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Signature from the Exponential Hard Lattices

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 117))

Abstract

We extend the lattice problem to the exponential lattice problem and construct signature schemes in the random oracle model and in the standard model based on the exponential hard lattice. Our signature schemes are strongly unforgeable under chosen message attacks if any one of factoring integer problem, computing discrete logarithm problem, and approximating standard worst-case lattice problems is hard.

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References

  1. Rivest, R.L., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. Communications of the ACM 21(2), 120–126 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. ACM Transactions on Information and System Security 3(3), 161–185 (1999); Preliminary version in CCS 1999

    Article  Google Scholar 

  3. El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

  4. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proc. 40th ACM Symp. on Theory of Computing (STOC), pp. 197–206 (2008)

    Google Scholar 

  5. Goldreich, O., Goldwasser, S., Halevi, S.: Public-key cryptosystems from lattice reduction problems. In: CRYPTO, pp. 112–131 (1997)

    Google Scholar 

  6. Hoffstein, J., Pipher, J., Silverman, J.H.: NSS: An NTRU lattice-based signature scheme. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 211–228. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Peikert, C.: Bonsai trees (or, arboriculture in lattice-based cryptography). Cryptology ePrint Archive, Report 2009/359 (July 2009), http://eprint.iacr.org/

  8. Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Rückert, M.: Strongly unforgeable signatures and hierarchical identity-based signatures from lattices without random oracles. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 182–200. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. SIAM J. Comput. 37(1), 267–302 (2004); Preliminary version in FOCS 2004

    Article  MathSciNet  Google Scholar 

  11. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proc. 37th ACM Symp. on Theory of Computing (STOC), pp. 84–93 (2005)

    Google Scholar 

  12. Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. In: STACS, pp. 75–86 (2009)

    Google Scholar 

  13. Cash, D., Hofheinz, D., Kiltz, E.: How to delegate a lattice basis. Cryptology ePrint Archive, Report 2009/351 (July 2009), http://eprint.iacr.org/

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Correspondence to Gu Chunsheng .

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© 2012 Springer Science+Business Media Dordrecht

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Chunsheng, G., Jixing, G., Zhengjun, J., Zhiming, Y. (2012). Signature from the Exponential Hard Lattices. In: Wu, Y. (eds) Advanced Technology in Teaching - Proceedings of the 2009 3rd International Conference on Teaching and Computational Science (WTCS 2009). Advances in Intelligent and Soft Computing, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25437-6_45

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  • DOI: https://doi.org/10.1007/978-3-642-25437-6_45

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25436-9

  • Online ISBN: 978-3-642-25437-6

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