Cryptography is the art of coding and decoding the communication. Cryptography ensures the security of delicate information over some confidentiality breaching resources. In the recent age Cryptography has turned into a battleground of some of the world’s best mathematicians and computer scientists. A number of transforms like Sumudu transform, Laplace transform, Fourier transform, Kamal transform, Mellin transform, Jafari transform, Aboodh transform, N-transform, ELzaki transform, MAHGOUB transform are frequently used in cryptography. Cryptography is of great importance in every field of life including data transmission, data storage, E-Commerce, confidential communication such as credit card transactions and Emails. Cryptography has been a hot topic among the researchers from 4000 years ago until now. In this work, a new cryptographic technique will be introduced. . In this work mathematical transformation known as Laplace transform on hyperbolic function is used for advancement of security purpose in the field of computers and telecommunications, this concept is known as Cryptography. This work includes a mathematical method known as “Laplace Transform” along with “Matrix Decomposition or Triangularization method” in cryptographic process (Encryption and Decryption). Both these mathematical concepts are used in this work to create a new cryptographic technique for the security of data and information in the world of computer. In this technique, Laplace transform on hyperbolic functions along with Matrix decomposition method will be incorporated. The Laplace Transform of hyperbolic function and Lower Triangular Matrix will be used as encryption and inverse Laplace Transformand upper triangular matrix will be used for decryption. Furthermore, the technique will also be explained with its applications.