Abstract: This paper is introduced a modification to Diffie-
Hellman protocol to be applicable on the decimal numbers, which
they are the numbers between zero and one. For this purpose we
extend the theory of the congruence. The new congruence is over
the set of the real numbers and it is called the “real congruence"
or the “real modulus". We will refer to the existing congruence by
the “integer congruence" or the “integer modulus". This extension
will define new terms and redefine the existing terms. As the
properties and the theorems of the integer modulus are extended as
well. Modified Diffie-Hellman key exchange protocol is produced a
sharing, secure and decimal secret key for the the cryptosystems that
depend on decimal numbers.