Following requirements are necessary when implementing public key cryptography in a mobile telecommunication terminal. (1) simultaneous highspeed double modular exponentiation calculation, (2) small size and low power consumption, (3) resistance to side channel attacks. We have developed a coprocessor that provides these requirements. In this coprocessor, right-to-left binary exponentiation algorithm was extended for double modular exponentiations by designing new circuit configuration and new schedule control methods. We specified the desired power consumption of the circuit at the initial design stage. Our proposed method resists side channel attacks that extract secret exponent by analyzing the target’s power consumption and calculation time.