On a Relation Between Verifiable Secret Sharing Schemes and a Class of Error-Correcting Codes

2006 ◽  
pp. 275-290 ◽  
Author(s):  
Ventzislav Nikov ◽  
Svetla Nikova
Keyword(s):  
Secret Sharing ◽  
Error Correcting Codes ◽  
Secret Sharing Schemes ◽  
Verifiable Secret Sharing

scholarly journals Ideals of Numerical Semigroups and Error-Correcting Codes

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1406
Author(s):  
Bras-Amorós
Keyword(s):  
Secret Sharing ◽  
Error Correcting Codes ◽  
Numerical Semigroups ◽  
Secret Sharing Schemes ◽  
List Decoding ◽  
Generalized Hamming Weights ◽  
Resilient Functions ◽  
Weierstrass Semigroups ◽  
Hamming Weights ◽  
Dual Sequences

Several results relating additive ideals of numerical semigroups and algebraic-geometrycodes are presented. In particular, we deal with the set of non-redundant parity-checks, the codelength, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometrycodes from the perspective of the related Weierstrass semigroups. These results are related tocryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, networkcoding, and ramp secret sharing schemes.

scholarly journals Linear Secret Sharing Schemes from Error Correcting Codes and Universal Hash Functions

2015 ◽  
pp. 313-336 ◽  
Author(s):  
Ronald Cramer ◽  
Ivan Bjerre Damgård ◽  
Nico Döttling ◽  
Serge Fehr ◽  
Gabriele Spini
Keyword(s):  
Secret Sharing ◽  
Hash Functions ◽  
Error Correcting Codes ◽  
Secret Sharing Schemes

An information theoretical model for quantum secret sharing schemes

2005 ◽  
Vol 5 (1) ◽  
pp. 68-79 ◽  
Author(s):  
H. Imai ◽  
J. Mueller-Quade ◽  
A.C.A. Nascimento ◽  
P. Tuyls ◽  
A. Winter
Keyword(s):  
Quantum Information ◽  
Theoretical Model ◽  
Secret Sharing ◽  
Quantum Secret Sharing ◽  
Error Correcting Codes ◽  
Secret Sharing Schemes ◽  
Secret Sharing Scheme ◽  
Sharing Scheme ◽  
Quantum Error ◽  
Quantum Secret Sharing Scheme

Similarly to earlier models for quantum error correcting codes, we introduce a quantum information theoretical model for quantum secret sharing schemes. This model provides new insights into the theory of quantum secret sharing. By using our model, among other results, we give a shorter proof of Gottesman's theorem that the size of the shares in a quantum secret sharing scheme must be as large as the secret itself. Also, we introduced approximate quantum secret sharing schemes and showed robustness of quantum secret sharing schemes by extending Gottesman's theorem to the approximate case.

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.

scholarly journals A note on ramp secret sharing schemes from error-correcting codes

2013 ◽  
Vol 57 (11-12) ◽  
pp. 2695-2702 ◽  
Author(s):  
Qi Chen ◽  
Dingyi Pei ◽  
Chunming Tang ◽  
Qiang Yue ◽  
Tongkai Ji
Keyword(s):  
Secret Sharing ◽  
Error Correcting Codes ◽  
Secret Sharing Schemes
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