Application of NTRU Using Group Rings to Partial Decryption Technique | SpringerLink
Skip to main content

Application of NTRU Using Group Rings to Partial Decryption Technique

  • Conference paper
  • First Online:
Trusted Systems (INTRUST 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9565))

Included in the following conference series:

  • 438 Accesses

Abstract

Partial decryption enables a ciphertext to be decrypted partially according to provided secret keys. In this paper, we propose a public key encryption scheme with the functionality of partial decryption. Our strategy is to use the NTRU cryptosystem. Under a design principle of the mathematical structure “group ring”, we extend the original NTRU into group ring NTRU (GR-NTRU). First, we propose a generic framework of our GR-NTRU. Our GR-NTRU allows partial decryption with a single encryption process using a single public key. Besides, when we execute partial decryption under a secret key of GR-NTRU, we need no information to identify each part in a whole ciphertext. Consequently, management of a public key and a corresponding set of secret keys is rather easier than the naive method. Next, we propose a concrete instantiation of our generic GR-NTRU. A multivariate polynomial ring NTRU scheme is obtained by employing a product of different cyclic groups as the basis of the group ring structure. We will show examples of those new variants of NTRU schemes with concrete parameter values, and explain how we can employ them to use the functionality of partial decryption.

This research is commissioned by “Strategic Information and Communications R&D Promotion Programme (SCOPE), No. 0159-0016” Ministry of Internal Affairs and Communications, Japan.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Ateniese, G., Chou, D.H., de Medeiros, B., Tsudik, G.: Sanitizable signatures. In: di Vimercati, S.C., Syverson, P.F., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 159–177. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Bellare, M., Boldyreva, A., Staddon, J.: Randomness re-use in multi-recipient encryption schemeas. In: Desmedt, G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 85–99. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Berkovits, S.: How to broadcast a secret. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 535–541. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  4. Boneh, D., Gentry, C., Waters, B.: Collusion resistant broadcast encryption with short ciphertexts and private keys. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 258–275. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Bovdi, A.A.: Group Algebra. Springer Publishing Company, Incorporated (2001)

    Google Scholar 

  6. Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 337–367. Springer, Heidelberg (2015)

    Google Scholar 

  7. Brzuska, C., Fischlin, M., Lehmann, A., Schröder, D.: Santizable signatures: how to partially delegate control for authenticated data. In: Proceedings of the Special Interest Group on Biometrics and Electronic Signatures BIOSIG 2009, 17-18 September 2009 in Darmstadt, Germany, pp. 117–128 (2009)

    Google Scholar 

  8. Hoffstein, J., Howgrave-Graham, N., Pipher, J., Silverman, J., Whyte, W.: Hybrid lattice reduction and meet in the middle resistant parameter selection for ntruencrypt

    Google Scholar 

  9. Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: a ring-based public key cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 267–288. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  10. Izu, T., Ito, K., Tsuda, H., Abiru, K., Ogura, T.: Privacy-protection technologies for secure utilization of sensor data. Fujitsu Sci. Tech. J. 50(1), 30–33 (2014)

    Google Scholar 

  11. Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Santis, A.D., Desmedt, Y., Frankel, Y., Yung, M.: How to share a function securely. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, 23–25 May 1994, Montréal, Québec, Canada, pp. 522–533 (1994)

    Google Scholar 

  13. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yamada, S., Attrapadung, N., Santoso, B., Schuldt, J.C.N., Hanaoka, G., Kunihiro, N.: Verifiable predicate encryption and applications to CCA security and anonymous predicate authentication. In: Proceedings 15th International Conference on Practice and Theory in Public Key Cryptography PKC–2012, Darmstadt, Germany, May 21–23 2012, pp. 243–261 (2012)

    Google Scholar 

  15. Yasuda, T., Dahan, X., Sakurai, K.: Characterizing NTRU-variants using group ring and evaluating their lattice security. To be appear as an IACR e-print paper

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Takanori Yasuda .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Yasuda, T., Anada, H., Sakurai, K. (2016). Application of NTRU Using Group Rings to Partial Decryption Technique. In: Yung, M., Zhang, J., Yang, Z. (eds) Trusted Systems. INTRUST 2015. Lecture Notes in Computer Science(), vol 9565. Springer, Cham. https://doi.org/10.1007/978-3-319-31550-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-31550-8_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31549-2

  • Online ISBN: 978-3-319-31550-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics