### Background  
The choice of certain encryption algorithms is determined by their application and the goals that are set. When implementing protection through an encryption procedure with a public asymmetric key, the mathematical method of the Rivest-Shamir-Adleman algorithm (RSA) is very often used [4]. This method remains highly valued to this day and is often used to ensure the encryption and integrity of the transmitted information, and verification of the originality of the data. Implementation of RSA keys to prevent cryptographic attacks when using smart cards on multiple devices is discussed in [5]. In [6], [PERSON] analyzes a cryptanalytic attack on the use of short RSA secret exponents. The presented algorithm is based on continuous fractions and seeks to find sufficiently short secret exponents in polynomial time. When the secret degree increases in size beyond a certain maximum, the time required to find the secret exponent increases rapidly (exponentially). The decomposition of prime numbers has been the subject of much research looking for fast and simple techniques [7; 8], including the creation of polynomials generating sums of squares with a targeted application in cryptography [9; 10]. The authors of [11] propose a new method for realizing a semisimple factorization based on the properties of Pythagorean triplets, proposing a new mathematical model based on the binary approach for the greatest common divisor with simple arithmetic operations to find the sum of two squares of one or both prime factors. Another commonly used mathematical method for the encryption process is elliptic curve cryptography, an approach to provide public key encryption that is based on the algebraic structure of elliptic curves on finite fields [12]. Security encryption systems based on public key cryptography, such as RSA systems, use semiprime factorization [11], an important numerical method. Elliptic curve cryptography uses smaller-length keys to implement the same level of security as the RSA algorithm [13]. The authors of [14] present a new cryptographic algorithm with a public key, using a matrix model to improve the efficiency and speed of encryption. The authors include several unknown quantities and one additional sub-equation during the encrypting process. The execution time of the algorithm proposed by the authors was found to be faster when compared with the RSA and elliptic curve cryptography algorithms. The use of cryptography in biomedical applications is a popular and well-functioning method for ensuring the confidentiality of medical research and the personal data of individuals. A symmetric encryption algorithm [15] based on the double chaotic layer encryption method was proposed and tested on electroencephalograms. This algorithm's intended usage is electroencephalograms, electrocardiograms, and blood pressure data and it is oriented for telemedical applications. The data used in the research were taken from the public database of PhysioBank [16]. The authors of [17] propose the use of the RSA algorithm in medical imaging, using watermark and Discrete Wavelet Transform of Daubechies with two coefficients (Db2) and two levels of decomposition. The proposed watermark procedure (the watermark is encrypted with a key generated by the RSA algorithm) was tested on three types of images (MRI, CT, and US). The proposed scheme shows a good degree of protection against alleged attacks before transmitting medical images through communication channels. In [18], the authors explore the issue of maintaining the integrity and confidentiality of patient's medical information when transmitted wirelessly, via Wireless Body Area Networks (BANs). A 128-bit secret key generation using an electrocardiographic (ECG) signal to protect communications via wireless BANs is proposed by the authors of [19]. The paper presents a scheme for creating the secret key, which uses the parameters of the patient's ECG signal.