Modifikasi Algoritma AES-128 Berbasis Deret Pell Numbers untuk Meningkatkan Keamanan Data Digital

Abstract

The rapid advancement of information technology requires reliable data security systems to protect information from unauthorized access. Cryptography plays an important role as one of the primary solutions for ensuring data security through encryption processes. One of the most widely used cryptographic algorithms is the 128-bit Advanced Encryption Standard (AES). Nevertheless, further development and modification of the AES-128 algorithm are still necessary to enhance its resistance to various cryptographic attacks. This study proposes a modification of the AES-128 algorithm based on the Pell number sequence, applied to the ShiftColumns stage as an enhancement of the conventional ShiftRows stage in the standard algorithm. The Pell numbers sequence is used as the basis for determining the number of column shifts in each encryption round, which is then adjusted using modulo four operations. Through this mechanism, each column undergoes a different number of shifts in every round, resulting in a more dynamic data transformation pattern. The algorithm is implemented using several test plaintexts to evaluate the proposed method's performance. The experimental results show that the modified AES-128 algorithm based on the Pell number sequence produces a more varied ciphertext structure than the standard AES-128 algorithm. Security analysis is conducted using the Character Change Rate (TPK) parameter and the avalanche effect on several test datasets to evaluate the sensitivity of ciphertext changes to small variations in the plaintext. The analysis results indicate that the modified AES-128 algorithm produces lower TPK values than the standard AES-128 algorithm. Despite the applied modification, the decryption process still correctly recovers the original plaintext. Based on these results, it can be concluded that the Pell numbers–based modification of the AES-128 algorithm enhances security characteristics without affecting the accuracy of the decryption process.