How to Prove Security of a Signature with a Tighter Security Reduction

It is a challenging task to construct a signature that it can be tightly reduced to a weak security assumption in the standard model. In this paper, we introduce a simple chameleon-hash-based transformation and show that it can tighten a security reduction of a signature scheme that suffers from a loose security reduction. Taking the Waters' signature from Eurocrypt 2005 as an example, we demonstrate an improvement of the security reduction that the probability of success in the security reduction can be made as a constant and independent of the signature queries from an adversary. Our reduction methodology has never been considered in the literature and is applicable to many signature schemes such as identity-based signature schemes, online/offline signatures, and signatures with strong unforeability.

[1]  Brent Waters,et al.  Strongly Unforgeable Signatures Based on Computational Diffie-Hellman , 2006, Public Key Cryptography.

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

[3]  Stanislaw Jarecki,et al.  A Signature Scheme as Secure as the Diffie-Hellman Problem , 2003, EUROCRYPT.

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

[5]  Yael Tauman Kalai,et al.  Improved Online/Offline Signature Schemes , 2001, CRYPTO.

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

[7]  Jonathan Katz,et al.  Efficiency improvements for signature schemes with tight security reductions , 2003, CCS '03.

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

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

[10]  Aggelos Kiayias,et al.  Public Key Cryptography - PKC 2006 , 2006, Lecture Notes in Computer Science.

[11]  Jan Camenisch,et al.  Batch Verification of Short Signatures , 2007, EUROCRYPT.

[12]  Brent Waters,et al.  Realizing Hash-and-Sign Signatures under Standard Assumptions , 2009, EUROCRYPT.

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

[14]  Craig Gentry,et al.  Practical Identity-Based Encryption Without Random Oracles , 2006, EUROCRYPT.

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

[16]  Silvio Micali,et al.  On-Line/Off-Line Digital Schemes , 1989, CRYPTO.

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

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

[19]  Ronald Cramer,et al.  Advances in Cryptology - EUROCRYPT 2005, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Aarhus, Denmark, May 22-26, 2005, Proceedings , 2005, EUROCRYPT.

[20]  Moni Naor.  Advances in Cryptology - EUROCRYPT 2007, 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Barcelona, Spain, May 20-24, 2007, Proceedings , 2007, EUROCRYPT.

[21]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[22]  Yi Mu,et al.  Efficient Generic On-Line/Off-Line Signatures Without Key Exposure , 2007, ACNS.

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

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

[25]  Aggelos Kiayias,et al.  Traitor Tracing with Constant Transmission Rate , 2002, EUROCRYPT.

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

[27]  Ben Lynn,et al.  Toward Hierarchical Identity-Based Encryption , 2002, EUROCRYPT.

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

[29]  Information Security and Privacy , 1996, Lecture Notes in Computer Science.

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

[31]  Yuliang Zheng,et al.  Advances in Cryptology — ASIACRYPT 2002 , 2002, Lecture Notes in Computer Science.

[32]  Craig Gentry,et al.  Hierarchical ID-Based Cryptography , 2002, ASIACRYPT.