Struktur Simplektik pada Aljabar Lie Affine aff(2,R)

In this research, we studied the affine Lie algebra aff(2,R). The aim of this research is to determine the 1-form in affine Lie algebra aff(2,R) which is associated with its symplectic structure so that affine Lie algebra aff(2,R) is a Frobenius Lie algebra. Realized the elements of the affine Lie algebra aff(2,R) in matrix form, then calculated the Lie brackets and formed the structure matrix of the affine Lie algebra aff(2,R). 1-form of the affine Lie algebra aff(2,R) is obtained from the determinant of the structure matrix of the affine Lie algebra aff(2,R). Furthermore, proved that the 2-form is symplectic and related to the 1-form. The result obtained is that the affine Lie algebra aff(2,R) has 1-form α=ε_12^*+ε_23^* on aff(2,R)^* which is related to its symplectic structure, β=ε_11^*∧ε_12^*+ε_12^*∧ε_22^*+ε_21^*∧ε_13^*+ε_22^*∧ε_23^* such that the affine Lie algebra aff(2,R) is a Frobenius Lie algebra. For further research, it can be developed into an affine Lie algebra with dimensions n(n+1)

Aplikasi Modifikasi Algoritma Vigenere Cipher dan Hill Cipher Menggunakan Konversi Suhu

Cryptography is a method used to maintain the confidentiality of messages and data. Modifications or combinations of algorithms can be made to make the process of cracking secret messages more difficult than just one algorithm. This research aims to apply a combination of modified Vigenere Cipher algorithm, modified Hill Cipher algorithm, and temperature conversion equations to maintain a message’s confidentiality. By determining one plaintext and the required keys, the encryption and decryption process uses a modified Vigenere Cipher algorithm, a modified Hill Cipher algorithm, and all temperature conversion equations. The results obtained in the encryption process of one plaintext are 12 different ciphertexts according to the temperature conversion equation used. Moreover, the results obtained in the decryption process of 12 different ciphertexts are the original plaintext