Let pk= (N,e) be an RSA public key with corresponding secret key ${\sf sk}=(p,q,d,d_p,d_q, q_p^{-1})$ . Assume that we obtain partial error-free information of sk, e.g., assume that we obtain half of the most significant bits of p. Then there are well-known algorithms to recover the full secret key. As opposed to these algorithms that allow for correcting erasures of the key sk, we present for the first time a heuristic probabilistic algorithm that is capable of correcting errors in sk provided that e is small. That is, on input of a full but error-prone secret key we reconstruct the original sk by correcting the faults.
More precisely, consider an error rate of $\delta \in [0,\frac 1 2)$ , where we flip each bit in sk with probability δ resulting in an erroneous key . Our Las-Vegas type algorithm allows to recover sk from in expected time polynomial in logN with success probability close to 1, provided that δ< 0.237. We also obtain a polynomial time Las-Vegas factorization algorithm for recovering the factorization (p,q) from an erroneous version with error rate δ< 0.084.