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# A Self Proxy Signature Scheme Over NTRU Lattices

## Abstract

The concept of self proxy signature (SPS) scheme was proposed by Kim and Chang in 2007. In a self proxy signatures, the signer wants to protect his original keys by generating temporary key pairs for a time period and then revoke them. The temporary keys can be generated by delegating the signing right to himself. Thus, in SPS the user can prevent the exposure of his private key from repeated use. If we are considering the existence of quantum computers, then scheme proposed by Kim and Chang’s is no more secure since its security is based on the hardness of discrete logarithm assumption. In this paper we propose the first lattice based self proxy signature scheme. Since hard problems of lattices are secure against quantum attacks, therefore, our proposed scheme is secure against quantum computer also. We designed our scheme on NTRU lattices since NTRU lattices are most efficient lattices than general lattices.

## Keywords

NTRU lattices Proxy signature scheme Random oracle SIS problem Identity based signatures## References

- 1.D.J. Bernstein, Introduction to post-quantum cryptography, in
*Post-Quantum Cryptography*, ed. by D.J. Bernstein, J. Buchmann, E. Dahmen (Springer, Berlin, 2009), pp. 1–14CrossRefGoogle Scholar - 2.J.Y. Cai, A. Nerurkar, Approximating the SVP to within a factor (1+1/dim ) is NP-hard under randomized reductions. J. Comput. Syst. Sci.
**59**(2), 221–239 (1998)CrossRefGoogle Scholar - 3.C. Gentry, C. Peikert, V. Vaikuntanathan, Trapdoors for hard lattices and new cryptographic constructions, in
*40th Annual ACM Symposium on Theory of Computing*(2008), pp. 197–206Google Scholar - 4.J. Hermans, F. Vercauteren, B. Preneel, Speed records for NTRU, in
*Topics in Cryptology-CT-RSA*(Springer, Basel, 2010), pp. 73–88zbMATHGoogle Scholar - 5.J. Hoffstein, J. Pipher, J.H. Silverman, NTRU: a new high speed public key cryptosystem (1996, preprint). Presented at the rump session of Crypto96Google Scholar
- 6.J. Hoffstein, J. Pipher, J.H. Silverman, NTRU : a ring based public key cryptosystem, in
*Proceedings of ANTS*, LNCS, vol. 1423 (Springer, Cham, 1998), pp. 267–288zbMATHGoogle Scholar - 7.J. Hoffstein, J.H. Silverman, Optimizations for NTRU, in
*Public-key Cryptography and Computational Number Theory*(DeGruyter, Berlin, 2000)Google Scholar - 8.Y.S. Kim, J.H. Chang, Self proxy signature scheme. Int. J. Comput. Sci. Netw. Secur.
**7**(2), 335–338 (2007)Google Scholar - 9.S. Lal, A.K. Awasthi, Proxy blind signature scheme. J. Inf. Sci. Eng. Cryptol. ePrint Archive. Report 2003/072. Available at http://eprint.iacr.org/
- 10.Z.H. Liu, Y.P. Hu, H. Ma, Secure proxy multi-signature scheme in the standard model, in
*Proceeding of the 2nd International Conference on Provable Security (ProvSec’08), Oct 30 Nov 1, Shanghai*. LNCS, vol. 5324 (Springer, Berlin, 2008), pp. 127–140Google Scholar - 11.V. Lyubashevsky, Lattice signatures without trapdoors, in
*31st Annual International Conference on the Theory and Applications of Cryptographic Techniques*(2012), pp. 738–755Google Scholar - 12.M. Mambo, K. Usuda, E. Okamoto, Proxy signatures: delegation of the power to sign messages. IEICE Trans. Fundam. Electron. Commun. Comput. Sci.
**79**(9), 1338–1354 (1996)Google Scholar - 13.M. Mambo, K. Usuda, E. Okamoto, Proxy signatures for delegating signing operation, in
*3*^{rd}*ACM Conference on Computer and Communication Security(CCS’96)*(1996), pp. 48–57Google Scholar - 14.S. Mashhadi, A novel secure self proxy signature scheme. Int. J. Netw. Secur.
**14**(1), 2226 (2012)Google Scholar - 15.P.Q. Nguyen, O. Regev, Learning a parallelepiped : cryptanalysis of GGH and NTRU signatures, in
*24th Annual International Conference on the Theory and Applications of Cryptographic Techniques*(2006), pp. 271–288Google Scholar - 16.S.S.D. Selvi, S.S. Vivek, S. Gopinath, C.P. Rangan, Identity based self delegated signature-self proxy signatures, in
*Network and System Security (NSS)*(2010), pp. 568–573Google Scholar - 17.S.H. Seo, K.A. Shim, S.H. Lee, A mediated proxy signature scheme with fast revocation for electronic transaction, in
*Proceeding of the 2nd International Conference on Trust, Privacy and Security in Digital Business, Aug 22–26, Copenhagen*. LNCS, vol. 3592 (Springer, Cham, 2005), pp. 216–225Google Scholar - 18.P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in
*Proceedings of 35th Annual IEEE Symposium on Foundations of Computer Science*(IEEE, Piscataway, 1994), pp. 124–134Google Scholar - 19.P. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput.
**26**, 1484–1509 (2006)MathSciNetCrossRefGoogle Scholar - 20.D. Stehle, R. Steinfeld, Making NTRUEncrypt and NTRUSign as secure as standard worst-case problems over ideal lattices (2013), Cryptology ePrint Archive 2013/004. Available from http://eprint.iacr.org/2013/004
- 21.N. Tahat, K.A. Alzubi, I. Abu-Falahah, An efficient self proxy signature scheme based on elliptic curve discrete logarithm problems. Appl. Math. Sci.
**7**(78), 3853–3860 (2013)MathSciNetGoogle Scholar - 22.Z. Tan, Z. Liu, C. Tang, Digital proxy blind signature schemes based on DLP and ECDLP. MM Research Preprints, No. 21, MMRC AMMS (Academia Sinica, Beijing, 2002), pp. 212–217Google Scholar
- 23.V. Verma, An efficient identity based selff proxy signature scheme with warrant. Int. J. Comput. Sci. Commun.
**3**(1), 111–113 (2012)Google Scholar - 24.G. Wang, Designated-verifier proxy signature schemes, in
*Security and Privacy in the Age of Ubiquitous Computing (IFIP/SEC 2005)*(Springer, New York, 2005), pp. 409–423CrossRefGoogle Scholar - 25.G. Wang, F. Bao, J. Zhou, R.H. Deng, Security analysis of some proxy signatures, in
*Information Security and Cryptology - ICISC 2003*. LNCS, vol. 2971 (Springer, Cham, 2004), pp. 305–319Google Scholar - 26.J. Xie, Y.P. Hu, J.T. Gao, W. Gao, Efficient identity based signature over NTRU lattice. Front. Inf. Technol. Electron. Eng.
**17**(2), 135–142 (2016)CrossRefGoogle Scholar - 27.Y. Yu, Y. Sun, B. Yang, Multi-proxy signature without random oracles. Chin. J. Electron.
**17**(3), 475–480 (2008)Google Scholar