Symmetric cryptography forms the backbone of secure data communication and storage by relying on the strength and randomness of cryptographic keys. This increases complexity, enhances cryptographic systems' overall robustness, and is immune to various attacks. The present work proposes a hybrid model based on the Latin square matrix (LSM) and subtractive random number generator (SRNG) algorithms for producing random keys. The hybrid model enhances the security of the cipher key against different attacks and increases the degree of diffusion. Different key lengths can also be generated based on the algorithm without compromising security. It comprises two phases. The first phase generates a seed value that depends on producing a randomly predefined set of key numbers of size n via the Donald E. Knuths SRNG algorithm (subtractive method). The second phase uses the output key (or seed value) from the previous phase as input to the Latin square matrix (LSM) to formulate a new key randomly. To increase the complexity of the generated key, another new random key of the same length that fulfills Shannon’s principle of confusion and diffusion properties is XORed. Four test keys for each 128, 192,256,512, and 1024–bit length are used to evaluate the strength of the proposed model. The experimental results and security analyses revealed that all test keys met the statistical National Institute of Standards (NIST) standards and had high values for entropy values exceeding 0.98. The key length of the proposed model for n bits is 25*n, which is large enough to overcome brute-force attacks. Moreover, the generated keys are very sensitive to initial values, which increases the complexity against different attacks.