Cipher Trigraphic Polyfunction (CTriPoly) developed by previous researchers is a modification of the Hill Cipher technique in modern cryptography. It was built on the system using three symbols or letters and more than one transformation of the original message. The modular arithmetic of a key matrix plays an important role in the encryption and decryption processes. A crucial aspect of the decryption process is to get the inverse matrix for involutory matrices. The objective of this paper is to obtain some solution of L22×2 ≡ A2×2 (mod N) and subsequently generate suitable involutory matrices which will be used as an encryption key in CTriPoly. This definitely reduces the computational time of finding the decryption key.
