Mathematical Approach for Recovering Secret Key from Its Noisy Version

In this paper, we discuss how to recover the RSA secret key from a noisy version of the secret key obtained through physical attacks such as cold boot and side channel attacks. For example, consider a cold boot attack to extract the RSA secret key stored in the memory. The attacker can obtain a degraded version of the secret key so that some bits are erased. In principle, if many erasures occur, the key recovery for the secret key becomes rather difficult. To date, many noise models other than the erasure model have been introduced. For the discrete noise case, the binary erasure model, binary error model, and binary erasure and error model have been introduced. Effective algorithms have been proposed for each noise model, and the conditions for noise which the original secret key can be recovered in polynomial time have been derived. Research has also been conducted on models that can obtain continuous leakage. In this case, several algorithms have been proposed according to the degree of knowledge of the leakage model. Many studies have been conducted on by taking heuristic approaches. In this paper, we provide a survey of existing research and then attempt to explain it within a unified framework.