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An efficient fully homomorphic symmetric encryption algorithm

  • Khalil Hariss
  • Hassan NouraEmail author
  • Abed Ellatif Samhat
Article
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Abstract

In this paper, we consider Homomorphic Encryption (HE) to process over encrypted data to achieve users privacy. We present a framework solution that provides a high level of security for the symmetric HE algorithms. The proposed solution introduces a dynamic structure and a dynamic diffusion primitives that enhance existing symmetric HE algorithms and overcome their weaknesses. Domingo Ferrer is a well known symmetric HE scheme that relies on polynomial computations but at the same time suffers from some vulnerabilities and especially sensitivity to known plain-text attack. We apply the concerned dynamic framework over the Domingo Ferrer encryption scheme to overcome its main weaknesses. Security analysis of the new encryption scheme that we called Enhanced Domingo Ferrer has shown that the latter became immune to several types of attack especially known plain-text attack. Crypt-analysis has also shown that this new implementation will be secure also with the lowest possible storage overhead. Implementation of the new scheme has shown an acceptable execution time. All the new specifications listed previously make the scheme a good candidate for efficiently preserving users privacy in a big variety of real-world modern applications.

Keywords

Fully homomorphic encryption Secure multimedia processing Dynamic diffusion and permutation primitives Polynomial resultant Known plain-text attack 

Notes

Acknowledgements

This paper was partially supported by funds from the Maroun Semaan Faculty of Engineering and Architecture at the American University of Beirut.

