We introduce a new cryptosystem based on decimal numbers. A secret key is shared between A and B to construct their decimal public keys. The secret key is distributed through the classic Deffie-Hellman protocol but after a modification that is introduced in order to enable this protocol to work on decimal numbers. The modification is applied by extends the theory of the modulus to be applicable on real numbers. We prove that there is no loss of any bit of information during the encryption and the decryption by introducing and proving a new concept that we call the rounding off theorem.

About the Author

Dr. Alfaris received her BSc 1995 in Math & Comp App/Alnahrain Univ- Iraq. MSc 1997 in Mathematical distributions from the same Univ. PhD 2010 in Cryptography and Number Theory/Univ Putra Malaysia. P. Doctoral 2012 Cryptography & Number Theory/Univ Science Malaysia. She is working as professor and researcher in a number of universities in USA.

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