Efficient Publicly Verifiable Secret Sharing Schemes with Fast or Delayed Recovery

1999 ◽  
pp. 87-102 ◽  
Author(s):  
Fabrice Boudot ◽  
Jacques Traoré
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Verifiable Secret Sharing ◽  
Delayed Recovery

Publicly Verifiable Secret Sharing Scheme Based on the Chinese Remainder Theorem

2013 ◽  
Vol 278-280 ◽  
pp. 1945-1951
Author(s):  
Xing Xing Jia ◽  
Dao Shun Wang ◽  
Yu Jiang Wu
Keyword(s):  
Secret Sharing ◽  
Lagrange Interpolation ◽  
Chinese Remainder Theorem ◽  
Secret Sharing Schemes ◽  
Secret Sharing Scheme ◽  
Verifiable Secret Sharing ◽  
Sharing Scheme ◽  
Encrypt Data ◽  
Elgamal Cryptosystem ◽  
Secret Reconstruction

Publicly verifiable secret sharing schemes based on Lagrange interpolation utilize public cryptography to encrypt transmitted data and the validity of their shares can be verified by everyone, not only the participants. However, they require O(klog2k) operations during secret reconstruction phase. In order to reduce the computational complexity during the secret reconstruction phase we propose a non-interactive publicly verifiable secret sharing scheme based on the Chinese Remainder Theorem utilizing ElGamal cryptosystem to encrypt data, whonly requires O(k) operations during secret reconstruction phase. Theoretical analysis proves the proposed scheme achieves computation security and is more efficient.

scholarly journals Span Programs and General Secure Multi-Party Computation

1997 ◽  
Vol 4 (28) ◽  
Author(s):  
Ronald Cramer ◽  
Ivan B. Damgård ◽  
Ueli Maurer
Keyword(s):  
Secret Sharing ◽  
Theoretic Model ◽  
Secret Sharing Schemes ◽  
Cryptographic Primitives ◽  
Information Theoretic ◽  
Verifiable Secret Sharing ◽  
Access Structures ◽  
Sharing Scheme ◽  
Multiplication Property ◽  
Span Programs

The contributions of this paper are three-fold. First, as an abstraction of previously proposed cryptographic protocols we propose two cryptographic primitives: homomorphic<br />shared commitments and linear secret sharing schemes with an additional multiplication property. We describe new constructions for general secure multi-party computation protocols, both in the cryptographic and the information-theoretic (or secure<br />channels) setting, based on any realizations of these primitives.<br />Second, span programs, a model of computation introduced by Karchmer and Wigderson, are used as the basis for constructing new linear secret sharing schemes, from which the two above-mentioned primitives as well as a novel verifiable secret sharing scheme can efficiently be realized. Third, note that linear secret sharing schemes can have arbitrary (as opposed to<br />threshold) access structures. If used in our construction, this yields multi-party protocols secure against general sets of active adversaries, as long as in the cryptographic (information-theoretic) model no two (no three) of these potentially misbehaving player sets cover the full player set. This is a strict generalization of the threshold-type adversaries and results previously considered in the literature. While this result is new for the cryptographic model, the result for the information-theoretic model was previously proved by Hirt and Maurer. However, in addition to providing an independent proof, our protocols are not recursive and have the potential of being more efficient.

A Strengthened Security Notion for Password-Protected Secret Sharing Schemes

2015 ◽  
Vol E98.A (1) ◽  
pp. 203-212 ◽  
Author(s):  
Shingo HASEGAWA ◽  
Shuji ISOBE ◽  
Jun-ya IWAZAKI ◽  
Eisuke KOIZUMI ◽  
Hiroki SHIZUYA
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Security Notion
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