Efficient identity-based signature over NTRU lattice

Article

Abstract

Identity-based signature has become an important technique for lightweight authentication as soon as it was proposed in 1984. Thereafter, identity-based signature schemes based on the integer factorization problem and discrete logarithm problem were proposed one after another. Nevertheless, the rapid development of quantum computers makes them insecure. Recently, many efforts have been made to construct identity-based signatures over lattice assumptions against attacks in the quantum era. However, their efficiency is not very satisfactory. In this study, an efficient identity-based signature scheme is presented over the number theory research unit (NTRU) lattice assumption. The new scheme is more efficient than other lattice- and identity-based signature schemes. The new scheme proves to be unforgeable against the adaptively chosen message attack in the random oracle model under the hardness of the γ-shortest vector problem on the NTRU lattice.

Keywords

Identity Signature Lattice Number theory research unit (NTRU) 

CLC number

TP309.7 

References

  1. Babai, L., 1986. On Lovász’ lattice reduction and the nearest lattice point problem. Combinatorica, 6(1):1–13. http://dx.doi.org/10.1007/BF02579403MathSciNetCrossRefGoogle Scholar
  2. Barreto, P.S.L.M., Libert, B., McCullagh, N., et al., 2005. Efficient and provably-secure identity-based signatures and signcryption from bilinear maps. 11th Int. Conf. on the Theory and Application of Cryptology and Information Security, p.515–532. http://dx.doi.org/10.1007/11593447_28Google Scholar
  3. Bernstein, D.J., 2009. Introduction to post-quantum cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (Eds.), Post-Quantum Cryptography. Springer-Verlag, Berlin, p.1–14. http://dx.doi.org/10.1007/978-3-540-88702-7_1CrossRefMATHGoogle Scholar
  4. Boneh, D., Franklin, M., 2001. Identity based encryption from the Weil pairing. 21st Annual Int. Cryptology Conf., p.213–229. http://dx.doi.org/10.1007/3-540-44647-8_13Google Scholar
  5. Desmedt, Y., Quisquater, J.J., 1987. Public-key systems based on the difficulty of tampering (Is there a difference between DES and RSA?). LNCS, 263:111–111. http://dx.doi.org/10.1007/3-540-47721-7_9MathSciNetGoogle Scholar
  6. Ducas, L., Lyubashevsky, V., Prest, T., 2014. Efficient identity-based encryption over NTRU lattice. 20th Int. Conf. on the Theory and Application of Cryptology and Information Security, p.22–41. http://dx.doi.org/10.1007/978-3-662-45608-8_2Google Scholar
  7. Gentry, C., Peikert, C., Vaikuntanathan, V., 2008. Trapdoors for hard lattices and new cryptographic constructions. 40th Annual ACM Symp. on Theory of Computing, p.197–206. http://dx.doi.org/10.1145/1374376.1374407Google Scholar
  8. Hess, F., 2003. Efficient identity based signature schemes based on pairings. 9th Annual Int. Workshop on Selected Areas in Cryptography, p.310–324. http://dx.doi.org/10.1007/3-540-36492-7_20CrossRefGoogle Scholar
  9. Krenn, M., Huber, M., Fickler, R., et al., 2014. Generation and confirmation of a (100×100)-dimensional entangled quantum system. PNAS, 111(17):6243–6247. http://dx.doi.org/10.1073/pnas.1402365111CrossRefGoogle Scholar
  10. Li, F.G., Muhaya, F.T.B., Khan, M.K., et al., 2012. Latticebased signcryption. Concurr. Comput. Pract. Exp., 25(14):2112–2122. http://dx.doi.org/10.1002/cpe.2826CrossRefGoogle Scholar
  11. Liu, Z.H., Hu, Y.P., Zhang, X.S., et al., 2013. Efficient and strongly unforgeable identity-based signature scheme from lattices in the standard model. Secur. Commun. Network., 6(1):69–77. http://dx.doi.org/10.1002/sec.531CrossRefGoogle Scholar
  12. Lyubashevsky, V., 2012. Lattice signatures without trapdoors. 31st Annual Int. Conf. on the Theory and Applications of Cryptographic Techniques, p.738–755. http://dx.doi.org/10.1007/978-3-642-29011-4_43Google Scholar
  13. Maurer, U.M., Yacobi, Y., 1991. Non-interactive public-key cryptography. Workshop on the Theory and Application of Cryptographic Techniques, p.498–507. http://dx.doi.org/10.1007/3-540-46416-6_43Google Scholar
  14. Micciancio, D., Regev, O., 2009. Lattice-based cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (Eds.), Post-Quantum Cryptography. Springer-Verlag, Berlin, p.147-191. http://dx.doi.org/10.1007/978-3-540-88702-7_5MATHGoogle Scholar
  15. Nguyen, P.Q., Regev, O., 2006. Learning a parallelepiped: cryptanalysis of GGH and NTRU signatures. 24th Annual Int. Conf. on the Theory and Applications of Cryptographic Techniques, p.271–288. http://dx.doi.org/10.1007/11761679_17Google Scholar
  16. Paterson, K.G., Schuldt, J.C.N., 2006. Efficient identity-based signatures secure in the standard model. 11th Australasian Conf. on Information Security and Privacy, p.207–222. http://dx.doi.org/10.1007/11780656_18CrossRefGoogle Scholar
  17. Rückert, M., 2010. Strongly unforgeable signatures and hierarchical identity-based signatures from lattices without random oracles. Proc. 3rd Int. Workshop on PQCrypto, p.182–200. http://dx.doi.org/10.1007/978-3-642-12929-2_14CrossRefGoogle Scholar
  18. Shamir, A., 1984. Identity-based cryptosystems and signature schemes. Proc. CRYPTO, p.47–53. http://dx.doi.org/10.1007/3-540-39568-7_5
  19. Shor, P.W., 1997. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput., 26(5):1484–1509. http://dx.doi.org/10.1137/S0097539795293172MathSciNetCrossRefGoogle Scholar
  20. Stehlé, D., Steinfeld, R., 2013. Making NTRUEncrypt and NTRUSign as secure as standard worst-case problems over ideal lattices. Cryptology ePrint Archive 2013/004. Available from http://eprint.iacr.org/2013/004.Google Scholar
  21. Tanaka, H., 1987. A realization scheme for the identity-based cryptosystem. CRYPTO, p.341–349. http://dx.doi.org/10.1007/3-540-48184-2_29Google Scholar
  22. Tian, M.M., Huang, L.S., 2014. Efficient identity-based signature from lattices. Proc. 29th IFIP TC 11 Int. Conf., p.321–329. http://dx.doi.org/10.1007/978-3-642-55415-5_26Google Scholar
  23. Tian, M.M., Huang, L.S., Yang, W., 2013. Efficient hierachical identity-based signatures from lattices. Int. J. Electron. Secur. Dig. Forens., 5(1):1–10. http://dx.doi.org/10.1504/IJESDF.2013.054403CrossRefGoogle Scholar
  24. Tsuji, S., Itoh, T., 1989. An ID-based cryptosystem based on the discrete logarithm problem. IEEE J. Sel. Areas Commun., 7(4):467–473. http://dx.doi.org/10.1109/49.17709CrossRefGoogle Scholar

Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Telecommunications EngineeringXidian UniversityXi’anChina
  2. 2.The State Key Laboratory of Integrated Services NetworkXi’anChina

Personalised recommendations