Resumen
In real practical problems relating to the issue of information security calculations are frequently carried out in the fields of characteristic 2. In modern computing technologies, particularly, the usage of supercomputers, allow us to conduct calculations for quite large values . By developing computer technology and exploitation of new methods for analysis of information security systems, the parameter should be increased.In order to construct a cyclical group of a large order, which is widely used in the synthesis of cryptographic protocols, it is proposed to construct towers of quadratic extensions fields in characteristic 2. The complexity of constructing such extensions depending on the degree of the field is established. The paper provides a method for constructing a quadratic extension field with the complexity of constructing an order ,where it does not depend on . The method is based on the construction of a two-dimensional algebra with one over the field. This process of doubling the degree of the field can be proceeded and construct the field every time, 2 times greater. In addition, It is not required to construct irreducible polynomials of higher degrees.