A New Signature Scheme Without Random Oracles from Bilinear Pairings

In this paper, we propose a new signature scheme that is existentially unforgeable under a chosen message attack without random oracle. The security of the proposed scheme depends on a new complexity assumption called the k+1 square roots assumption. Moreover, the k+1 square roots assumption can be used to construct shorter signatures under the random oracle model.

[1]  Ueli Maurer,et al.  Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms , 1994, CRYPTO.

[2]  Jan Camenisch,et al.  Signature Schemes and Anonymous Credentials from Bilinear Maps , 2004, CRYPTO.

[3]  Hideki Imai,et al.  Short Signature and Universal Designated Verifier Signature Without Random Oracles , 2005, ACNS.

[4]  Paulo S. L. M. Barreto,et al.  Efficient Algorithms for Pairing-Based Cryptosystems , 2002, CRYPTO.

[5]  Jung Hee Cheon,et al.  An Identity-Based Signature from Gap Diffie-Hellman Groups , 2003, Public Key Cryptography.

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

[7]  Serge Vaudenay,et al.  Advances in Cryptology - EUROCRYPT 2006 , 2006, Lecture Notes in Computer Science.

[8]  Jan Camenisch,et al.  A Signature Scheme with Efficient Protocols , 2002, SCN.

[9]  Ronald Cramer,et al.  Signature schemes based on the strong RSA assumption , 2000, TSEC.

[10]  Yvo Desmedt.  Public Key Cryptography — PKC 2003 , 2002, Lecture Notes in Computer Science.

[11]  Silvio Micali,et al.  A "Paradoxical" Solution to the Signature Problem (Extended Abstract) , 1984, FOCS.

[12]  Jung Hee Cheon,et al.  Security Analysis of the Strong Diffie-Hellman Problem , 2006, EUROCRYPT.

[13]  Chi Sung Laih,et al.  Advances in Cryptology - ASIACRYPT 2003 , 2003 .

[14]  Ron Steinfeld,et al.  Universal Designated-Verifier Signatures , 2003, ASIACRYPT.

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

[16]  Rainer A. Rueppel,et al.  A new signature scheme based on the DSA giving message recovery , 1993, CCS '93.

[17]  Iwan M. Duursma,et al.  Tate Pairing Implementation for Hyperelliptic Curves y2 = xp-x + d , 2003, ASIACRYPT.

[18]  Dan Boneh,et al.  A Secure Signature Scheme from Bilinear Maps , 2003, CT-RSA.

[19]  Craig Gentry,et al.  Certificate-Based Encryption and the Certificate Revocation Problem , 2003, EUROCRYPT.

[20]  Marc Fischlin.  The Cramer-Shoup Strong-RSASignature Scheme Revisited , 2003, Public Key Cryptography.

[21]  Aggelos Kiayias,et al.  Self Protecting Pirates and Black-Box Traitor Tracing , 2001, CRYPTO.

[22]  Magnus Daum,et al.  On the Security of HFE, HFEv- and Quartz , 2003, Public Key Cryptography.

[23]  Kenneth G. Paterson,et al.  ID-based Signatures from Pairings on Elliptic Curves , 2002, IACR Cryptol. ePrint Arch..

[24]  Yi Mu,et al.  A New Signature Scheme without Random Oracles and Its Applications ? , 2006 .

[25]  Colin Boyd,et al.  Advances in Cryptology - ASIACRYPT 2001 , 2001 .

[26]  Louis Goubin,et al.  QUARTZ, 128-Bit Long Digital Signatures , 2001, CT-RSA.

[27]  Florian Hess,et al.  Efficient Identity Based Signature Schemes Based on Pairings , 2002, Selected Areas in Cryptography.

[28]  Jeffrey Shallit,et al.  Algorithmic Number Theory , 1996, Lecture Notes in Computer Science.

[29]  David Naccache,et al.  Topics in Cryptology — CT-RSA 2001 , 2001, Lecture Notes in Computer Science.

[30]  Steven D. Galbraith,et al.  Implementing the Tate Pairing , 2002, ANTS.

[31]  Shai Halevi,et al.  Secure Hash-and-Sign Signatures Without the Random Oracle , 1999, EUROCRYPT.

[32]  Hovav Shacham,et al.  Aggregate and Verifiably Encrypted Signatures from Bilinear Maps , 2003, EUROCRYPT.

[33]  Aggelos Kiayias,et al.  Traceable Signatures , 2004, EUROCRYPT.

[34]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[35]  Silvio Micali,et al.  A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks , 1988, SIAM J. Comput..

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

[37]  Dan Boneh,et al.  Short Signatures Without Random Oracles , 2004, EUROCRYPT.

[38]  Hovav Shacham,et al.  Short Group Signatures , 2004, CRYPTO.

[39]  Jacques Stern,et al.  Advances in Cryptology — EUROCRYPT ’99 , 1999, Lecture Notes in Computer Science.

[40]  Yi Mu,et al.  A New Short Signature Scheme Without Random Oracles from Bilinear Pairings , 2005, IACR Cryptol. ePrint Arch..

[41]  Moti Yung,et al.  Advances in Cryptology — CRYPTO 2002 , 2002, Lecture Notes in Computer Science.

[42]  Jacques Stern,et al.  Signing on a Postcard , 2000, Financial Cryptography.

[43]  Ahmad-Reza Sadeghi,et al.  Assumptions Related to Discrete Logarithms: Why Subtleties Make a Real Difference , 2001, EUROCRYPT.

[44]  Walter M. Lioen,et al.  Factorization of RSA-140 Using the Number Field Sieve , 1999, CRYPTO 1999.

[45]  Robert H. Deng,et al.  Public Key Cryptography – PKC 2004 , 2004, Lecture Notes in Computer Science.

[46]  Ueli Maurer,et al.  Advances in Cryptology — EUROCRYPT ’96 , 2001, Lecture Notes in Computer Science.

[47]  Antoine Joux,et al.  The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems , 2002, ANTS.

[48]  Hugo Krawczyk,et al.  Chameleon Hashing and Signatures , 1998, IACR Cryptol. ePrint Arch..

[49]  Matthieu Finiasz,et al.  How to Achieve a McEliece-Based Digital Signature Scheme , 2001, ASIACRYPT.

[50]  Matthew Franklin,et al.  Advances in Cryptology – CRYPTO 2004 , 2004, Lecture Notes in Computer Science.

[51]  Dan Boneh,et al.  Secure Identity Based Encryption Without Random Oracles , 2004, CRYPTO.

[52]  Reihaneh Safavi-Naini,et al.  An Efficient Signature Scheme from Bilinear Pairings and Its Applications , 2004, Public Key Cryptography.

[53]  Marc Joye,et al.  Topics in Cryptology — CT-RSA 2003 , 2003 .

[54]  Tatsuaki Okamoto,et al.  A Signature Scheme with Message Recovery as Secure as Discrete Logarithm , 1999, ASIACRYPT.

[55]  Mihir Bellare,et al.  The Exact Security of Digital Signatures - HOw to Sign with RSA and Rabin , 1996, EUROCRYPT.