In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probab...In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.展开更多
Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subr...Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subring which is a subfield containing 1. It is shown that R/NUVW, where U is a finite ring, V is a finite direct sum of matrix rings over B rings, and W is a ring containing no nonzero finite subrings.展开更多
The goal of this paper is to show that there are infinitely many number fields K/Q, for which there is no inert prime p ∈ N*, i.e. ∀p ∈ N* a prime number, prime ideal of K such that where: Zk</sub> i...The goal of this paper is to show that there are infinitely many number fields K/Q, for which there is no inert prime p ∈ N*, i.e. ∀p ∈ N* a prime number, prime ideal of K such that where: Zk</sub> is the Dedekind domain of the integer elements of K. To prove such a result, consider for any prime p, the decomposition into a product of prime ideals of Zk</sub>, of the ideal . From this point, we use on the one hand: 1) The well- known property that says: If , then the ideal pZ<sub>k</sub> decomposes into a product of prime ideals of Zk</sub> as following: . (where:;is the irreducible polynomial of θ, and, is its reduction modulo p, which leads to a product of irreducible polynomials in Fp[X]). It is clear that because if is reducible in Fp[X], then consequently p is not inert. Now, we prove the existence of such p, by proving explicit such p as follows. So we use on the other hand: 2) this property that we prove, and which is: If , is an irreducible normalized integer polynomial, whose splitting field is , then for any prime number p ∈ N: is always a reducible polynomial. 3) Consequently, and this closes our proof: let’s consider the set (whose cardinality is infinite) of monogenic biquadratic number fields: . Then each f<sub>θ</sub>(X) checks the above properties, this means that for family M, all its fields, do not admit any inert prime numbers p ∈ N. 2020-Mathematics Subject Classification (MSC2020) 11A41 - 11A51 - 11D25 - 11R04 - 11R09 - 11R11 - 11R16 - 11R32 - 11T06 - 12E05 - 12F05 -12F10 -13A05-13A15 - 13B02 - 13B05 - 13B10 - 13B25 -13F05展开更多
Elliptic Curve Cryptography recently gained a lot of attention in industry. The principal attraction of ECC compared to RSA is that it offers equal security for a smaller key size. The present paper includes the study...Elliptic Curve Cryptography recently gained a lot of attention in industry. The principal attraction of ECC compared to RSA is that it offers equal security for a smaller key size. The present paper includes the study of two elliptic curve and defined over the ring where . After showing isomorphism between and , we define a composition operation (in the form of a mapping) on their union set. Then we have discussed our proposed cryptographic schemes based on the elliptic curve . We also illustrate the coding of points over E, secret key exchange and encryption/decryption methods based on above said elliptic curve. Since our proposed schemes are based on elliptic curve of the particular type, therefore the proposed schemes provides a highest strength-per-bit of any cryptosystem known today with smaller key size resulting in faster computations, lower power assumption and memory. Another advantage is that authentication protocols based on ECC are secure enough even if a small key size is used.展开更多
Let R be a commutative ring without nil-factor. In this paper, we discuss the problem of quasi-valuation ring presented in the reference 'Wang Shianghaw, On quasi-valuation ring, Northeast People's Univ. Natur...Let R be a commutative ring without nil-factor. In this paper, we discuss the problem of quasi-valuation ring presented in the reference 'Wang Shianghaw, On quasi-valuation ring, Northeast People's Univ. Natur. Sci. J., (1)(1957), 27-40', when the quotient field of R is an algebraic number field or an algebraic function field, and we obtain a characterization of quasi-valuation rings.展开更多
A concept of [GRAPHICS] diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a [GRAPHICS] diagonalization one are discussed, and...A concept of [GRAPHICS] diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a [GRAPHICS] diagonalization one are discussed, and a method of [GRAPHICS] diagonalization of matrices over quaternion field is given.展开更多
In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obta...In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.展开更多
随着高压直流屏蔽金具国产化的推进,越来越多的国产金具如屏蔽环等逐渐应用到换流站中,而屏蔽环电晕起始特性随自身尺寸变化规律目前尚不清楚。为研究屏蔽环的电晕特性,依据±500 k V木家换流站和昭通换流站阀厅典型屏蔽环的尺寸,...随着高压直流屏蔽金具国产化的推进,越来越多的国产金具如屏蔽环等逐渐应用到换流站中,而屏蔽环电晕起始特性随自身尺寸变化规律目前尚不清楚。为研究屏蔽环的电晕特性,依据±500 k V木家换流站和昭通换流站阀厅典型屏蔽环的尺寸,设计了环径分别为600、800、1 000 mm的3组屏蔽环,在昆明南网特高压试验基地(海拔约为2 100 m)开展试验,采用阶梯升压方式对屏蔽环加载电压,通过紫外成像仪判断屏蔽环是否发生电晕,以确定对应的电晕起始电压,并根据试验布置建立3D电场仿真模型,采用有限元数值仿真方法,计算出各屏蔽环对应的电晕起始场强。通过对屏蔽环电晕特性的分析研究得出屏蔽环电晕起始电压与场强随环径、管径的变化趋势,并给出各典型尺寸屏蔽环在高海拔地区的电晕起始控制场强,其中最小的起晕场强控制值>21k V/cm,这为实际工程提供了校核参考数据,并为屏蔽金具的国产化设计和选型提供参考。展开更多
基金Foundation item:The Key Project(03060)of Chinese Ministry of Education.
