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Linear Codes From Perfect Nonlinear Mappings and Their Secret Sharing Schemes

C. Carlet, C. Ding, J. Yuan
2005 IEEE Transactions on Information Theory  
In this paper, error-correcting codes from perfect nonlinear mappings are constructed, and then employed to construct secret sharing schemes.  ...  The secret sharing schemes obtained in this paper have two types of access structures.  ...  Extending a Secret Sharing Scheme With a Small Secret Space Given a secret sharing scheme in which the secret space is small, one could extend it into a secret sharing scheme where the secret space is  ... 
doi:10.1109/tit.2005.847722 fatcat:htwxphuonbdofntccxg7pod5du

Nonlinear Secret Image Sharing Scheme

Sang-Ho Shin, Gil-Je Lee, Kee-Young Yoo
2014 The Scientific World Journal  
In this paper, we propose a(t,n)-threshold nonlinear secret image sharing scheme with steganography concept.  ...  Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing.  ...  In 1996, Renvall and Ding [21] have proposed a nonlinear secret sharing scheme.  ... 
doi:10.1155/2014/418090 pmid:25140334 pmcid:PMC4130320 fatcat:6gh6yjqktrdxblh7mazizwhhuq

Page 1456 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
Actually, they gave an explicit construction for a visual 2 out of 2 secret sharing scheme. The paper presents two general k out of n secret sharing schemes.  ...  In a visual k out of n secret sharing scheme an image (e.g. picture or text) is transformed into n shares, in such a way that if one puts together any k-tuple of shares the original image is again visible  ... 

On the Power of Nonlinear Secret-Sharing

Amos Beimel, Yuval Ishai
2005 SIAM Journal on Discrete Mathematics  
A secret-sharing scheme enables a dealer to distribute a secret among n parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares.  ...  A family of secret-sharing schemes is called efficient if the total length of the n shares is polynomial in n.  ...  Table 3 . 3 1 A secret-sharing scheme for NQRP p . Table 4 . 4 1 A secret-sharing scheme for NQR m . Table A . A 1 A secret-sharing scheme for A R,G .  ... 
doi:10.1137/s0895480102412868 fatcat:5es4ktqclbfgziq67gg7ucb7bi

Page 1667 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
The paper investigates cryptographic properties of the defining function of secret sharing so the scheme is k-cheating immune. Constructions of secret sharing immune against k cheaters are given.”  ...  Summary: “The work addresses the problem of cheating preven- tion in secret sharing. Two cheating scenarios are considered.  ... 

Ideal Threshold Schemes from Orthogonal Arrays [chapter]

Josef Pieprzyk, Xiam-Mo Zhang
2002 Lecture Notes in Computer Science  
The last part of the work shows how to construct nonlinear secret sharing based on orthogonal arrays.  ...  We showed that each orthogonal array is exactly a defining matrix of an ideal threshold scheme.  ...  It should be noticed that a defining matrix uniquely determines a secret sharing scheme but a secret sharing scheme has more defining matrices.  ... 
doi:10.1007/3-540-36159-6_40 fatcat:6ruhs6o63bandhsxuw5a622gca

On alternative approach for verifiable secret sharing [article]

Kamil Kulesza, Zbigniew Kotulski, Joseph Pieprzyk
2002 arXiv   pre-print
Secret sharing allows split/distributed control over the secret (e.g. master key). Verifiable secret sharing (VSS) is the secret sharing extended by verification capacity.  ...  Let's denote 0 C as the combiner algorithm for that secret sharing scheme. 2.  ...  Illustrative example: ( ) n t v , , secret sharing scheme We assume that ) (x f is balanced, nonlinear Boolean function with ( ) 2 1 ' , ' 2 1 = i i s s P x ) (x  ... 
arXiv:math/0211267v1 fatcat:pw5mmqlckbgqnc5tom3badimx4

Page 6571 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
Summary: “A secret sharing scheme for an incomplete access struc- ture (I, A) is a method of distributing information about a secret among a group of participants in such a way that sets of partici- pants  ...  In this pa- per we present a more precise definition of secret sharing schemes in terms of information theory, and a new decomposition theo- rem.  ... 

