Efficient Publicly Verifiable Secret Sharing with Correctness, Soundness and ZK Privacy

A PVSS is a secret sharing scheme with public verification of share validity. A general PVSS must support efficient and immediate secret recovery and have no special requirement on the secret to be shared. No existing general PVSS scheme can achieve correctness, soundness, ZK privacy and practical efficiency simultaneously. A new general PVSS scheme is designed to overcome the existing drawbacks. It is correct, sound and efficient. Moreover, its public verification procedure is strict honest-verifier zero knowledge. In addition, it has an efficient and immediate secret recovery function and has no special requirement on the secret. Another contribution in this paper is that the public verification procedure has independent value.

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

[2]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[3]  Tatsuaki Okamoto,et al.  A Practical and Provably Secure Scheme for Publicly Verifiable Secret Sharing and Its Applications , 1998, EUROCRYPT.

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

[5]  Torben P. Pedersen.  Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing , 1991, CRYPTO.

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

[7]  Jacques Traoré,et al.  Efficient Publicly Verifiable Secret Sharing Schemes with Fast or Delayed Recovery , 1999, ICICS.

[8]  Markus Stadler,et al.  Publicly Verifiable Secret Sharing , 1996, EUROCRYPT.

[9]  Vijay Varadharajan,et al.  Information and Communication Security , 1999, Lecture Notes in Computer Science.

[10]  Andrew Odlyzko,et al.  Advances in Cryptology — CRYPTO’ 86 , 2000, Lecture Notes in Computer Science.

[11]  John M. DeLaurentis,et al.  A Further Weakness in the Common Modulus Protocol for the RSA Cryptoalgorithm , 1984, Cryptologia.

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

[13]  Torben P. Pedersen,et al.  Distributed Provers and Verifiable Secret Sharing Based on the Discrete Logarithm Problem , 1992 .

[14]  Arto Salomaa,et al.  Public-Key Cryptography , 1991, EATCS Monographs on Theoretical Computer Science.

[15]  Gary L. Miller.  Riemann's Hypothesis and Tests for Primality , 1976, J. Comput. Syst. Sci..

[16]  Wenbo Mao,et al.  Guaranteed Correct Sharing of Integer Factorization with Off-Line Shareholders , 1998, Public Key Cryptography.

[17]  Amos Fiat,et al.  How to Prove Yourself: Practical Solutions to Identification and Signature Problems , 1986, CRYPTO.

[18]  Berry Schoenmakers,et al.  A Simple Publicly Verifiable Secret Sharing Scheme and Its Application to Electronic , 1999, CRYPTO.

[19]  Mihir Bellare,et al.  Verifiable partial key escrow , 1997, CCS '97.

[20]  Torben P. Pedersen.  Distributed Provers with Applications to Undeniable Signatures , 1991, EUROCRYPT.

[21]  Kaisa Nyberg,et al.  Advances in Cryptology — EUROCRYPT'98 , 1998 .

[22]  Donald W. Davies,et al.  Advances in Cryptology — EUROCRYPT ’91 , 2001, Lecture Notes in Computer Science.