Akbıyık, MücahitAlo, Jeta2021-12-232021-12-232021Mathematics 2021, 9(20), 26060035-8711https://doi.org/10.3390/math9202606In this study, we firstly obtain De Moivre-type identities for the second-order Bronze Fibonacci sequences. Next, we construct and define the third-order Bronze Fibonacci, third-order Bronze Lucas and modified third-order Bronze Fibonacci sequences. Then, we define the generalized third-order Bronze Fibonacci sequence and calculate the De Moivre-type identities for these sequences. Moreover, we find the generating functions, Binet’s formulas, Cassini’s identities and matrix representations of these sequences and examine some interesting identities related to the third-order Bronze Fibonacci sequences. Finally, we present an encryption and decryption application that uses our obtained results and we present an illustrative example.enAffine-Hill chipherBinet’s formulaDe Moivre-type identityThird-order Bronze Fibonacci numbersArticle10.3390/math92026062-s2.0-85117449859Q1WOS:000744817300001Q1