Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of system of equations an...Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of system of equations and elimination of necessity to evaluate polynomials in points with larger coordinates. It is demonstrated that a two-stage implementation of the proposed and Toom-Cook algorithms asymptotically require twice as many standard multiplications than their direct implementation. A multistage implementation of these algorithms is also less efficient than their direct implementation. Although the proposed algorithms as well as the corresponding Toom-Cook algorithms require numerous algebraic additions, the Generalized Horner rule for evaluation of homogeneous polynomials, provided in the paper, decrease this number twice.展开更多
Securing large corporate communication networks has become an increasingly difficult task. Sensitive information routinely leaves the company network boundaries and falls into the hands of unauthorized users. New tech...Securing large corporate communication networks has become an increasingly difficult task. Sensitive information routinely leaves the company network boundaries and falls into the hands of unauthorized users. New techniques are required in order to classify packets based on user identity in addition to the traditional source and destination host addresses. This paper introduces Gaussian cryptographic techniques and protocols to assist network administrators in the complex task of identifying the originators of data packets on a network and more easily policing their behavior. The paper provides numerical examples that illustrate certain basic ideas.展开更多
文摘Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of system of equations and elimination of necessity to evaluate polynomials in points with larger coordinates. It is demonstrated that a two-stage implementation of the proposed and Toom-Cook algorithms asymptotically require twice as many standard multiplications than their direct implementation. A multistage implementation of these algorithms is also less efficient than their direct implementation. Although the proposed algorithms as well as the corresponding Toom-Cook algorithms require numerous algebraic additions, the Generalized Horner rule for evaluation of homogeneous polynomials, provided in the paper, decrease this number twice.
文摘Securing large corporate communication networks has become an increasingly difficult task. Sensitive information routinely leaves the company network boundaries and falls into the hands of unauthorized users. New techniques are required in order to classify packets based on user identity in addition to the traditional source and destination host addresses. This paper introduces Gaussian cryptographic techniques and protocols to assist network administrators in the complex task of identifying the originators of data packets on a network and more easily policing their behavior. The paper provides numerical examples that illustrate certain basic ideas.
