Efficient On-line/Off-line Signature Schemes Based on Multiple-Collision Trapdoor Hash Families

The first on-line/off-line signature scheme introduced by Even et al. in 1990 has two problems: (a) impractical signature length and (b) a one-time use of signature generated during the off-line phase. In 2001, Shamir and Tauman significantly shortened the length of the signature by using trapdoor hash families introduced by Krawczyk and Rabin in 2000. However, each trapdoor hash value and its signature in the off-line phase of Shamir and Tauman's signature scheme can be used for signing only one message in the on-line phase. In this paper, we propose multiple-collision trapdoor hash families based on discrete logarithm and factoring assumptions, and provide formal proofs of their security. We also introduce an efficient on-line/off-line signature scheme based on our proposed trapdoor hash families. Our on-line/off-line signature scheme can re-use a trapdoor hash value for signing multiple messages. If a signer includes this trapdoor hash value in the public-key digital certificate, there is no need to have any regular digital signature scheme to sign the trapdoor hash value in the off-line phase.

[1]  David A. Wagner,et al.  Generic On-Line/Off-Line Threshold Signatures , 2006, Public Key Cryptography.

[2]  Yi Mu,et al.  Efficient generic on-line/off-line (threshold) signatures without key exposure , 2008, Inf. Sci..

[3]  Jacques Stern,et al.  Security Proofs for Signature Schemes , 1996, EUROCRYPT.

[4]  Kaoru Kurosawa,et al.  New Online/Offline Signature Schemes Without Random Oracles , 2006, Public Key Cryptography.

[5]  Rosario Gennaro,et al.  Off-Line/On-Line Signatures: Theoretical Aspects and Experimental Results , 2008, Public Key Cryptography.

[6]  Silvio Micali,et al.  On-line/off-line digital signatures , 1996, Journal of Cryptology.

[7]  Willy Susilo,et al.  Online/Offline Signatures and Multisignatures for AODV and DSR Routing Security , 2006, IACR Cryptol. ePrint Arch..

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

[9]  Tsuyoshi Takagi,et al.  Paillier's Cryptosystem Modulo p2q and Its Applications to Trapdoor Commitment Schemes , 2005, Mycrypt.

[10]  Emmanuel Bresson,et al.  Improved On-Line/Off-Line Threshold Signatures , 2007, Public Key Cryptography.

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

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

[13]  Marc Fischlin,et al.  Trapdoor commitment schemes and their applications , 2001 .

[14]  Stephen R. Tate,et al.  An Online/Offline Signature Scheme Based on the Strong RSA Assumption , 2007, 21st International Conference on Advanced Information Networking and Applications Workshops (AINAW'07).

[15]  C. Q. Lee,et al.  The Computer Journal , 1958, Nature.

[16]  Taher El Gamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, IEEE Trans. Inf. Theory.

[17]  A. Shamir,et al.  Improved On-line / Off-line Signature Schemes , 2022 .

[18]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[19]  Gary L. Miller,et al.  Riemann's Hypothesis and tests for primality , 1975, STOC.