We show that elliptic-curve cryptography implementations on mobile devices are vulnerable to electromagnetic and power side-channel attacks. We demonstrate full extraction of ECDSA secret signing keys from OpenSSL and CoreBitcoin running on iOS devices, and partial key leakage from OpenSSL running on Android and from iOS's Common-Crypto. These non-intrusive attacks use a simple magnetic probe placed in proximity to the device, or a power probe on the phone's USB cable. They use a bandwidth of merely a few hundred kHz, and can be performed cheaply using an audio card and an improvised magnetic probe. * The authors thank Noam Nissan for programming and lab support during the course of this research.

We present new side-channel attacks on RSA and ElGamal implementations that use sliding-window or fixed-window (m-ary) modular exponentiation. The attacks extract decryption keys using a very low measurement bandwidth (a frequency band of less than 100 kHz around a carrier under 2 MHz) even when attacking multi-GHz CPUs.We demonstrate the attacks' feasibility by extracting keys from GnuPG (unmodified ElGamal and non-blinded RSA), within seconds, using a nonintrusive measurement of electromagnetic emanations from laptop computers. The measurement equipment is cheap and compact, uses readily-available components (a Software Defined Radio USB dongle or a consumer-grade radio receiver), and can operate untethered while concealed, e.g., inside pita bread.The attacks use a few non-adaptive chosen ciphertexts, crafted so that whenever the decryption routine encounters particular bit patterns in the secret key, intermediate values occur with a special structure that causes observable fluctuations in the electromagnetic field. Through suitable signal processing and cryptanalysis, the bit patterns and eventually the whole secret key are recovered.

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Computers broadcast their secrets via inadvertent physical emanations that are easily measured and exploited.