A New Approach to Robust Threshold RSA Signature Schemes

In a threshold RSA signature scheme, dishonest participants can disrupt signature generation by submitting junk instead of their partial signatures. A threshold signature system is robust if it allows generation of correct signatures for a group of t honest participants, and in the presence of malicious participants. The purpose of this paper is two-fold. First we show that a robust (t, n) threshold RSA signature scheme, proposed by Rabin in Crypto’98, lacks an essential property of (t, n) threshold schemes and allows an adversary to forge signatures. Then we propose a new approach to the construction of t-robust (t, n) threshold RSA signature scheme which can be seen as the dual to Rabin’s approach. We discuss the efficiency of our system and show that when t is small (compared to n) our scheme is much more efficient than other existing schemes.

[1]  Ernest F. Brickell,et al.  The Detection of Cheaters in Threshold Schemes , 1988, CRYPTO.

[2]  Hugo Krawczyk,et al.  Robust and Efficient Sharing of RSA Functions , 1996, CRYPTO.

[3]  Paul Feldman,et al.  A practical scheme for non-interactive verifiable secret sharing , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[4]  Tal Rabin,et al.  A Simplified Approach to Threshold and Proactive RSA , 1998, CRYPTO.

[5]  Matthew K. Franklin,et al.  Efficient generation of shared RSA keys , 2001, JACM.

[6]  Moti Yung,et al.  Robust efficient distributed RSA-key generation , 1998, STOC '98.

[7]  Yair Frankel,et al.  A Practical Protocol for Large Group Oriented Networks , 1990, EUROCRYPT.

[8]  Shafi Goldwasser,et al.  Advances in Cryptology — CRYPTO’ 88: Proceedings , 1990, Lecture Notes in Computer Science.

[9]  Ehud D. Karnin,et al.  On secret sharing systems , 1983, IEEE Trans. Inf. Theory.

[10]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[11]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[12]  George Havas,et al.  Perfect Hashing , 1997, Theor. Comput. Sci..

[13]  Moti Yung,et al.  On Threshold RSA-Signing with no Dealer , 1999, ICISC.

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

[15]  Matthew K. Franklin,et al.  Efficient Generation of Shared RSA Keys (Extended Abstract) , 1997, CRYPTO.

[16]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[17]  Jean-Jacques Quisquater,et al.  Advances in Cryptology — EUROCRYPT ’89 , 1991, Lecture Notes in Computer Science.

[18]  Yvo Desmedt,et al.  A Comment on the Efficiency of Secret Sharing Scheme over Any Finite Abelian Group , 1998, ACISP.

[19]  Yvo Desmedt,et al.  Some Recent Research Aspects of Threshold Cryptography , 1997, ISW.

[20]  Giovanni Di Crescenzo,et al.  Multiplicative Non-abelian Sharing Schemes and their Application to Threshold Cryptography , 1994, ASIACRYPT.

[21]  Moti Yung,et al.  Witness-based cryptographic program checking and robust function sharing , 1996, STOC '96.

[22]  Burton S. Kaliski.  Advances in Cryptology - CRYPTO '97 , 1997 .

[23]  Moti Yung,et al.  Optimal-resilience proactive public-key cryptosystems , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[24]  Douglas R Stinson,et al.  Some recursive constructions for perfect hash families , 1996 .

[25]  S. Harari.  Secret Sharing Systems , 1983 .

[26]  Manuel Blum,et al.  Designing programs that check their work , 1989, STOC '89.

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

[28]  Yvo Desmedt,et al.  Society and Group Oriented Cryptography: A New Concept , 1987, CRYPTO.

[29]  Neal Koblitz,et al.  Advances in Cryptology — CRYPTO ’96 , 2001, Lecture Notes in Computer Science.

[30]  Moti Yung,et al.  How to share a function securely , 1994, STOC '94.

[31]  Silvio Micali,et al.  Proofs that yield nothing but their validity and a methodology of cryptographic protocol design , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[32]  Yvo Desmedt,et al.  Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group , 1994, SIAM J. Discret. Math..

[33]  Yvo Desmedt,et al.  Efficient Multiplicative Sharing Schemes , 1996, EUROCRYPT.

[34]  Tsutomu Matsumoto,et al.  Incidence structures for key sharing , 1995 .

[35]  Carl Pomerance,et al.  Advances in Cryptology — CRYPTO ’87 , 2000, Lecture Notes in Computer Science.