The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we ...The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.展开更多
基金supported by Overseas Scholars Research Fund of Heilongjiang Provinicial Education Department
文摘The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.
