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Literature Survey

  • Ayantika ChatterjeeEmail author
  • Khin Mi Mi Aung
Chapter
Part of the Computer Architecture and Design Methodologies book series (CADM)

Abstract

Fully homomorphic encryption (FHE) scheme enables computation of arbitrary functions on encrypted data, hence considered as “holy grail” of modern cryptography. This chapter presents the relevance of FHE in present day cloud computing, a brief history of different homomorphic encryption schemes and formally defines fully homomorphic encryption along with basic idea behind Gentry’s construction. Gradually, few recent works will be described in this area those are proposed following Gentry’s scheme but with simpler constructions and better efficiency.

References

  1. Akin IH, Sunar B (2014) On the difficulty of securing web applications using cryptdb. In: 2014 IEEE fourth international conference on big data and cloud computing, BDCloud 2014, Sydney, Australia, 3–5 Dec 2014, pp 745–752Google Scholar
  2. ALCHEMY, https://github.com/cpeikert/ALCHEMY. Accessed 11 Oct 2018
  3. Alperin-Sheriff J, Peikert C (2014) Faster bootstrapping with polynomial error. In: CRYPTO. Springer, pp 297–314Google Scholar
  4. Boneh D, Gentry C, Halevi S, Wang F, Wu DJ (2013) Private database queries using somewhat homomorphic encryption. Springer, Berlin, pp 102–118Google Scholar
  5. Boneh D, Goh E, Nissim K (2005) Evaluating 2-dnf formulas on ciphertexts. In: Proceedings of the theory of cryptography, second theory of cryptography conference, TCC 2005, Cambridge, MA, USA, 10–12 Feb 2005, pp 325–341Google Scholar
  6. Brakerski Z, Gentry C, Vaikuntanathan V (2012) (leveled) fully homomorphic encryption without bootstrapping. In: Innovations in theoretical computer science, pp 309–325Google Scholar
  7. Brakerski Z, Vaikuntanathan V (2014) Lattice-based FHE as secure as PKE. In: Innovations in theoretical computer science, ITCS’14, Princeton, NJ, USA, 12–14 Jan 2014, pp 1–12Google Scholar
  8. Brenner M, Dai W, Halevi S, Han K, Jalali A, Kim M, Laine K, Malozemoff A, Paillier P, Polyakov Y, Rohloff K, Savas E, Sunar B (2017) A standard api for rlwe-based homomorphic encryption. HomomorphicEncryption.org, Redmond WA, Technical reportGoogle Scholar
  9. Brenner M, Perl H, Smith M (2012a) How practical is homomorphically encrypted program execution? an implementation and performance evaluation. In: Proceedings of the 11th IEEE international conference on trust, security and privacy in computing and communications, TrustCom 2012, Liverpool, United Kingdom, 25–27 June 2012, pp 375–382Google Scholar
  10. Brenner M, Perl H, Smith M (2012b) Practical applications of homomorphic encryption. In: SECRYPT 2012 - Proceedings of the international conference on security and cryptography, Rome, Italy, 24–27 July 2012, pp 5–14Google Scholar
  11. Brenner M, Wiebelitz J, Voigt G, Smith M (2011) Secret program execution in the cloud applying homomorphic encryption. In: Proceedings of 5th IEEE international conference on digital ecosystems and technologies (IEEE DEST 2011), pp 114–119Google Scholar
  12. Bugiel S, Nürnberger S, Sadeghi AR, Schneider T (2011) Twin clouds: secure cloud computing with low latency. In: Proceedings of the 12th IFIP international conference on communications and multimedia security, CMS’11, pp 32–44Google Scholar
  13. Cheon JH, Coron J, Kim J, Lee MS, Lepoint T, Tibouchi M, Yun A (2013) Batch fully homomorphic encryption over the integers. In: Advances in cryptology - EUROCRYPT 2013, 32nd annual international conference on the theory and applications of cryptographic techniques, pp 315–335Google Scholar
  14. Choudhury A, Loftus J, Orsini E, Patra A, Smart NP (2013) Between a rock and a hard place: interpolating between MPC and FHE. In: Advances in cryptology - ASIACRYPT 2013 - 19th international conference on the theory and application of cryptology and information security, Bengaluru, India, 1–5 Dec 2013, Proceedings, Part II, pp 221–240Google Scholar
  15. Cingulata, https://github.com/CEA-LIST/Cingulata/wiki. Accessed 11 Oct 2018
