The article reviews the problem of ensuring the security of storage, processing, and transmission of images based on a cryptographic method using chaotic maps. The encryption algorithm is based on a three-dimensional mapping. The encryption algorithm strength when using systems with chaotic dynamics depends on the value of the largest (positive) Lyapunov characteristic exponent. Therefore, the problem of increasing resistance to various kinds of attacks is reduced to determining the control parameters, at which the leading Lyapunov characteristic exponent increases. The authors propose a procedure for changing the chaotic map characteristics (entropy and Lyapunov characteristic exponents) based on introducing feedback into the system. The procedure is developed using the modal control method based on reducing the system to the canonical Frobenius form. The use of the proposed algorithm is considered on the example of the Rössler system. The test results confirmed an increase in the strength of the proposed encryption algorithm against statistical and differential analysis due to an increase in the Lyapunov characteristic exponent.