Certificateless short sequential and broadcast multisignature schemes using elliptic curve bilinear pairings

Several certificateless short signature and multisignature schemes based on traditional public key infrastructure (PKI) or identity-based cryptosystem (IBC) have been proposed in the literature; however, no certificateless short sequential (or serial) multisignature (CL-SSMS) or short broadcast (or parallel) multisignature (CL-SBMS) schemes have been proposed. In this paper, we propose two such new CL-SSMS and CL-SBMS schemes based on elliptic curve bilinear pairing. Like any certificateless public key cryptosystem (CL-PKC), the proposed schemes are free from the public key certificate management burden and the private key escrow problem as found in PKI- and IBC-based cryptosystems, respectively. In addition, the requirements of the expected security level and the fixed length signature with constant verification time have been achieved in our schemes. The schemes are communication efficient as the length of the multisignature is equivalent to a single elliptic curve point and thus become the shortest possible multisignature scheme. The proposed schemes are then suitable for communication systems having resource constrained devices such as PDAs, mobile phones, RFID chips, and sensors where the communication bandwidth, battery life, computing power and storage space are limited.

[1]  Ashutosh Saxena,et al.  An Efficient Certificateless Signature Scheme , 2005, CIS.

[2]  Tibor Juhas.  The use of elliptic curves in cryptography , 2007 .

[3]  G. P. Biswas,et al.  A pairing-free identity-based authenticated group key agreement protocol for imbalanced mobile networks , 2012, Ann. des Télécommunications.

[4]  Sk Hafizul Islam,et al.  A provably secure identity-based strong designated verifier proxy signature scheme from bilinear pairings , 2014, J. King Saud Univ. Comput. Inf. Sci..

[5]  Joe Suzuki,et al.  Elliptic Curve Discrete Logarithms and the Index Calculus , 1998, ASIACRYPT.

[6]  Jerome A. Solinas.  Generalized Mersenne Prime , 2005, Encyclopedia of Cryptography and Security.

[7]  Marc Girault,et al.  Self-Certified Public Keys , 1991, EUROCRYPT.

[8]  Xiao-Ping Zhang,et al.  ID-Based Designed-verifier Multisignature without Trusted PKG , 2010, 2010 Third International Conference on Information and Computing.

[9]  Lein Harn,et al.  Efficient identity-based RSA multisignatures , 2008, Comput. Secur..

[10]  Yi Mu,et al.  Certificateless Signature Revisited , 2007, ACISP.

[11]  Yang Guang,et al.  An identity-based multisignature scheme from the Weil pairing , 2010, 2010 International Conference On Computer Design and Applications.

[12]  Fuw-Yi Yang,et al.  Improvement of an Efficient ID-Based RSA Multisignature , 2010, 2010 International Conference on Complex, Intelligent and Software Intensive Systems.

[13]  Qiaoyan Wen,et al.  Efficient and provably-secure certificateless short signature scheme from bilinear pairings , 2009, Comput. Stand. Interfaces.

[14]  Alfred Menezes,et al.  Reducing elliptic curve logarithms to logarithms in a finite field , 1991, STOC '91.

[15]  K. Itakura,et al.  A public-key cryptosystem suitable for digital multisignatures , 1983 .

[16]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[17]  Mu-Yen Chen,et al.  Further Remarks on Identity-Based RSA Multi-signature , 2009, 2009 Fifth International Conference on Intelligent Information Hiding and Multimedia Signal Processing.

[18]  Debasis Giri,et al.  An Improved Efficient Multisignature Scheme in Group Communication Systems , 2007, 15th International Conference on Advanced Computing and Communications (ADCOM 2007).

[19]  Kenneth G. Paterson,et al.  Certificateless Public Key Cryptography , 2003 .

[20]  Yu-Fang Chung,et al.  ID-based digital signature scheme on the elliptic curve cryptosystem , 2007, Comput. Stand. Interfaces.

