Using pentagonal intuitionistic fuzzy numbers and assuming α and β cut values, the idea of modified arithmetic operations on interval valued intuitionistic fuzzy numbers is used to solve interval valued non-singular matrices in cryptography. Information protection has always depended on the study of cryptography, or the encoding of messages in secret codes. The basic idea behind cryptography is that data can be encrypted so that anyone who knows how to do so can decrypt it. Lastly, a numerical example was suggested.