Complex key generation with secured seed exchange for Vernam cipher in security applications

The randomness of a number used for coding the data with a complex algorithm that makes more difficult for the middle-man or the intruder or an unauthorized person to decrypt. The paper is about the three different methods of pseudorandom generation and analysis by comparing the number of occurrences of digits with respect to length of the different keys. The methods are Vulgar fractions, 3n + 1 algorithm, Magic square nxn and the combination of this numbers generated sequences. The conclusion is based on the analysis of number of occurrences of digits; hence, the cryptographer can select and adopt any appropriate key for data encryption. The three different methods are for number generation; of sequences of numbers (keys) used for encryption with strong algorithm in combination with existing cryptosystems such as Vernam cipher or seed exchange Massey-Omura protocol. Applications are in banks, OTP generation, and authentication and in other domains like online shopping etc.