文摘In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.
文摘Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subring which is a subfield containing 1. It is shown that R/NUVW, where U is a finite ring, V is a finite direct sum of matrix rings over B rings, and W is a ring containing no nonzero finite subrings.
文摘The goal of this paper is to show that there are infinitely many number fields K/Q, for which there is no inert prime p ∈ N*, i.e. ∀p ∈ N* a prime number, prime ideal of K such that where: Zk</sub> is the Dedekind domain of the integer elements of K. To prove such a result, consider for any prime p, the decomposition into a product of prime ideals of Zk</sub>, of the ideal . From this point, we use on the one hand: 1) The well- known property that says: If , then the ideal pZ<sub>k</sub> decomposes into a product of prime ideals of Zk</sub> as following: . (where:;is the irreducible polynomial of θ, and, is its reduction modulo p, which leads to a product of irreducible polynomials in Fp[X]). It is clear that because if is reducible in Fp[X], then consequently p is not inert. Now, we prove the existence of such p, by proving explicit such p as follows. So we use on the other hand: 2) this property that we prove, and which is: If , is an irreducible normalized integer polynomial, whose splitting field is , then for any prime number p ∈ N: is always a reducible polynomial. 3) Consequently, and this closes our proof: let’s consider the set (whose cardinality is infinite) of monogenic biquadratic number fields: . Then each f<sub>θ</sub>(X) checks the above properties, this means that for family M, all its fields, do not admit any inert prime numbers p ∈ N. 2020-Mathematics Subject Classification (MSC2020) 11A41 - 11A51 - 11D25 - 11R04 - 11R09 - 11R11 - 11R16 - 11R32 - 11T06 - 12E05 - 12F05 -12F10 -13A05-13A15 - 13B02 - 13B05 - 13B10 - 13B25 -13F05
文摘Elliptic Curve Cryptography recently gained a lot of attention in industry. The principal attraction of ECC compared to RSA is that it offers equal security for a smaller key size. The present paper includes the study of two elliptic curve and defined over the ring where . After showing isomorphism between and , we define a composition operation (in the form of a mapping) on their union set. Then we have discussed our proposed cryptographic schemes based on the elliptic curve . We also illustrate the coding of points over E, secret key exchange and encryption/decryption methods based on above said elliptic curve. Since our proposed schemes are based on elliptic curve of the particular type, therefore the proposed schemes provides a highest strength-per-bit of any cryptosystem known today with smaller key size resulting in faster computations, lower power assumption and memory. Another advantage is that authentication protocols based on ECC are secure enough even if a small key size is used.
文摘Let R be a commutative ring without nil-factor. In this paper, we discuss the problem of quasi-valuation ring presented in the reference 'Wang Shianghaw, On quasi-valuation ring, Northeast People's Univ. Natur. Sci. J., (1)(1957), 27-40', when the quotient field of R is an algebraic number field or an algebraic function field, and we obtain a characterization of quasi-valuation rings.
文摘A concept of [GRAPHICS] diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a [GRAPHICS] diagonalization one are discussed, and a method of [GRAPHICS] diagonalization of matrices over quaternion field is given.
文摘In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.
