A new encryption task for mathematically gifted students: Encryption arising from patterns

Abstract

The concept of encryption is noteworthy in terms of both familiarizing mathematically gifted students with technological developments and working with mathematically challenging tasks. Once the proper foundations are established, students can begin to formalize encryption and decryption with algebraic formulas. Encryption can be an important resource for developing functional thinking. Based on the given information, this study designed an encryption algorithm through linear patterns that can be presented as a teaching task in classroom environments to students who are learning at elementary school level and explained the implementation process. The task named “Encryption arising from patterns” is considered important in terms of both creating an encryption algorithm and providing content for the development of mathematical patterns and therefore functional thinking. In the task of “Encryption arising from patterns”, the general term of the linear pattern was created by starting from two prime numbers. The numbers corresponding to the first 29 terms of this linear pattern have been calculated. The letters of the alphabet and the terms of the pattern were paired in order. Then, Caeser’s Cipher was applied to the letters in the alphabet. Thus, the numbers corresponding to the key letters were assigned to the letters in plaintext. The letters of plaintext were sent to the receiver along with the numbers corresponding to the key letters and the first three steps of the linear pattern, and the encryption task was completed.