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Correcting Errors in RSA Private Keys

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6223)

Abstract

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 \(\widetilde{\sf sk}\) 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 \(\widetilde{\sf sk}\). Our Las-Vegas type algorithm allows to recover sk from \(\widetilde{\sf sk}\) 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.

Keywords

RSA error correction statistical cryptanalysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Horst Görtz Institute for IT-SecurityRuhr-University Bochum, Faculty of MathematicsGermany

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