One&Done: A Single-Decryption EM-Based Attack on OpenSSL’s Constant-Time Blinded RSA

Authors: 

Monjur Alam, Haider Adnan Khan, Moumita Dey, Nishith Sinha, Robert Callan, Alenka Zajic, and Milos Prvulovic, Georgia Tech

Abstract: 

This paper presents the first side channel attack approach that, without relying on the cache organization and/or timing, retrieves the secret exponent from a single decryption on arbitrary ciphertext in a modern (current version of OpenSSL) fixed-window constant-time implementation of RSA. Specifically, the attack recovers the exponent’s bits during modular exponentiation from analog signals that are unintentionally produced by the processor as it executes the constant-time code that constructs the value of each “window” in the exponent, rather than the signals that correspond to squaring/multiplication operations and/or cache behavior during multiplicand table lookup operations. The approach is demonstrated using electromagnetic (EM) emanations on two mobile phones and an embedded system, and after only one decryption in a fixed-window RSA implementation it recovers enough bits of the secret exponents to enable very efficient (within seconds) reconstruction of the full private RSA key.

Since the value of the ciphertext is irrelevant to our attack, the attack succeeds even when the ciphertext is unknown and/or when message randomization (blinding) is used. Our evaluation uses signals obtained by demodulating the signal from a relatively narrow band (40 MHz) around the processor’s clock frequency (around 1GHz), which is within the capabilities of compact sub-$1,000 software-defined radio (SDR) receivers.

Finally, we propose a mitigation where the bits of the exponent are only obtained from an exponent in integer-sized groups (tens of bits) rather than obtaining them one bit at a time. This mitigation is effective because it forces the attacker to attempt recovery of tens of bits from a single brief snippet of signal, rather than having a separate signal snippet for each individual bit. This mitigation has been submitted to OpenSSL and was merged into its master source code branch prior to the publication of this paper.

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BibTeX
@inproceedings {217605,
author = {Monjur Alam and Haider Adnan Khan and Moumita Dey and Nishith Sinha and Robert Callan and Alenka Zajic and Milos Prvulovic},
title = {One\&Done: A Single-Decryption EM-Based Attack on OpenSSL{\textquoteright}s Constant-Time Blinded {RSA}},
booktitle = {27th {USENIX} Security Symposium ({USENIX} Security 18)},
year = {2018},
isbn = {978-1-931971-46-1},
address = {Baltimore, MD},
pages = {585--602},
url = {https://www.usenix.org/conference/usenixsecurity18/presentation/alam},
publisher = {{USENIX} Association},
}