Scientific Tamil Lexicon: The Revelation of Cryptographic Connection Between Tamil Language and Galois Field

This paper presents a computational framework that helps enhance the confidentiality protection of communication in cybersecurity by leveraging the scientific properties of the Tamil language and the advanced encryption standard (AES). It defines a product set of vowels and consonants sounds of the Tamil language and reveals its connection to Hardy-Ramanujan prime factors and Tamil letters as a one-to-one function. It also reveals that the letters of the Tamil alphabet, combined with the digits from 1 to 9, form a Galois field of 2^8 over an irreducible polynomial of degree 8. In addition, it implements these two mathematical properties and builds an encoder for the AES algorithm to transform the Tamil texts to their hexadecimal states, and replace the pre-round transformation module of AES. It empirically shows that the Tamil-based encoder enhances the cryptographic strength of the AES algorithm at every step of its encryption flow. The cryptographic strength is measured by the runs test scores of the bit sequences of the ciphers of AES and compared with that of the English language. This modeling and simulation approach concludes that the Tamil-based encryption enhances the cryptographic strength of AES than English-based encryption.