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The Computer Journal Advance Access originally published online on November 4, 2005
The Computer Journal 2006 49(1):108-112; doi:10.1093/comjnl/bxh144
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© The Author 2005. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Can Unbreakable Mean Incomputable?

Alexei Vernitski

Department of Electronic Systems Engineering, University of Essex, Colchester CO4 3SQ, UK

Email: asvern{at}essex.ac.uk

Among methods of breaking a cipher, exhaustive key search stands out as the most successful (albeit the least efficient) method. We demonstrate that various algorithmic implementations of exhaustive key search are not equally effective, and cryptosystems can be devised which make some implementations of exhaustive key search unsuccessful (in the sense that the problem these algorithms try to solve turns out to be incomputable). We observe that there are implementations of exhaustive key search that are always successful (i.e. they terminate and generate a correct result irrespective of the cryptosystem they are used against). As to those implementations of exhaustive key search that are not always successful, we describe them and those cryptosystems that can make them unsuccessful.


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