The basic principle is “A Function easy to evaluate but its inverse is Infeasible unless a secret key is known”.
Some implementations of cryptographic algorithms often leak “side channel information.” Side channel information includes power consumption, electromagnetic fields and timing to process. Side channel attacks, which use side channel information leaked from real implementation of cryptographic algorithms .The security of system lies in extracting k from points P and Q on elliptic curve. These attacks are two types. They are Simple Power Analysis Attacks (SPA) and Differential Power Attacks (DPA). These attacks monitor the power consumption or the Electromagnetic emanations of a device example smart cards or mobile devices. The attacker’s goal is to retrieve partial or full information about a long-term key that is employed in several Elliptic Curve Scalar Multiplication (ECSM) executions.
We analyze and study Major and Minor Collisions and provide an analytic result for their probability of occurrence as well as effect of the fixed sequence window method.
We present performance comparisons of 163 bit equivalent 1024 bit RSA on elliptic curve exponentiation for general curves. Also we provide the performance analysis between EKR Modified Montgomery Inversion algorithm to Fast Exponentiation.
We implement a secret key to avoid retrieving the valuable information by the attacker through Simple Power Analysis Attacks. The secret key t is proposed as a prime integer in E Kesavulu Reddy modified Montgomery inversion algorithm based on window method between 1 to n and t is a number of pre-computed values. The developer or user to assigned the value of secret key t.