Title: Towards Quantitative Analysis of Cyber Security

Abstract:

Cyber security had become an extremely hot topic in the last few years, but
almost all the research results published so far had been qualitative in
nature: they do not formulate a precise mathematical model of the problem,
do not numerically compare alternatives, and do not  try to find optimal
solutions for cyber security problems. In this paper I will describe some
initial attempts (developed jointly with Bar-On Dinur Dunkelman Hod Keller
and Ronen)  to create such a quantitative theory of some particular
subproblems in cyber security. In particular, I will consider the problem of
how to protect a computer system against cyber and ransomware attacks by
choosing an optimal backup scheme using k storage devices. While in standard
backup schemes it is beneficial to backup as frequently as possible, in the
case of sophisticated cyber attacks any attempt to connect a backup device
to an already infected computer is likely to stealthily corrupt its data and
thus make it unusable when the actual attack happens. Our formalization of
the problem casts it as a special case of an online/offline optimization
problem, in which the defender tries to minimize the maximal extra cost
caused by his lack of knowledge about the time of the infection, and the
strategies he can use resemble a pebbling game with k tokens which can be
placed anywhere along the timeline. However, the optimal solution of this
simple pebbling game is surprisingly complicated: concrete provably optimal
backup strategies are known only for k<10, and only asymptotically optimal
strategies are known for larger k.