Underlying Assumptions and Designated Verifier Signatures

In this paper, we define an underlying computational problem and its decisional problem. As an application of their problems, we propose an efficient designated verifier signature (DVS) scheme without random oracles (related to symmetric pairings). We formally redefine the (Strong) Privacy of Signature’s Identity, and prove our DVS scheme satisfying security based on the difficulty of the problems. Also we prove that the difficulty of the computational problem is tightly equivalent to the Strong Unforgeability of our proposed conventional signature scheme (without random oracles) related to asymmetric pairings. We believe that our underlying problems are profitable to propose many efficient cryptographic schemes.

[1]  Jianhong Zhang,et al.  An Efficient Designated Verifier Signature Scheme without Random Oracles , 2007, The First International Symposium on Data, Privacy, and E-Commerce (ISDPE 2007).

[2]  Takeshi Okamoto,et al.  Sender Authenticated Key Agreements Without Random Oracles , 2007, 2007 International Conference on Convergence Information Technology (ICCIT 2007).

[3]  Taiichi Saito,et al.  Candidate One-Way Functions on Non-Supersingular Elliptic Curves , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[4]  Jean-Jacques Quisquater,et al.  Universal Designated Verifier Signatures Without Random Oracles or Non-black Box Assumptions , 2006, SCN.

[5]  Takeshi Okamoto,et al.  Strongly unforgeable ID-based signatures without random oracles , 2009, Int. J. Appl. Cryptogr..

[6]  Reihaneh Safavi-Naini,et al.  Construction of Universal Designated-Verifier Signatures and Identity-Based Signatures from Standard Signatures , 2008, Public Key Cryptography.

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

[8]  Fabien Laguillaumie,et al.  Designated Verifier Signatures: Anonymity and Efficient Construction from Any Bilinear Map , 2004, SCN.

[9]  Yi Mu,et al.  Designated Verifier Signature: Definition, Framework and New Constructions , 2007, UIC.

[10]  Hideki Imai,et al.  Efficient hybrid encryption from ID-based encryption , 2010, Des. Codes Cryptogr..

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

[13]  Markus Jakobsson,et al.  Designated Verifier Proofs and Their Applications , 1996, EUROCRYPT.

[14]  Brent Waters,et al.  Efficient Identity-Based Encryption Without Random Oracles , 2005, EUROCRYPT.

[15]  Qiong Huang,et al.  Generic Transformation to Strongly Unforgeable Signatures , 2007, ACNS.

[16]  Guomin Yang,et al.  Efficient Strong Designated Verifier Signature Schemes without Random Oracles or Delegatability , 2009, IACR Cryptol. ePrint Arch..

[17]  Kenneth G. Paterson,et al.  Efficient Identity-Based Signatures Secure in the Standard Model , 2006, ACISP.