Apparatus in form of a microelectronic assembly including an integrated circuit (IC) for execution of an embedded modular exponentiation program utilizing a square-and-multiply algorithm, wherein in the modular exponentiation program a secret exponent having a plurality of bits characterizes a private key, a method of providing a digital signature to prevent the detection of the secret exponent when monitoring power variations during the IC execution, the method comprising the steps of for a first operation in the modular exponentiation, selecting at least one predetermined bit, wherein the at least one predetermined bit is a bit other than a least significant bit (LSB) and the most significant bit (MSB); using the square-and-multiply algorithm, sequentially selecting bits to the left of the at least one predetermined bit for exponentiation until the MSB is selected; subsequent to selecting the MSB, sequentially selecting bits to the right of the at least one predetermined bit for exponentiation until the LSB is selected.