Recent research has demonstrated the vulnerability of certain smart card architectures to power and electro-magnetic analysis when multiplier operations are insufficiently shielded from external monitoring. Here several standard multipliers are investigated in more detail in order to provide the foundation for understanding potential weaknesses and enabling the subsequent successful repair of those systems. A model is built which accurately predicts power use as a function of the Hamming weights of inputs without the combinatorial explosion of exhaustive simulation. This confirms that power use is indeed data dependent at least for those multipliers. Laboratory experiments confirm that EMR also corresponds closely to these power predictions over a wide range of frequencies.