Stealing keys from pcs using a radio: Cheap electromagnetic attacks on windowed exponentiation

Abstract

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.