  16. Coron JS, Mandal A, Naccache D, Tibouchi M (2011) Fully homomorphic encryption over the integers with shorter public keys. In: Proceedings of the 31st annual conference on advances in cryptology, pp 487–504Google Scholar
  17. Coron J, Lepoint T, Tibouchi M (2014) Scale-invariant fully homomorphic encryption over the integers. In: Public-key cryptography - PKC 2014 - 17th international conference on practice and theory in public-key cryptography, pp 311–328Google Scholar
  18. Coron J, Naccache D, Tibouchi M (2012) Public key compression and modulus switching for fully homomorphic encryption over the integers. In: Advances in cryptology - EUROCRYPT 2012 - 31st annual international conference on the theory and applications of cryptographic techniques, Cambridge, UK, 15–19 April 2012. Proceedings, pp 446–464Google Scholar
  19. Doröz Y, Hu Y, Sunar B (2014) Homomorphic AES evaluation using NTRU. IACR Cryptology ePrint ArchiveGoogle Scholar
  20. Ducas L, Micciancio D (2015) FHEW: bootstrapping homomorphic encryption in less than a second. In: Advances in cryptology - EUROCRYPT 2015 - 34th annual international conference on the theory and applications of cryptographic techniques, Sofia, Bulgaria, 26–30 April 2015, Proceedings, Part I, pp 617–640Google Scholar
  21. Eric Crockett, Chris Peikert, Chad Sharp (2018) ALCHEMY: a language and compiler for homomorphic encryption made easy. ACM Conf Comput Commun Secur 2018:1020–1037Google Scholar
  22. Fraleigh JB (2002) First course in abstract algebra. Addison-Wesley, BostonzbMATHGoogle Scholar
  23. Gamal TE (1985) A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans Inf Theory 31(4):469–472MathSciNetCrossRefGoogle Scholar
  24. Gennaro R, Gentry C, Parno B (2010) Non-interactive verifiable computing: Outsourcing computation to untrusted workers. In: Proceedings of the 30th annual conference on advances in cryptology, CRYPTO’10. Springer, Berlin, pp 465–482Google Scholar
  25. Gentry C (2009a) A fully homomorphic encryption scheme. PhD thesis, Stanford UniversityGoogle Scholar
  26. Gentry C (2009b) Fully homomorphic encryption using ideal lattices. In: Mitzenmacher M (ed) STOC. ACM, pp 169–178Google Scholar
  27. Gentry C, Halevi S (2011a) Fully homomorphic encryption without squashing using depth-3 arithmetic circuits. In: IEEE 52nd annual symposium on foundations of computer science, FOCS 2011, Palm Springs, CA, USA, 22–25 Oct 2011, pp 107–109Google Scholar
  28. Gentry C, Halevi S (2011b) Implementing gentry’s fully-homomorphic encryption scheme. In: Advances in cryptology - EUROCRYPT 2011 - 30th annual international conference on the theory and applications of cryptographic techniques, Tallinn, Estonia, 15–19 May 2011. Proceedings, pp 129–148Google Scholar
  29. Gentry C, Halevi S, Smart NP (2012a) Better bootstrapping in fully homomorphic encryption. In: Public key cryptography - PKC 2012 - 15th international conference on practice and theory in public key cryptography, pp 1–16Google Scholar
  30. Gentry C, Halevi S, Smart NP 2012b Homomorphic evaluation of the AES circuit. In: Advances in cryptology - CRYPTO 2012 - 32nd annual cryptology conference, pp 850–867Google Scholar
  31. Gentry C, Sahai A, Waters B (2013) Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. In: Advances in cryptology - CRYPTO 2013 - 33rd annual cryptology conference, pp 75–92Google Scholar
  32. Goldreich O, Ostrovsky R (1996) Software protection and simulation on oblivious RAMs. J ACM 43(3):431–473.  https://doi.org/10.1145/233551.233553
  33. Goldwasser S, Kalai Y, Popa RA, Vaikuntanathan V, Zeldovich N (2013a) Reusable garbled circuits and succinct functional encryption. In: Proceedings of the Forty-fifth annual ACM symposium on theory of computing, STOC ’13. ACM, New York, NY, USA, pp 555–564Google Scholar
  34. Goldwasser S, Micali S (1982) Probabilistic encryption & amp; how to play mental poker keeping secret all partial information. In: Proceedings of the Fourteenth annual ACM symposium on theory of computing, STOC ’82, pp 365–377Google Scholar
