A New Design Partially Blind Signature Scheme Based on Two Hard Mathematical Problems
Recently, many existing partially blind signature scheme based on a single hard problem such as factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. However sooner or later these systems will become broken and vulnerable, if the factoring or discrete logarithms problems are cracked. This paper proposes a secured partially blind signature scheme based on factoring (FAC) problem and elliptic curve discrete logarithms (ECDL) problem. As the proposed scheme is focused on factoring and ECDLP hard problems, it has a solid structure and will totally leave the intruder bemused because it is very unlikely to solve the two hard problems simultaneously. In order to assess the security level of the proposed scheme a performance analysis has been conducted. Results have proved that the proposed scheme effectively deals with the partial blindness, randomization, unlinkability and unforgeability properties. Apart from this we have also investigated the computation cost of the proposed scheme. The new proposed scheme is robust and it is difficult for the malevolent attacks to break our scheme.
 D. Chaum, "Blind signature for untraceable payments," Advances in
Cryptology, Proceedings of CRYPTO -82, pp. 199-203, 2000.
 A. Juels, M. Luby, and R. Ostrovsky, "Security of blind signatures,"
Advances in Cryptology - Crypto 1997, LNCS 1294. Springer-Verlag,
pp. 150-164., 1997.
 D. Pointcheval, "Strengthened security for blind signatures," Advances
in Cryptology -Eurocrypt 1998, LNCS 1403. Springer-Verlag,, pp. 391-
 D. Pointcheval and J. Stern, "Provably secure blind signature schemes,"
Advances in Cryptology - Asiacrypt 1996, LNCS 1163. Springer- Verlag,
pp. 252-265, 1996.
 D. Pointchval and J. Stern, "Security arguments for digital signatures
and blind signatures," Journal of Cryptography, vol. 13 (3), pp. 361-
 M. Abe and E. Fujisaki, "How to date blind signatures," Lecture Notes
in Computer Science, 1163.Springer-Verlag, pp. 244-251, 1996.
 C. I. Fan and C. Lei, "Low-computation partially blind signatures for
electronic cash," IEICE Transaction on Fundamentals, vol. E81-A, pp.
 M. S. Hwang, C. C. Lee, and Y. Lai, "Traceability on low computation
partially blind signatures for electronic cash," IEICE Transaction on
Fundamentals, vol. 85, pp. 1181-1182, 2002.
 H. Chien, H. Y. Jan, and Y. M. Tseng, "Rsa-based partially blind
signature with low computation," in 8th International Conference On
Parallel and Distribute Systemes, 2001, pp. 385-389.
 G. Maitland and C. Boyd, "A provably secure restrictive partially blind
signature scheme," PKC 2002, LNCS 2274. Springer-Verlag,, pp. 99-
 T. Abe, M. Okamoto, "Provably secure partially blind signatures,"
Advances In Cryptology-Crypto,LNCS 1880.Springer-Verlag, vol. 5, pp.
 H. Chien, H. Y. Jan, and Y. M. Tseng, "A new design of efficient partially
blind signature scheme," Journal of Systems and Software, vol. 73, pp.
 F. Zhang and X. Chen, "Cryptanalysis of huangchang partially blind
signature scheme," The Journal of Systems and Software, vol. 76, pp.
76: 323-325, 2005.
 D. A. Johnson, D. A. Menezes, and S. Vanstone, "The elliptic curve digital
signature algorithm," International Journal of Information Security,
vol. 1(1), pp. 36-63, 2001.
 N. Koblitz, "Elliptic curve cryptosystems," Mathematics of Computation,
vol. 48(177), pp. 203-209, 1987.
 N. Koblizt, A. Menezes, and S. Vanstone, "The state of elliptic curve
cryptography," Design, Code Cryptography, vol. 19(2-3), pp. 173-193,
 V. Miller, "Uses of elliptic curve in cryptography," Advances in
Cryptology-Proceeding of CRYPTO-85. LNCS 218, Springer-Verlag, pp.