Recovering RSA Secret Keys from Noisy Key Bits with Erasures and Errors

Noboru KUNIHIRO  Naoyuki SHINOHARA  Tetsuya IZU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.6   pp.1273-1284
Publication Date: 2014/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.1273
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
RSA,  key-recovery,  cold boot attack,  side-channel attack,  maximal likelihood,  

Full Text: PDF(570.9KB)>>
Buy this Article

We discuss how to recover RSA secret keys from noisy key bits with erasures and errors. There are two known algorithms recovering original secret keys from noisy keys. At Crypto 2009, Heninger and Shacham proposed a method for the case where an erroneous version of secret keys contains only erasures. Subsequently, Henecka et al. proposed a method for an erroneous version containing only errors at Crypto 2010. For physical attacks such as side-channel and cold boot attacks, we need to study key recovery from a noisy secret key containing both erasures and errors. In this paper, we propose a method to recover a secret key from such an erroneous version and analyze the condition for error and erasure rates so that our algorithm succeeds in finding the correct secret key in polynomial time. We also evaluate a theoretical bound to recover the secret key and discuss to what extent our algorithm achieves this bound.