10.1109/MECO.2013.6601318

  3. Vinogradov, I.M.: Elements of Number Theory. Courier Dover Publications (2016)

    Google Scholar 

  4. Yu, D.-J., Hu, J., Tang, Z.-M., Shen, H.-B., Yang, J., Yang, J.-Y.: Improving protein-ATP binding residues prediction by boosting SVMs with random under-sampling. Neurocomputing 104, 180–190 (2013). https://doi.org/10.1016/j.neucom.2012.10.012

    CrossRef  Google Scholar 

  5. Hu, J., Li, Y., Yan, W.-X., Yang, J.-Y., Shen, H.-B., Yu, D.-J.: KNN-based dynamic query-driven sample rescaling strategy for class imbalance learning. Neurocomputing 191, 363–373 (2016). https://doi.org/10.1016/j.neucom.2016.01.043

    CrossRef  Google Scholar 

  6. Babenko, M., et al.: Positional characteristics for efficient number comparison over the homomorphic encryption. Program. Comput. Softw. 45(8), 532–543 (2019). https://doi.org/10.1134/S0361768819080115

    MathSciNet  CrossRef  MATH  Google Scholar 

  7. Tchernykh, A., et al.: Scalable data storage design for non-stationary IoT environment with adaptive security and reliability. IEEE Internet Things J. 7(10), 10171–10188 (2020). https://doi.org/10.1109/JIOT.2020.2981276

    CrossRef  Google Scholar 

  8. Burgess, N.: Scaling an RNS number using the core function. In: Proceedings 2003 16th IEEE Symposium on Computer Arithmetic, pp. 262–269 (2003). https://doi.org/10.1109/ARITH.2003.1207687

  9. Tchernykh, A., et al.: Performance evaluation of secret sharing schemes with data recovery in secured and reliable heterogeneous multi-cloud storage. Cluster Comput. 22(4), 1173–1185 (2019). https://doi.org/10.1007/s10586-018-02896-9

    CrossRef  Google Scholar 

  10. Miranda-López, V., Tchernykh, A., Babenko, M., Avetisyan, A., Toporkov, V., Drozdov. A.Y.: 2Lbp-RRNS: two-levels RRNS with backpropagation for increased reliability and privacy-preserving of secure multi-clouds data storage. IEEE Access 8, 199424–199439 (2020). https://doi.org/10.1109/ACCESS.2020.3032655

  11. Babenko, M., Shiriaev, E., Tchernykh, A., Golimblevskaia, E.: Neural network method for base extension in residue number system. In: Bychkov, I., Tchernykh, A., Feoktistov, A. (eds.) ICCS-DE 2020- 2nd International Workshop on Information, Computation, and Control Systems for Distributed Environments, Irkutsk, Russia, 6–7 July 2020, vol. 2638, pp. 9–22. CEUR-WS (2020). http://ceur-ws.org/Vol-2638/paper1.pdf

  12. Babenko, M., Tchernykh, A., Golimblevskaia, E., Hung, N.V., Chaurasiya, V.K.: Computationally secure threshold secret sharing scheme with minimal redundancy. In: Bychkov, I., Tchernykh, A., Feoktistov, A. (eds.) ICCS-DE 2020- 2nd International Workshop on Information, Computation, and Control Systems for Distributed Environments, Irkutsk, Russia, 6–7 July 2020, vol. 2638, pp. 23–32. CEUR-WS (2020). http://ceur-ws.org/Vol-2638/paper2.pdf

  13. Davies, M., et al.: Loihi: a neuromorphic manycore processor with on-chip learning. IEEE Micro 38(1), 82–99 (2018). https://doi.org/10.1109/MM.2018.112130359

    CrossRef  Google Scholar 

  14. DeBole, M.V., et al.: TrueNorth: accelerating from zero to 64 million neurons in 10 years. Computer 52(5), 20–29 (2019). https://doi.org/10.1109/MC.2019.2903009.

    CrossRef  Google Scholar 

  15. Babenko, M., et al.: RNS number comparator based on a modified diagonal function. Electronics 9, 1784 (2020). https://doi.org/10.3390/electronics9111784

    CrossRef  Google Scholar 

  16. Miranda-Lopez, V., et al.: Weighted two-levels secret sharing scheme for multi-clouds data storage with increased reliability. In: 2019 International Conference on High Performance Computing & Simulation (HPCS), pp. 915–922. IEEE (2019). https://doi.org/10.1109/HPCS48598.2019.9188057

  17. Babenko, M., Deryabin, M., Tchernykh, A.: The accuracy estimation of the interval-positional characteristic in residue number system. In: 2019 International Conference on Engineering and Telecommunication (EnT), pp. 1–5. IEEE (2019). https://doi.org/10.1109/EnT47717.2019.9030549

  18. Kucherov, N., Babenko, M., Tchernykh, A., Kuchukov, V., Vashchenko, I.: Increasing reliability and fault tolerance of a secure distributed cloud storage. In: The International Workshop on Information, Computation, and Control Systems for Distributed Environments (2020) https://doi.org/10.47350/ICCS-DE.2020.16.

Download references

Acknowledgments

This work was partially supported by the Ministry of Education and Science of the Russian Federation (Project 075–15-2020–788).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrei Tchernykh .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Tchernykh, A. et al. (2021). Cryptographic Primitives Optimization Based on the Concepts of the Residue Number System and Finite Ring Neural Network. In: Dorronsoro, B., Amodeo, L., Pavone, M., Ruiz, P. (eds) Optimization and Learning. OLA 2021. Communications in Computer and Information Science, vol 1443. Springer, Cham. https://doi.org/10.1007/978-3-030-85672-4_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-85672-4_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85671-7

  • Online ISBN: 978-3-030-85672-4

  • eBook Packages: Computer ScienceComputer Science (R0)