Efficient methods of algebraic cryptanalysis and protection against them

The paper contains the basic information about methods of cryptanalysis used in algebraic cryptography. Main elements of linear and non-linear decomposition attacks by the author and so-called span-method by B. Tsaban are described as well as the examples of using them. To protect existing cryptographic algorithms against the cryptanalytic attacks, some improvements of this algorithms are proposed. For this purpose, the author has introduced the concept of a marginal set and with the use of it has protected the widely known key distibution protocol AAG against the attack by the span-method.