[21]  Adi Shamir,et al.  Identity-Based Cryptosystems and Signature Schemes , 1984, CRYPTO.

[22]  Bok-Min Goi,et al.  Java Implementation for Pairing-Based Cryptosystems , 2010, ICCSA.

[23]  Hovav Shacham,et al.  Short Signatures from the Weil Pairing , 2001, J. Cryptol..

[24]  Xiaoni Du,et al.  A pairing-free identity-based authenticated key agreement protocol with minimal message exchanges , 2010, Inf. Sci..

[25]  Futai Zhang,et al.  An Efficient Certificateless Short Designated Verifier Signature Scheme , 2008, 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing.

[26]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[27]  Wenjing Lou,et al.  On Broadcast Authentication in Wireless Sensor Networks , 2007 .

[28]  L. Harn.  New digital signature scheme based on discrete logarithm , 1994 .

[29]  Sanjay Burman,et al.  Cryptography and security - future challenges and issues , 2007, 15th International Conference on Advanced Computing and Communications (ADCOM 2007).

[30]  Neal Koblitz,et al.  Hyperelliptic cryptosystems , 1989, Journal of Cryptology.

[31]  Dong Hoon Lee,et al.  A new provably secure certificateless short signature scheme , 2011, Comput. Math. Appl..

[32]  Gerhard Frey,et al.  The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems , 1999, IEEE Trans. Inf. Theory.

[33]  Yi Mu,et al.  Certificateless Designated Verifier Signature Schemes , 2006, 20th International Conference on Advanced Information Networking and Applications - Volume 1 (AINA'06).

[34]  Erl-Huei Lu,et al.  Dynamic reblocking RSA-based multisignatures scheme for computer and communication networks , 2002, IEEE Communications Letters.

[35]  Yu-Fang Chung,et al.  Digital multi-signature scheme based on the Elliptic Curve cryptosystem , 2004, Journal of Computer Science and Technology.

[36]  Ashutosh Saxena,et al.  Identity Based Multisignatures , 2006, Informatica.

[37]  K. Nyberg.  New digital signature scheme based on discrete logarithm , 1994 .

[38]  He Debiao,et al.  An ID-based proxy signature schemes without bilinear pairings , 2011 .

[39]  Sagar Patil,et al.  A novel proxy signature scheme based on user hierarchical access control policy , 2013, J. King Saud Univ. Comput. Inf. Sci..

[40]  Yinliang Zhao,et al.  Two Efficient Digital Multisignature Schemes , 2008, 2008 International Symposium on Computational Intelligence and Design.

[41]  Shenghe Sun,et al.  An ID-based Multi-signature Scheme , 2007, Third International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP 2007).

[42]  Duc-Phong Le,et al.  A New Multisignature Scheme based on Strong Diffie-Hellman Assumption , 2007 .

[43]  Sk Hafizul Islam,et al.  Provably secure certificateless strong designated verifier signature scheme based on elliptic curve bilinear pairings , 2013, J. King Saud Univ. Comput. Inf. Sci..

[44]  G. P. Biswas,et al.  Provably secure and pairing-free certificateless digital signature scheme using elliptic curve cryptography , 2013, Int. J. Comput. Math..

[45]  Pierrick Gaudry,et al.  An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves , 2000, EUROCRYPT.

[46]  G. P. Biswas,et al.  Certificateless strong designated verifier multisignature scheme using bilinear pairings , 2012, ICACCI '12.

[47]  Kyung-Ah Shim,et al.  Forgery attacks on the ID-based multisignature scheme without reblocking and predetermined signing order , 2008, Comput. Stand. Interfaces.

[48]  Tzonelih Hwang,et al.  Identity-based conference key broadcast systems , 1994 .

[49]  Jianhua Chen,et al.  An ID-based proxy signature schemes without bilinear pairings , 2011, Ann. des Télécommunications.

[50]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[51]  Paulo S. L. M. Barreto,et al.  On the Selection of Pairing-Friendly Groups , 2003, Selected Areas in Cryptography.