RSA cryptographic algorithm used to encrypt and decrypt the messages to send it over the secure transmission channel like internet. The RSA algorithm is a secure, high quality, public key algorithm. In this paper, a new architecture and modeling has been proposed for RSA public key algorithm, the suggested system uses 1024-bit RSA encryption/decryption for restricted system. The system uses the multiply and square algorithm to perform modular operation. The design has been described by VHDL and simulated by using Xilinx ISE 12.2 tool. The architectures have been implemented on reconfigurable platforms FPGAs. Accomplishment when implemented on Xilinx_Spartan3 (device XC3S50, package PG208, speed -4) which confirms that the proposed architectures have minimum hardware resource, where only 29% of the chip resources are used for RSA algorithm design with realizable operating clock frequency of 68.573 MHz.