Correcting Errors in RSA Private Keys

Abstract. Let pk = (N , e) be an RSA public key with corresponding secret key sk = (p, q, d, dp, dq , q-1 p ). 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 sk we reconstruct the original sk by correcting the faults. More precisely, consider an error rate of [0, 1 2 ), where we flip each bit in sk with probability resulting in an erroneous key sk. Our Las-Vegas type algorithm allows to recover sk from sk in expected time polynomial in log N with success probability close to 1, provided that < 0.237. We also obtain a polynomial time Las-Vegas factorization algorithm...

• Type: Conference
• Year: 2010
• Where: CRYPTO
• Authors: Wilko Henecka, Alexander May, Alexander Meurer
• Keywords: CRYPTO 2010, Cryptology, Erroneous Key Sk, Key Sk, Secret Key Sk