Journal of Kufa for Mathematics and Computer

The importance of studying private networks in communication and information exchange has
increased due to the ease and speed of building in emergency situations among members of rescue teams in
the site of large-scale disasters when the infrastructure cannot be used at the time of the disaster, and that
the technology of private networks is non-wireless stations without the use of base stations or Router or
Access point. The routing protocol for establishing a path is important because the stations move frequently,
and the connection break cannot be known in real-time. Therefore, a proactive way to find link separation is
by continuous exchange of routing information. In the proactive routing protocol, each party sends routing
information on a regular basis. In this paper, information about the application layer was added when
creating the route and a simple information distribution system was created through the simultaneous
distribution of information held by each station at that time.

Discrete cryptographic such as RSA, knapsack, and discrete logarithms are the oldest and best
cryptographic techniques. They are worked during finite field. In this paper, an attempt to another branch of
cryptography was introduced. In this proposed method, the interpolation branch of mathematics is used for text
cryptography. Proposed method was introduced to cipher the plaintext message as word by word. In encryption part,
three steps are implemented for product cipher word. First, each letter of the word transformed to decimal number,
then to binary. Second, the binary codeword transformed to decimal. Third, the finally cipher word is represented as
triple. So it transformed to three numbers by descending the original number. A quadratic polynomial is constructed
where the three numbers are represented in the coefficients of the polynomial. By choosing of three temp small
independent values, three dependent values are calculated as the code word. For decryption part, the special
polynomial technique is used for recover the quadratic polynomial. The rest steps are deduced conversely with the
encryption part procedure.

In this paper, we propose the cyclic decomposition of the factor group ????????(???????????? × ????????), ????)/????(???????????? ×
????????), and the group ????????(???????????? × ????????) is Z-valued class functions of the direct product group (???????????? × ????????) under the
operation of addition, and ????(???????????? × ????????)is the subgroup of the generalized characters of the group ????????(???????????? ×
????????, ????).Then ????????(???????????? × ????????)/(???????????? × ????????) is an abelian factor group denoted by ????(???????????? × ????????) when ???????????? the
quaternion group |????????????| = ????????, and|????????| = ????. Also, we find the rational valued characters table of the group (???????????? ×
????????) when ???? is prime numbers is given as following: