Advertisement

Trapdoor function based on the Ring-LWE and applications in communications

  • Chengli ZhangEmail author
  • Wenping Ma
  • Feifei Zhao
Original Research

Abstract

The “strong trapdoor function for lattice” has been constructed by Daniele Micciancio and Chris Peikert in EUROCRYPT 2012, which is simple, efficient, and easy to implement. In this paper, we present a new trapdoor function based on “ring learning with errors” problem (Ring-LWE) on lattice, and simultaneously the corresponding efficient inverse algorithm is given which involves two sub-algorithms: the trapdoor inverse algorithm and the iterative inverse algorithm. Our trapdoor function for lattice based on Ring-LWE is simultaneously more simple and efficient because of the ring structure. In addition to these advantages, our algorithm extends the parameters, and this can make our trapdoor function have a wider choice of applications.

Keywords

Lattice Trapdoor function Learning with errors Ring Cryptography 

Notes

Acknowledgements

This work was funded by National Key R&D Program of China under Grant no. 2017YFB0802400, National Natural Science Foundation of China under Grant no. 61373171 and 111 Project under Grant no. B08038.

References

  1. Ajtai M (1996) Generating hard instances of lattice problems. In: Proceedings of the twenty-eighth annual ACM symposium on Theory of computing. ACM, pp 99–108Google Scholar
  2. Boneh D, Franklin M (2001) Identity-based encryption from the Weil pairing. In: Annual international cryptology conference. Springer, Berlin, Heidelberg, pp 213–229Google Scholar
  3. Brakerski Z, Vaikuntanathan V (2011) Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Annual cryptology conference. Springer, Berlin, Heidelberg, pp 505–524Google Scholar
  4. Brakerski Z, Vaikuntanathan V (2014) Efficient fully homomorphic encryption from (standard) LWE. SIAM J Comput 43(2):831–871MathSciNetCrossRefzbMATHGoogle Scholar
  5. Canetti R, Halevi S, Katz J (2004) Chosen-ciphertext security from identity-based encryption. In: International conference on the theory and applications of cryptographic techniques. Springer, Berlin, Heidelberg, pp 207–222Google Scholar
  6. Chatterjee S, Sarkar P (2011) Identity-based encryption. Springer, BerlinCrossRefzbMATHGoogle Scholar
  7. Diffie W, Hellman M (1976) New directions in cryptography. IEEE Trans Inf Theory 22(6):644–654MathSciNetCrossRefzbMATHGoogle Scholar
  8. Gentry C (2006) Practical identity-based encryption without random oracles. In: Annual international conference on the theory and applications of cryptographic techniques. Springer, Berlin, Heidelberg, pp 445–464Google Scholar
  9. Gentry C (2009) A fully homomorphic encryption scheme. Stanford University, StanfordzbMATHGoogle Scholar
  10. Gentry CB (2015) US fully homomorphic encryption. Patent No. 9,083,526. U.S. Patent and Trademark Office, Washington, DCGoogle Scholar
  11. Lyubashevsky V, Peikert C, Regev O (2010) On ideal lattices and learning with errors over rings. In: Annual international conference on the theory and applications of cryptographic techniques. Springer, Berlin, Heidelberg, pp 1–23Google Scholar
  12. Micciancio D, Peikert C (2012) Trapdoors for lattices: simpler, tighter, faster, smaller. In: Annual international conference on the theory and applications of cryptographic techniques. Springer, Berlin, Heidelberg, pp 700–718Google Scholar
  13. Micciancio D, Regev O (2007) Worst-case to average-case reductions based on Gaussian measures. SIAM J Comput 37(1):267–302MathSciNetCrossRefzbMATHGoogle Scholar
  14. Peikert C, Rosen A (2006) Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices. In: Theory of cryptography conference. Springer, Berlin, Heidelberg, pp 145–166Google Scholar
  15. Peikert C, Waters B (2011) Lossy trapdoor functions and their applications. SIAM J Comput 40(6):1803–1844MathSciNetCrossRefzbMATHGoogle Scholar
  16. Regev O (2009) On lattices, learning with errors, random linear codes, and cryptography. J ACM 56(6):34MathSciNetCrossRefzbMATHGoogle Scholar
  17. Schneider M (2013) Sieving for shortest vectors in ideal lattices. In: International conference on cryptology in Africa. Springer, Berlin, Heidelberg, pp 375–391Google Scholar
  18. Smart NP, Vercauteren F (2010) Fully homomorphic encryption with relatively small key and ciphertext sizes. In: International workshop on public key cryptography. Springer, Berlin, Heidelberg, pp 420–443Google Scholar
  19. Stehl D, Steinfeld R, Tanaka K, Xagawa K (2009) Efficient public key encryption based on ideal lattices. In: International conference on the theory and application of cryptology and information security. Springer, Berlin, Heidelberg, pp 617–635Google Scholar
  20. Van Dijk M, Gentry C, Halevi S, Vaikuntanathan V (2010) Fully homomorphic encryption over the integers. In: Annual international conference on the theory and applications of cryptographic techniques. Springer, Berlin, Heidelberg, pp 24–43Google Scholar
  21. Waters B (2005) Efficient identity-based encryption without random oracles. In: Annual international conference on the theory and applications of cryptographic techniques. Springer, Berlin, Heidelberg, pp 114–127Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Integrated Services NetworksXidian UniversityXi’anPeople’s Republic of China

Personalised recommendations