References

  1. 1.
    Aguilar-Melchor C, Fau S, Fontaine C, Gogniat G, Sirdey R (2013) Recent advances in homomorphic encryption: a possible future for signal processing in the encrypted domain. IEEE Signal Process Mag 30(2):108–117CrossRefGoogle Scholar
  2. 2.
    Anggriane SM, Nasution SM, Azmi F (2016) Advaned e-voting system using paillier homomorphic encryption algorithm. In: International conference on informatics and computing, pp 338–342Google Scholar
  3. 3.
    Brakerski Z, Gentry C, Vaikuntanathan (2012) (leveled) fully homomorphic encryption without bootstrapping. In: Proceedings of the 3rd innovations in theoretical computer science conference, ITCS ’12. ACM, New York, pp 309–325Google Scholar
  4. 4.
    Brent RP (1987) Determinants and ranks of random matrices over zm. Discret Math 66(1):35–49CrossRefGoogle Scholar
  5. 5.
    Challa R, VijayaKumari G, Sunny B (2015) Secure image processing using LWE based homomorphic encryption. In: IEEE International conference on electrical, computer and communication Technologies (ICECCT). Coimbatore, pp 1–6Google Scholar
  6. 6.
    Chan AC-F (2009) Symmetric-key homomorphic encryption for encrypted data processing. In: 2009 IEEE International conference on communications, pp 1–5Google Scholar
  7. 7.
    Chauhan KK, Sanger AKS, Verma A (2015) Homomorphic encryption for data security in cloud computing. In: 2015 International conference on information technology (ICIT), pp 206–209Google Scholar
  8. 8.
    Chen Y, Nguyen PQ (2012) Faster algorithms for approximate common divisors: breaking fully- homomorphic-encryption challenges over the integers. In: Pointcheval D, Johansson T (eds) EUROCRYPT 2012, volume 7237 of lecture notes in computer science. IACR, Springer, Cambridge, pp 502–519CrossRefGoogle Scholar
  9. 9.
    Coron J-S, Mandal A, Naccache D, Tibouchi M (2011) Fully homomorphic encryption over the integers with shorter public keys. In: Rogaway P (ed) Advances in cryptology – CRYPTO 2011. Springer, Berlin, pp 487–504CrossRefGoogle Scholar
  10. 10.
    Fau S, Sirdey R, Fontaine C, Aguilar-Melchor C, Gogniat G (2013) Towards practical program execution over fully homomorphic encryption schemes. In: 2013 IEEE Eighth international conference on P2P, parallel, grid, cloud and internet computing (3PGCIC), pp 284–290Google Scholar
  11. 11.
    Ferrer JD (1996) A new privacy homomorphism and applications. Inform Process Lett 60(5):277–282MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ferrer JD (2002) A provably secure additive and multiplicative privacy homomorphism. Universitat Rovira i Virgili, Dept. of Computer Engineering and Maths. In: ISC ’02 Proceedings of the 5th international conference on information security. Springer, London, pp 471–483Google Scholar
  13. 13.
    Fontaine C, Galand F (2007) A survey of homomorphic encryption for nonspecialists. Springer EURASIP J Inf Secur 2007(1):1–10Google Scholar
  14. 14.
    Gentry C (2009) A fully homomorphic encryption scheme. PhD thesis. Stanford UniversityGoogle Scholar
  15. 15.
    Gentry C (2009) Fully homomorphic encryption using ideal lattices. In: STOC ’09 Proceedings of the forty-first annual ACM symposium on theory of computing. ACM, New York, pp 169–178Google Scholar
  16. 16.
    Haridas D, Venkataraman S, Varadan G (2012) Strengthened iterated Hill cipher for encrypted processing. In: 2012 2nd IEEE International conference on parallel distributed and grid computing (PDGC), pp 491–496Google Scholar
  17. 17.
    Hariss K, Noura H, Samhat AE, Chamoun M (2018) Design and realization of a fully homomorphic encryption algorithm for cloud applications. In: Cuppens N, Cuppens F, Lanet JL, Legay A, Garcia-Alfaro J (eds) Risks and security of internet and systems. Springer International Publishing, Cham, pp 127–139Google Scholar
  18. 18.
    Jin B, Jiang D, Xiong J, Chen L, Li Q (2018) D2D data privacy protection mechanism based on reliability and homomorphic encryption. IEEE Access 6:51140–51150CrossRefGoogle Scholar
  19. 19.
    Kapusta K, Memmi G, Noura H (2019) Additively homomorphic encryption and fragmentation scheme for data aggregation inside unattended wireless sensor networks. Ann Telecommun 74(3-4):157–165CrossRefGoogle Scholar
  20. 20.
    Kipnis A, Hibshoosh E (2012) Efficient methods for practical fully homomorphic symmetric-key encryption. Randomization and Verification IACR Cryptology ePrint Archive 2012:637Google Scholar
  21. 21.
    Kocabas O, Soyata T (2014) Medical data analytics in the cloud using homomorphic encryption, pp 471–488Google Scholar
  22. 22.
    Kwok SHM, Lam EY (2008) Effective uses of FPGAs for brute-force attack on RC4 ciphers. EEE Trans Very Large Scale Integr Syst 16:8Google Scholar
  23. 23.
    Li J, Li YK, Chen X, Lee PPC, Lou W (2015) A hybrid cloud approach for secure authorized deduplication. IEEE Trans Parallel Distrib Syst 26(5):1206–1216CrossRefGoogle Scholar
  24. 24.
    Li P, Li J, Huang Z, Li T, Gao C-Z, Yiu S-M, Chen K (2017) Multi-key privacy-preserving deep learning in cloud computing. Futur Gener Comput Syst 74:76–85CrossRefGoogle Scholar
  25. 25.
    Mister S, Tavares SE (1998) Cryptanalysis of RC4-like Ciphers. Selected Areas in CryptographyGoogle Scholar
  26. 26.
    Noura H, Courrousé D (2015) Hldca-wsn:homomorphic lightweight data confidentiality for wireless sensor network. Int Assoc Cryptogr Res IACR 2015:928Google Scholar
  27. 27.
    Noura H, Salman O, Chehab A, Couturier R (2019) Preserving data security in distributed fog computing. Ad Hoc Netw, p 101937Google Scholar
  28. 28.
    Noura H, Samhat AE, Harkous Y, Yahiya TA (2015) Design and realization of a neural block cipher. In: 2015 International conference on applied research in computer science and engineering (IACR). Beirut, pp 1–6.  https://doi.org/10.1109/ARCSE2015.7338131
  29. 29.
    Rivest R, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21(2):120–126MathSciNetCrossRefGoogle Scholar
  30. 30.
    Sharma I (2013) Fully homomorphic encryption scheme with symmetric keys. Rajasthan Technical University, Kota. University College of Engineering, Department of Computer Science and EngineeringGoogle Scholar
  31. 31.
    Sylvester J (1851) On a remarkable discovery in the theory of canonical forms and of hyperdeterminantsGoogle Scholar
  32. 32.
    Tong L, Wenbin C, Yi T, Hongyang Y (2018) A homomorphic network coding signature scheme for multiple sources and its application in IoT. Secur Commun Netw, 1–6.  https://doi.org/10.1155/2018/9641273 Google Scholar
  33. 33.
    van Dijk M, Gentry C, Halevi S, Vaikuntanathan V (2010) Fully homomorphic encryption over the integers. EUROCRYPT’2010 (LNCS) 6110:24—43MathSciNetzbMATHGoogle Scholar
  34. 34.
    Vogel M (2010) An introduction to the theory of numbers, 6th edition by g.h. hardy and e.m. wright. Contemp Phys 51:283–283CrossRefGoogle Scholar
  35. 35.
    Wagner D (2003) Cryptanalysis of an algebraic privacy homomorphism. Inform Secur 2851:234–239CrossRefGoogle Scholar
  36. 36.
    Wang L, Li L, Li J, Li J, Gupta BB, Liu X (2019) Sensing of medical images with confidentially homomorphic aggregations. IEEE Internet Things J 6(2):1402–1409.  https://doi.org/10.1109/JIOT.2018.2844727 CrossRefGoogle Scholar
  37. 37.
    Xiao L, Bastani O, Yen I-L (2012) An efficient homomorphic encryption protocol for Multi-user systems Citeseer. IACR Cryptology ePrint Archive, vol 2012, pp 193Google Scholar
  38. 38.
    Yang P, Gui X, An J, Tian F (2017) An efficient secret key homomorphic encryption used. Image Process Serv Secur Commun Netw 2017(Article ID 7695751):11Google Scholar
  39. 39.
    Zhang P, Jiang Y, Lin C, Fan Y, Shen X (2010) P-coding: secure network coding against eavesdropping attacks. INFOCOM, 2010 Proceedings IEEE, pp 1-9Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  • Khalil Hariss
    • 1
    • 2
  • Hassan Noura
    • 3
    • 4
    Email author
  • Abed Ellatif Samhat
    • 1
  1. 1.Faculty of Engineering - CRSILebanese UniversityHadathLebanon
  2. 2.Engineering School, ESIBSaint Joseph UniversityBeirutLebanon
  3. 3.Department of Electrical and Computer EngineeringAmerican University of BeirutBeirutLebanon
  4. 4.Department of Computer SciencesArab Open UniversityBeirutLebanon

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