Paillier-based publicly verifiable (non-interactive) secret sharing

A verifiable secret sharing is a secret sharing scheme with an untrusted dealer that allows participants to verify validity of their own shares. A publicly verifiable secret sharing (PVSS) scheme is a verifiable secret sharing scheme that allows a third party to verify correctness of the distributed shares. We propose an efficient non-interactive PVSS scheme using Paillier additively homomorphic encryption system, and analyze its security in a model that we define in line with the classic semantic-security definition and offering stronger security compared to the previous models. We reduce security of our PVSS scheme to the well studied decisional composite residuosity assumption in this model.

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

[2]  Serge Fehr,et al.  Adaptively Secure Feldman VSS and Applications to Universally-Composable Threshold Cryptography , 2004, CRYPTO.

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

[4]  Jorge Luis Villar,et al.  Public Verifiability from Pairings in Secret Sharing Schemes , 2009, Selected Areas in Cryptography.

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

[6]  Ivan Damgård,et al.  A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System , 2001, Public Key Cryptography.

[7]  Silvio Micali,et al.  Fair Public-Key Cryptosystems , 1992, CRYPTO.

[8]  Victor Shoup,et al.  Practical Threshold Signatures , 2000, EUROCRYPT.

[9]  Yuval Ishai,et al.  The round complexity of verifiable secret sharing and secure multicast , 2001, STOC '01.

[10]  Jorge Luis Villar,et al.  Publicly Verfiable Secret Sharing from Paillier's Cryptosystem , 2005, WEWoRC.

[11]  David Chaum,et al.  Multiparty Unconditionally Secure Protocols (Extended Abstract) , 1988, STOC.

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

[13]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[14]  Kouichi Sakurai,et al.  Distributed Paillier Cryptosystem without Trusted Dealer , 2010, WISA.

[15]  Thomas Beth,et al.  Zur Sicherheit der Informationstechnik - Zur Diskussion gestellt , 1990, Informatik-Spektrum.

[16]  Jacques Stern,et al.  Sharing Decryption in the Context of Voting or Lotteries , 2000, Financial Cryptography.

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

[18]  C. Pandu Rangan,et al.  The Round Complexity of Verifiable Secret Sharing Revisited , 2009, CRYPTO.

[19]  David Chaum,et al.  Wallet Databases with Observers , 1992, CRYPTO.

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

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

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

[23]  Bart Preneel,et al.  Increased Resilience in Threshold Cryptography: Sharing a Secret with Devices That Cannot Store Shares , 2010, Pairing.

[24]  Ali Aydin Selçuk,et al.  Threshold Cryptography Based on Asmuth-Bloom Secret Sharing , 2006, ISCIS.

[25]  Baruch Awerbuch,et al.  Verifiable secret sharing and achieving simultaneity in the presence of faults , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

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

[27]  Mahabir Prasad Jhanwar,et al.  A Practical (Non-interactive) Publicly Verifiable Secret Sharing Scheme , 2011, ISPEC.

[28]  Ilya Mironov,et al.  Publicly Verifiable Secret Sharing for Cloud-Based Key Management , 2011, INDOCRYPT.

[29]  G. R. BLAKLEY.  Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).