Abstract: A main problem in current countermeasures of side channel attack on PKC is the cost of compromising computational efficiency. Against the problem, a cryptographic implementation for modular exponentiation over finite field by coding with equivalent power consumption is presented for the goal of thwarting side channel attacks by erasing the difference of power consumption among the operational components. It is demonstrated that the expected goal of preventing timing measurement and power attack is reached to. Finally, it comes to the conclusion that one needs not compromise the computational efficiency on modular exponentiation in order to thwart side channel attack.