Digital signature schemes are often built based on the difficulty of the discrete logarithm problems,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the...Digital signature schemes are often built based on the difficulty of the discrete logarithm problems,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above.In this paper,we use the new difficult problem,which is to find the wth root in the finite ground field GF(p)to build representative collective signature schemes,but the chosen modulo p has a special structure distinct p=Nt_(0)t_(1)t_(2)+1,where N is an even number and t_(0),t_(1),t_(2) are prime numbers of equal magnitude,about 80 bits.The characteristics of the proposed scheme are:i)The private key of each signer consists of 2 components(K_(1),K_(2)),randomly selected,but the public key has only one component(Y)calculated by the formula Y=K_(w)^(1)_(1) K^(w)_(2)^(2);w_(1)=t_(0)t_(1) and w_(2)=t_(0)t_(2);and ii)The generated signature consists of a set of 3 components(e,S_(1),S_(2)).We use the technique of hiding the signer’s public key Y,which is the coefficientλgenerated by the group nanager,in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.展开更多
Digital signature schemes in general and representative collective digital signature schemes,in particular,are often built based on the difficulty of the discrete logarithm problem on the finite field,of the discrete ...Digital signature schemes in general and representative collective digital signature schemes,in particular,are often built based on the difficulty of the discrete logarithm problem on the finite field,of the discrete logarithm problem of the elliptic curve,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above.In this paper,we use the new difficult problem,which is to find W^(th)the root in the finite ground field to build representative collective signature schemes,but the chosen modulo has a special structure distinct p=Nt_(0)t_(1)t_(2)+1,where is an even number and t_(0),t_(1),t_(2)are prime numbers of equal magnitude,about 80bits.The characteristics of the proposed scheme are:i)The private key of each signer consists of 2 components(K_(1),K_(2)),randomly selected,but the public key has only one component(Y)calculated by the formula Y=K^(W_(1))_(1)K^(W_(2))_(2);and t_(0)t_(2);and ii)The generated signature consists of a set of 3 components(e,S_(1),S_(2)).We use the technique of hiding the signer’s public key Y,which is the coefficientλgenerated by the group manager,in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.展开更多
In this paper,we propose a fifth-order scheme for solving systems of nonlinear equations.The convergence analysis of the proposed technique is discussed.The proposed method is generalized and extended to be of any odd...In this paper,we propose a fifth-order scheme for solving systems of nonlinear equations.The convergence analysis of the proposed technique is discussed.The proposed method is generalized and extended to be of any odd order of the form 2n1.The scheme is composed of three steps,of which the first two steps are based on the two-step Homeier’s method with cubic convergence,and the last is a Newton step with an appropriate approximation for the derivative.Every iteration of the presented method requires the evaluation of two functions,two Fréchet derivatives,and three matrix inversions.A comparison between the efficiency index and the computational efficiency index of the presented scheme with existing methods is performed.The basins of attraction of the proposed scheme illustrated and compared to other schemes of the same order.Different test problems including large systems of equations are considered to compare the performance of the proposed method according to other methods of the same order.As an application,we apply the new scheme to some real-life problems,including the mixed Hammerstein integral equation and Burgers’equation.Comparisons and examples show that the presented method is efficient and comparable to the existing techniques of the same order.展开更多
A distribution theory of the roots of a polynomial and a parallel algorithm for finding roots of a complex polynomial based on that theory are developed in this paper. With high parallelism, the algorithm is an im- pr...A distribution theory of the roots of a polynomial and a parallel algorithm for finding roots of a complex polynomial based on that theory are developed in this paper. With high parallelism, the algorithm is an im- provement over the Wilf algorithm.展开更多
文摘Digital signature schemes are often built based on the difficulty of the discrete logarithm problems,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above.In this paper,we use the new difficult problem,which is to find the wth root in the finite ground field GF(p)to build representative collective signature schemes,but the chosen modulo p has a special structure distinct p=Nt_(0)t_(1)t_(2)+1,where N is an even number and t_(0),t_(1),t_(2) are prime numbers of equal magnitude,about 80 bits.The characteristics of the proposed scheme are:i)The private key of each signer consists of 2 components(K_(1),K_(2)),randomly selected,but the public key has only one component(Y)calculated by the formula Y=K_(w)^(1)_(1) K^(w)_(2)^(2);w_(1)=t_(0)t_(1) and w_(2)=t_(0)t_(2);and ii)The generated signature consists of a set of 3 components(e,S_(1),S_(2)).We use the technique of hiding the signer’s public key Y,which is the coefficientλgenerated by the group nanager,in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.
基金funding for this research from Duy Tan University,Danang,Vietnam.
文摘Digital signature schemes in general and representative collective digital signature schemes,in particular,are often built based on the difficulty of the discrete logarithm problem on the finite field,of the discrete logarithm problem of the elliptic curve,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above.In this paper,we use the new difficult problem,which is to find W^(th)the root in the finite ground field to build representative collective signature schemes,but the chosen modulo has a special structure distinct p=Nt_(0)t_(1)t_(2)+1,where is an even number and t_(0),t_(1),t_(2)are prime numbers of equal magnitude,about 80bits.The characteristics of the proposed scheme are:i)The private key of each signer consists of 2 components(K_(1),K_(2)),randomly selected,but the public key has only one component(Y)calculated by the formula Y=K^(W_(1))_(1)K^(W_(2))_(2);and t_(0)t_(2);and ii)The generated signature consists of a set of 3 components(e,S_(1),S_(2)).We use the technique of hiding the signer’s public key Y,which is the coefficientλgenerated by the group manager,in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.
基金We are grateful for the financial support from UKM’s research Grant GUP-2019-033.
文摘In this paper,we propose a fifth-order scheme for solving systems of nonlinear equations.The convergence analysis of the proposed technique is discussed.The proposed method is generalized and extended to be of any odd order of the form 2n1.The scheme is composed of three steps,of which the first two steps are based on the two-step Homeier’s method with cubic convergence,and the last is a Newton step with an appropriate approximation for the derivative.Every iteration of the presented method requires the evaluation of two functions,two Fréchet derivatives,and three matrix inversions.A comparison between the efficiency index and the computational efficiency index of the presented scheme with existing methods is performed.The basins of attraction of the proposed scheme illustrated and compared to other schemes of the same order.Different test problems including large systems of equations are considered to compare the performance of the proposed method according to other methods of the same order.As an application,we apply the new scheme to some real-life problems,including the mixed Hammerstein integral equation and Burgers’equation.Comparisons and examples show that the presented method is efficient and comparable to the existing techniques of the same order.
文摘A distribution theory of the roots of a polynomial and a parallel algorithm for finding roots of a complex polynomial based on that theory are developed in this paper. With high parallelism, the algorithm is an im- provement over the Wilf algorithm.
