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May 2013
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Events on Monday 23 April 2012

Correcting Errors in RSA Private Keys
12:10 Mon 23 Apr 12 :: 5.57 Ingkarni Wardli :: Mr Wilko Henecka :: University of Adelaide

Media...
Let pk=(N,e) be an RSA public key with corresponding secret key sk=(d,p,q,...). 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 d in [0,1), where we flip each bit in sk with probability d resulting in an erroneous key sk'. Our Las-Vegas type algorithm allows to recover sk from sk' in expected time polynomial in logN with success probability close to 1, provided that d is strictly less than 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 d strictly less than 0.084.
View from Ingkarni Wardli

Recent news
Summer Research Student Thomas Brown wins the AMSI/Cambridge University Press Prize for 2013
Congratulations to Thomas Brown, jointly supervised by Ed Green and Ben Binder who won the AMSI/Cambridge University Press Prize for the best talk at the 2013 CSIRO Big Day In, recently held this month. After completion of their summer project, vacation scholars must submit a project report which summarises the project and addresses the nature of the topic, methods of investigation, results found, and benefits of the experience. The scholars then present a 15-minute presentation about their project at the CSIRO Big Day In (BDI). This experience enables students to meet and socialise with their peers, gain experience presenting to their colleagues and supervisors and learn about a range of careers in science by interacting with several CSIRO scientists (including mathematicians) in a discussion panel. This is a very pleasing result for Thomas, Ed and Ben as well as for the School of Mathematical Sciences. Well done Thomas.
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