Paper 2014/513 Original: eprint.iacr.org/2014/513 ↗

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

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.