**RSA meets DPA: Recovering RSA Secret Keys from Noisy Analog Data**

*Noboru Kunihiro and Junya Honda*

**Abstract: **We discuss how to recover RSA secret keys from noisy analog data
obtained through physical attacks such as cold boot and side channel
attacks. Many studies have focused on recovering correct secret keys
from noisy binary data. Obtaining noisy binary keys typically involves
first observing the analog data and then obtaining the binary data
through quantization process that discards much information pertaining
to the correct keys. In this paper, we propose two algorithms for
recovering correct secret keys from noisy analog data, which are
generalized variants of Paterson et al.'s algorithm. Our algorithms
fully exploit the analog information. More precisely, consider observed
data which follows the Gaussian distribution
with mean $(-1)^b$ and variance $\sigma^2$ for a secret key bit $b$.
We propose a polynomial time algorithm based on
the maximum likelihood approach and show that it can recover secret keys
if $\sigma < 1.767$. The first algorithm works only if the noise
distribution is explicitly known. The second algorithm does not need to
know the explicit form of the noise distribution. We implement the first
algorithm and verify its effectiveness.

**Category / Keywords: **public-key cryptography / RSA, Key-Recovery, Cold Boot Attack, Side Channel Attack, Maximum Likelihood

**Original Publication**** (with major differences): **IACR-CHES-2014

**Date: **received 30 Jun 2014

**Contact author: **kunihiro at k u-tokyo ac jp

**Available format(s): **PDF | BibTeX Citation

**Note: **This is the full version of our paper in CHES2014.

**Version: **20140701:052105 (All versions of this report)

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