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A strong provably secure IBE scheme without bilinear map. (English) Zbl 1339.94071
Summary: Identity-based encryption (IBE) allows one party to send ciphered messages to another using an arbitrary identity string as an encryption key. Since IBE does not require prior generation and distribution of keys, it greatly simplifies key management in public-key cryptography. According to the Menezes-Okamoto-Vanstone (MOV) reduction theory, the IBE scheme based on bilinear map loses the high efficiency of elliptic curve because of the requirement of large security parameters. Therefore, it is important to build a provably secure IBE scheme without bilinear map. To this end, this paper proposes an improved IBE scheme that is different from the previous schemes because this new scheme does not use symmetric encryption algorithm. Furthermore, it can be proven to be secure against adaptively chosen identity and chosen plaintext attacks in the standard model. Elaborated security and performance analysis demonstrate that this new scheme outperforms the previous ones in terms of the time complexity for encryption and decryption.

##### MSC:
 94A60 Cryptography
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##### References:
 [1] Shamir, A., Identity-based cryptosystems and signature schemes, Lecture Notes in Computer Science, vol. 196, 48-53, (1985), Springer-Verlag · Zbl 1359.94626 [2] Boneh, D.; Franklin, M., Identity-based encryption from the Weil pairing, Lecture Notes in Computer Science, vol. 2139, 213-229, (2001), Springer-Verlag · Zbl 1002.94023 [3] Katz, J.; Koo, C., On expected constant-round protocols for Byzantine agreement, J. Comput. Syst. Sci., 75, 2, 91-112, (2009) · Zbl 1162.68431 [4] Boneh, D.; Boyen, X., Efficient selective-ID identity based encryption without random oracles, Lecture Notes in Computer Science, vol. 3027, 223-238, (2004), Springer-Verlag · Zbl 1122.94355 [5] Boneh, D.; Boyen, X., Secure identity based encryption without random oracles, Lecture Notes in Computer Science, vol. 3152, 443-459, (2004), Springer-Verlag · Zbl 1104.94019 [6] Waters, B., Efficient identity-based encryption without random oracles, Lecture Notes in Computer Science, vol. 3494, 114-127, (2005), Springer-Verlag · Zbl 1137.94360 [7] Mathew, K.; Vasant, S.; Venkatesan, S.; Rangan, C., An efficient IND-CCA2 secure variant of the Niederreiter encryption scheme in the standard model, Lecture Notes in Computer Science, vol. 7372, 166-179, (2012), Springer-Verlag · Zbl 1305.94074 [8] Seo, J.; Cheon, J., Fully secure anonymous hierarchical identity-based encryption with constant size ciphertexts, Cryptology ePrint Archive, Report 2011/021 [9] Seo, J.; Kobayashi, T.; Ohkubo, M.; Suzuki, K., Anonymous hierarchical identity-based encryption with constant size ciphertexts, Lecture Notes in Computer Science, vol. 5443, 215-234, (2009), Springer-Verlag · Zbl 1227.94064 [10] Zhang, L.; Hu, Y.; Wu, Q., Unbounded hierarchical identity-based encryption in the standard model, Inf. J., 15, 1, 105-112, (2012) · Zbl 1323.94145 [11] Zhang, L.; Hu, Y.; Wu, Q., New constructions of identity-based broadcast encryption without random oracles, KSII Trans. Internet Inform. Syst., 5, 2, 247-476, (2011) [12] Cocks, C., An identity-based encryption scheme based on quadratic residues, (Proceedings of the 8th IMA International Conference on Cryptography and Coding, (2001)), 360-363 · Zbl 0999.94532 [13] Boneh, D.; Gentry, C.; Hamburg, M., Space-efficient identity based encryption without pairings, (Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, (2008)), 647-657 [14] Xu, P.; Cui, G.; Lei, F., An efficient and provably secure IBE scheme without bilinear map, J. Comput. Res. Dev., 45, 10, 1687-1695, (2008) [15] Xu, P.; Cui, G.; Fu, C.; Tang, X., A more efficient accountable authority IBE scheme under the DL assumption, Sci. China, 53, 3, 581-592, (2010) [16] Benasser, A.; Samsudin, A., A new identity based encryption (IBE) scheme using extended Chebyshev polynomial over finite fields Z, Phys. Lett. A, 374, 46, 4670-4674, (2010) · Zbl 1238.94026 [17] Yang, X.; Wu, L.; Zhang, M.; Wei, P.; Wei, L., An ideal lattice based IBE scheme in the standard model, Wuhan Univ. J. Nat. Sci., 16, 5, 439-446, (2011) [18] Luo, S.; Shen, Q.; Jin, Y.; Chen, Y., A variant of boyen-waters anonymous IBE scheme, Lecture Notes in Computer Sciences, vol. 7043, 42-56, (2011), Springer-Verlag [19] Katz, J.; MacKenzie, P.; Taban, G.; Gligor, V., Two-server password-only authenticated key exchange, J. Comput. Syst. Sci., 78, 2, 651-669, (2012) · Zbl 1277.94059 [20] Attrapadung, N.; Furukawa, J.; Gomi, T., Efficient identity-based encryption with tight security reduction, Lecture Notes in Computer Science, vol. 4301, 19-36, (2006), Springer-Verlag · Zbl 1307.94034 [21] Menezes, A.; Okamoto, T.; Vanstone, S., Reducing elliptic curve logarithms to logarithms in a finite field, IEEE Trans. Inf. Theory, 39, 5, 1639-1646, (1993) · Zbl 0801.94011 [22] Islam, S.; Biswas, G., An improved ID-based client authentication with key agreement scheme on ECC for mobile client-server environments, Theor. Appl. Inform., 24, 4, 293-312, (2012) [23] Barreto, P.; Kim, H.; Lynn, B.; Scott, M., Efficient algorithms for pairing-based cryptosystems, Lecture Notes in Computer Sciences, vol. 2442, 354-369, (2002), Springer-Verlag · Zbl 1026.94520
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