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Linear Codes From Perfect Nonlinear Mappings and Their Secret Sharing Schemes

2005
*
IEEE Transactions on Information Theory
*

In this paper, error-correcting codes from perfect

doi:10.1109/tit.2005.847722
fatcat:htwxphuonbdofntccxg7pod5du
*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 ...##
###
Nonlinear Secret Image Sharing Scheme

2014
*
The Scientific World Journal
*

In this paper, we propose

doi:10.1155/2014/418090
pmid:25140334
pmcid:PMC4130320
fatcat:6gh6yjqktrdxblh7mazizwhhuq
*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*. ...##
###
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

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 . ...

##
###
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]

2002
*
Lecture Notes in Computer Science
*

The last part of the work shows how to construct

doi:10.1007/3-540-36159-6_40
fatcat:6ruhs6o63bandhsxuw5a622gca
*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. ...##
###
On alternative approach for verifiable secret sharing
[article]

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 ...

##
###
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

2013
*
Cryptography and Communications
*

We then generalise

doi:10.1007/s12095-013-0082-1
fatcat:5aczimg7efdjjexnoatnfs5bbi
*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. ...##
###
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

2019
*
IEEE Transactions on Information Theory
*

We refer to

doi:10.1109/tit.2018.2852276
fatcat:jusvkmbcnrglvijng4lvh72o5e
*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 ...##
###
High-order Masking by Using Coding Theory and Its Application to AES
[chapter]

2013
*
Lecture Notes in Computer Science
*

It is known besides that there is

doi:10.1007/978-3-642-45239-0_12
fatcat:mk2pteeqdvft7et5k5wopovdae
*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*. ...##
###
An estimation approach to extract multimedia information in distributed steganographic images

2007
*
2007 10th International Conference on Information Fusion
*

The

doi:10.1109/icif.2007.4407976
dblp:conf/fusion/BaiBB07
fatcat:qmzrlfm6dje7zo54anym6uywfi
*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. ...##
###
Privacy-Preserving Blockchain-Based Nonlinear SVM Classifier Training for Social Networks

2020
*
Security and Communication Networks
*

In this paper, we propose

doi:10.1155/2020/8872853
fatcat:afdb5s73fnd2tbpnzvu6k4r4ym
*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*. ...
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