  35. Ishai Y, Paskin A (2007) Evaluating branching programs on encrypted data. In: TCC 2007Google Scholar
  36. Kolesnikov V, reza Sadeghi A, Schneider T (2009) How to combine homomorphic encryption and garbled circuits improved circuits and computing the minimum distance efficientlyGoogle Scholar
  37. López-Alt A, Tromer E, Vaikuntanathan V (2012) On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: Proceedings of the 44th symposium on theory of computing conference, STOC, pp 1219–1234Google Scholar
  38. Martins P, Sousa L, Mariano A (2018) A survey on fully homomorphic encryption: an engineering perspective. ACM Comput Surv 50(6): 83:1–83:33Google Scholar
  39. Melchor CA, Gaborit P, Herranz J (2008) Additively homomorphic encryption with d-operand multiplications. IACR Cryptology ePrint ArchiveGoogle Scholar
  40. Micciancio D (2010) A first glimpse of cryptography’s holy grail. Commun ACM 53(3):96CrossRefGoogle Scholar
  41. Paillier P (1999) Public-key cryptosystems based on composite degree residuosity classes. In: Proceedings of the 17th international conference on theory and application of cryptographic techniques, EUROCRYPT’99, pp 223–238Google Scholar
  42. Perl H, Mohammed Y, Brenner M, Smith M (2012) Fast confidential search for bio-medical data using bloom filters and homomorphic cryptography. In: eScience. IEEE Computer Society, pp 1–8Google Scholar
  43. Perl H, Mohammed Y, Brenner M, Smith M (2014) Privacy/performance trade-off in private search on bio-medical data. Future Generation Computer Systems, pp 441–452Google Scholar
  44. Popa RA (2014) Building practical systems that compute on encrypted data. PhD thesis, Massachusetts Institute of TechnologyGoogle Scholar
  45. Popa RA, Redfield Catherine MS, Zeldovich N, Balakrishnan H (2011) Cryptdb: Protecting confidentiality with encrypted query processing. In: Proceedings of the 23rd ACM symposium on operating systems principles, SOSP ’11, pp 85–100Google Scholar
  46. Rass S, Slamanig D (2013) Cryptography for security and privacy in cloud computing. Artech House Inc, NorwoodGoogle Scholar
  47. reza Sadeghi A, Schneider T, Win M (2010) Token-based cloud computing secure outsourcing of data and arbitrary computations with lower latency. Workshop on trust in the cloudGoogle Scholar
  48. Rivest RL, Adleman L, Dertouzos ML (1978a) Foundations of Secure Computation. On data banks and privacy homomorphisms. Academia Press, Cambridge, pp 169–179Google Scholar
  49. Sahai A (2008) Computing on encrypted data. In: ICISS. Springer, pp 148–153Google Scholar
  50. Sander T, Young AL, Yung M (1999) Non-interactive cryptocomputing for nc1. In: FOCS. IEEE Computer Society, pp 554–567Google Scholar
  51. Smart NP, Vercauteren F (2010) Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Proceedings of the 13th international conference on practice and theory in public key cryptography, PKC’10, pp 420–443Google Scholar
  52. Stallings W (2005) Cryptography and network security, 4th edn. Prentice-Hall Inc, Upper Saddle RiverGoogle Scholar
  53. Stehle D, Steinfeld R (2010) Faster fully homomorphic encryption. Cryptology, ASIACRYPT 2010:377–394MathSciNetzbMATHGoogle Scholar
  54. van Dijk M, Gentry C, Halevi S, Vaikuntanathan V (2009) Fully homomorphic encryption over the integers. IACR Cryptology ePrint ArchiveGoogle Scholar
  55. Yao AC (1982) Protocols for secure computations. In: Proceedings of the 23rd annual symposium on foundations of computer science, SFCS ’82, pp 160–164Google Scholar
  56. Zhang Z (2014) Revisiting fully homomorphic encryption schemes and their cryptographic primitives. PhD thesis, University of WollongongGoogle Scholar
  57. Zhou H, Wornell GW (2014) Efficient homomorphic encryption on integer vectors and its applications. In: 2014 Information theory and applications workshop, ITA 2014, San Diego, CA, USA, 9–14 Feb 2014, pp 1–9Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Indian Institute of Technology KharagpurKharagpurIndia
  2. 2.Institute for Infocomm ResearchA*STARSingaporeSingapore

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