Power Analysis Attacks of Modular Exponentiation in Smartcards

Three new types of power analysis attacks against smartcard implementations of modular exponentiation algorithms are described. The first attack requires an adversary to exponentiate many random messages with a known and a secret exponent. The second attack assumes that the adversary can make the smartcard exponentiate using exponents of his own choosing. The last attack assumes the adversary knows the modulus and the exponentiation algorithm being used in the hardware. Experiments show that these attacks are successful. Potential countermeasures are suggested.