A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

Maura B. Paterson, Douglas R. Stinson
2013 Cryptography and Communications  
We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes.  ...  We give easy proofs of some recent results concerning threshold gaps in ramp schemes.  ...  Codes and Ramp Schemes Constructions of secret sharing schemes and ramp schemes from linear codes have been used for over 30 years.  ... 
doi:10.1007/s12095-013-0082-1 fatcat:5aczimg7efdjjexnoatnfs5bbi

Page 5882 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
Summary: “Nonperfect secret sharing schemes (NSSs) have an advantage such that the size of shares can be shorter than that of perfect secret sharing schemes.  ...  {For the entire collection see MR 98g:94001.} 99h:94052 94A60 Ogata, Wakaha (J-HJT; Himeji) ; Kurosawa, Kaoru (J-TOKYTE; Meguro) Some basic properties of general nonperfect secret sharing schemes.  ... 

Page 3626 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
An Y, perfect secret-sharing scheme is a probabilistic mapping of a secret to nm shares, such that the secret can be reconstructed from any set 7 of shares such that T € .Y,, and no subset T ¢ FY, of shares  ...  “We contrast these results with the case where both the secrets and the shares are real numbers. Simple perfect secret-sharing schemes (and perfect private-key encryption schemes) are pre- sented.  ... 

Optimal Uniform Secret Sharing

Maki Yoshida, Toru Fujiwara, Marc P. C. Fossorier
2019 IEEE Transactions on Information Theory  
We refer to schemes with such uniform access structures as uniform secret sharing. We first derive a tight lower bound for share entropy and then present an optimal construction.  ...  An important problem in secret sharing schemes is minimizing the share size. For (k, n)-threshold schemes and (k, L, n)-ramp schemes, constructions that minimize the share size are known.  ...  INTRODUCTION A SECRET sharing scheme is a method of encoding a secret s into n shares v 1 , v 2 , . . . , v n so that the secret can be recovered only from predefined subsets of shares called authorized  ... 
doi:10.1109/tit.2018.2852276 fatcat:jusvkmbcnrglvijng4lvh72o5e

High-order Masking by Using Coding Theory and Its Application to AES [chapter]

Guilhem Castagnos, Soline Renner, Gilles Zémor
2013 Lecture Notes in Computer Science  
It is known besides that there is a strong connection between secret sharing schemes and error-correcting codes, namely every linear code gives rise to a linear secret sharing scheme.  ...  However, the schemes mostly used in practice are the so-called Boolean masking and Shamir's secret sharing scheme and it is widely thought that they are the most adapted to masking techniques because they  ...  Definitions Let K be a field. A secret sharing scheme is a method to split a secret s ∈ K among a set of n shares.  ... 
doi:10.1007/978-3-642-45239-0_12 fatcat:mk2pteeqdvft7et5k5wopovdae

An estimation approach to extract multimedia information in distributed steganographic images

Li Bai, Saroj Biswas, Erik P. Blasch
2007 2007 10th International Conference on Information Fusion  
The secret images may be nonlinear, non-Gaussian and nonstationary in nature, and can be disclosed by using some estimation techniques such as Kalman filtering.  ...  The key idea is to estimate secret image as a random process, which is corrupted by a noise source (i.e. host image).  ...  Consider a simple example for a (2, 4) threshold-based secret sharing scheme where the secret s is equal to 3.  ... 
doi:10.1109/icif.2007.4407976 dblp:conf/fusion/BaiBB07 fatcat:qmzrlfm6dje7zo54anym6uywfi

Privacy-Preserving Blockchain-Based Nonlinear SVM Classifier Training for Social Networks

Nan Jia, Shaojing Fu, Ming Xu, Ilsun You
2020 Security and Communication Networks  
In this paper, we propose a novel privacy-preserving nonlinear SVM classifier training scheme based on blockchain.  ...  Then, leveraging these building blocks, we propose a blockchain-based secure nonlinear SVM classifier training scheme that realizes collaborative training while protecting privacy.  ...  Secret Sharing-Based Secure Computing Protocols In this section, we mainly introduce the secure computation protocols used in our scheme which are based on additive secret sharing.  ... 
doi:10.1155/2020/8872853 fatcat:afdb5s73fnd2tbpnzvu6k4r4ym
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