FPGA Implementation of Non-Linear Cryptography

The paper focuses on the design and Field Programmable Gate Array (FPGA) implementation of embedded system for time based dual encryption scheme with Delay Compulsion Function (DCF) and also illustrates the application of DCF in time based cryptography. Further, the strength of the time based FPGA encryption algorithm with and without using DCF is analyzed using a Nios II processor. This proposed scheme enhances the security of vital data against Brute force attack by incorporating a temporal key distribution where two different keys encrypt the data simultaneously, one being the regular key and the other being the time. The time is included using a dynamically varying number of shifts thereby allowing the system to wait for the duration and this forms the second dimension of the key. Presently, available encryption systems suffer from Brute Force attack in which all the key combinations are tried in order to find the correct key. In such a case, the time taken for breaking the key depends on the speed of the system used for cryptanalysis. The proposed system adds complexity by using dynamically varying sequence of operations, by including the time as a second dimension of the key besides minimizing the possibility of Brute Force attack and increasing the time required for cryptanalysis irrespective of the system capability. As the proposed system needs concurrent execution and real time processing, the system is implemented using Altera Stratix II FPGA and the results are presented.

Gauss Principle of Least Compulsion for Relative Motion Dynamics and Differential Equations of Motion

This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of particles, we give the Gauss principle of relative motion dynamics. By constructing a compulsion function of relative motion, we prove that at any instant, its real motion minimizes the compulsion function under Gaussian variation, compared with the possible motions with the same configuration and velocity but different accelerations. Secondly, the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane. Thirdly, the Gauss principle we obtained is expressed as Appell, Lagrange, and Nielsen forms in generalized coordinates. Utilizing Gauss principle, the dynamical equations of relative motion are established. Finally, two relative motion examples also verify the results' correctness.