Some rank equalities are established for anti-involutory matrices. In particular, we get the formulas for the rank of the difference, the sum and the commutator of anti-involutory matrices.
Two constructions of Cartesian authentication codes form involutory and idempotent matrices over finitefields are presented and their size Parameters are computed. Moreover, assume that the encoding rules are chosen a...Two constructions of Cartesian authentication codes form involutory and idempotent matrices over finitefields are presented and their size Parameters are computed. Moreover, assume that the encoding rules are chosen ac-cording to a uniform Probablity distribution, the PI and Ps which dend the largest Probablities of a successful impersonation attack and a successful substitution attack respectively of these codes are also computed. Finially, it is Provedthat thase two Cartesian authentication codes are isomorphic.展开更多
Suppose R is a commutative ring with 1, and 2 is a unit of R. Let Tn(R) be the n × n upper triangular matrix modular over R, and let (?)i(R) (i=2 or 3) be the set of all R-module automorphisms on Tn(R) that prese...Suppose R is a commutative ring with 1, and 2 is a unit of R. Let Tn(R) be the n × n upper triangular matrix modular over R, and let (?)i(R) (i=2 or 3) be the set of all R-module automorphisms on Tn(R) that preserve involutory or tripotent. The main result in this paper is that f ∈ (?)i(R) if and only if there exists an invertible matrix U ∈ Tn(R) and orthogonal idempotent elements e1,e2,e3 ande4 in R with such that where展开更多
This paper studies the problem of constructing lightweight involutory maximal distance separable(MDS)matrices.The authors find the exact lower bound of the XOR counts for 4×4 involutory MDS matrices over F2^4.Fur...This paper studies the problem of constructing lightweight involutory maximal distance separable(MDS)matrices.The authors find the exact lower bound of the XOR counts for 4×4 involutory MDS matrices over F2^4.Further,some new structures of 4×4 involutory MDS matrices over F2^mare provided to construct involutory MDS matrices and the authors constructed the lightest4×4 involutory MDS matrices over F2^8so far by using these structures.展开更多
Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper, we introduce the concept of. I-feature filters and involutory filters in fat ti...Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper, we introduce the concept of. I-feature filters and involutory filters in fat tice implication algebras, and discussed some propert ies of them. Finally, the characterization of filters of any lattice implication algebra which satisfies Increasing Chain Conditions (I. C. C) is given.展开更多
Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enros...Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.展开更多
The diffusion layers in substitution-permutation network（SPN） block ciphers are almost invertible linear transformations, which is optimal if the branch number reaches the maximum value. The method of constructing i...The diffusion layers in substitution-permutation network（SPN） block ciphers are almost invertible linear transformations, which is optimal if the branch number reaches the maximum value. The method of constructing involutory optimal diffusion layers is proposed based on the Cauchy matrix, which can decrease the cost of implementation. The analysis to experimental results indicates that the diffusion layer ensures the security of the SPN block cipher against differential cryptanalysis（DC） and linear cryptanalysis（LC）, and decreases half the cost of implementation.展开更多
文摘Some rank equalities are established for anti-involutory matrices. In particular, we get the formulas for the rank of the difference, the sum and the commutator of anti-involutory matrices.
文摘Two constructions of Cartesian authentication codes form involutory and idempotent matrices over finitefields are presented and their size Parameters are computed. Moreover, assume that the encoding rules are chosen ac-cording to a uniform Probablity distribution, the PI and Ps which dend the largest Probablities of a successful impersonation attack and a successful substitution attack respectively of these codes are also computed. Finially, it is Provedthat thase two Cartesian authentication codes are isomorphic.
基金Foundation item:The NSF(10271021)of China and NSF(10531130)of Heilongjiang Education Committee
文摘Suppose R is a commutative ring with 1, and 2 is a unit of R. Let Tn(R) be the n × n upper triangular matrix modular over R, and let (?)i(R) (i=2 or 3) be the set of all R-module automorphisms on Tn(R) that preserve involutory or tripotent. The main result in this paper is that f ∈ (?)i(R) if and only if there exists an invertible matrix U ∈ Tn(R) and orthogonal idempotent elements e1,e2,e3 ande4 in R with such that where
基金supported in part by the National Natural Science Foundation of China under Grant No.11371356&61877058CAS Project QYZDJ-SSW-SYS022the Strategy Cooperation Project AQ-1701。
文摘This paper studies the problem of constructing lightweight involutory maximal distance separable(MDS)matrices.The authors find the exact lower bound of the XOR counts for 4×4 involutory MDS matrices over F2^4.Further,some new structures of 4×4 involutory MDS matrices over F2^mare provided to construct involutory MDS matrices and the authors constructed the lightest4×4 involutory MDS matrices over F2^8so far by using these structures.
文摘Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper, we introduce the concept of. I-feature filters and involutory filters in fat tice implication algebras, and discussed some propert ies of them. Finally, the characterization of filters of any lattice implication algebra which satisfies Increasing Chain Conditions (I. C. C) is given.
文摘Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.
文摘The diffusion layers in substitution-permutation network（SPN） block ciphers are almost invertible linear transformations, which is optimal if the branch number reaches the maximum value. The method of constructing involutory optimal diffusion layers is proposed based on the Cauchy matrix, which can decrease the cost of implementation. The analysis to experimental results indicates that the diffusion layer ensures the security of the SPN block cipher against differential cryptanalysis（DC） and linear cryptanalysis（LC）, and decreases half the cost of implementation.
