As an effective way to securely transfer secret images,secret image sharing(SIS)has been a noteworthy area of research.Basically in a SIS scheme,a secret image is shared via shadows and could be reconstructed by havin...As an effective way to securely transfer secret images,secret image sharing(SIS)has been a noteworthy area of research.Basically in a SIS scheme,a secret image is shared via shadows and could be reconstructed by having the required number of them.A major downside of this method is its noise-like shadows,which draw the malicious users'attention.In order to overcome this problem,SIS schemes with meaningful shadows are introduced in which the shadows are first hidden in innocent-looking cover images and then shared.In most of these schemes,the cover image cannot be recovered without distortion,which makes them useless in case of utilising critical cover images such as military or medical images.Also,embedding the secret data in Least significant bits of the cover image,in many of these schemes,makes them very fragile to steganlysis.A reversible IWT-based SIS scheme using Rook polynomial and Hamming code with authentication is proposed.In order to make the scheme robust to steganalysis,the shadow image is embedded in coefficients of Integer wavelet transform of the cover image.Using Rook polynomial makes the scheme more secure and moreover makes authentication very easy and with no need to share private key to participants.Also,utilising Hamming code lets us embed data with much less required modifications on the cover image which results in high-quality stego images.展开更多
In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a re...In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.展开更多
Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem...Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.展开更多
Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ＋ V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^×...Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ＋ V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^×n in FRn, which comes from some one-dimensional two-sided ideal of rook monoid algebra. We show that the two-sided ideal generated by this element is indeed the whole annihilator of U^×n in FR^n.展开更多
基金Iran National Science Foundation,Grant/Award Number:99009224。
文摘As an effective way to securely transfer secret images,secret image sharing(SIS)has been a noteworthy area of research.Basically in a SIS scheme,a secret image is shared via shadows and could be reconstructed by having the required number of them.A major downside of this method is its noise-like shadows,which draw the malicious users'attention.In order to overcome this problem,SIS schemes with meaningful shadows are introduced in which the shadows are first hidden in innocent-looking cover images and then shared.In most of these schemes,the cover image cannot be recovered without distortion,which makes them useless in case of utilising critical cover images such as military or medical images.Also,embedding the secret data in Least significant bits of the cover image,in many of these schemes,makes them very fragile to steganlysis.A reversible IWT-based SIS scheme using Rook polynomial and Hamming code with authentication is proposed.In order to make the scheme robust to steganalysis,the shadow image is embedded in coefficients of Integer wavelet transform of the cover image.Using Rook polynomial makes the scheme more secure and moreover makes authentication very easy and with no need to share private key to participants.Also,utilising Hamming code lets us embed data with much less required modifications on the cover image which results in high-quality stego images.
文摘In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.
文摘Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.
基金Supported by National Natural Science Foundation of China(Grant No.11301195)a research foundation of Huaqiao University(Grant No.2014KJTD14)
文摘Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ＋ V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^×n in FRn, which comes from some one-dimensional two-sided ideal of rook monoid algebra. We show that the two-sided ideal generated by this element is indeed the whole annihilator of U^×n in FR^n.
