We demonstrate the extraction of secret decryption keys from laptop computers, by nonintrusively measuring electromagnetic emanations for a few seconds from a distance of 50 cm. The attack can be executed using cheap and readily-available equipment: a consumer-grade radio receiver or a Software Defined Radio USB dongle. The setup is compact and can operate untethered; it can be easily concealed, e.g., inside pita bread. Common laptops, and popular implementations of RSA and ElGamal encryptions, are vulnerable to this attack, including those that implement the decryption using modern exponentiation algorithms such as sliding-window, or even its side-channel resistant variant, fixed-window (m-ary) exponentiation. We successfully extracted keys from laptops of various models running GnuPG (popular open source encryption software, implementing the OpenPGP standard), within a few seconds. The attack sends a few carefully-crafted ciphertexts, and when these are decrypted by the target computer, they trigger the occurrence of specially-structured values inside the decryption software. These special values cause observable fluctuations in the electromagnetic field surrounding the laptop, in a way that depends on the pattern of key bits (specifically, the key-bits window in the exponentiation routine). The secret key can be deduced from these fluctuations, through signal processing and cryptanalysis.