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Side-channel attacks are used by cryptanalysts to compromise the implementation of secure systems. One very powerful class of side-channel attacks is power analysis, which tries to extract cryptographic keys and passwords by examining the power consumption of a device. We examine the applicability of this threat to electromagnetically coupled RFID tags. Compared to standard power analysis attacks, our attack is unique in that it requires no physical contact with the device under attack. Power analysis can be carried out even if both the tag and the attacker are passive and transmit no data, making the attack very hard to detect. As a proof of concept, we describe a password extraction attack on Class 1 Generation 1 EPC tags. We also show how the privacy of Class 1 Generation 2 tags can be compromised by this attack. Finally, we examine possible modifications to the tag and its RF front end which help protect against power analysis attacks.