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Summary: Moderately Hard, Memory-bound Functions
MARTIN ABADI
University of California at Santa Cruz
and
MIKE BURROWS
Google
and
MARK MANASSE and TED WOBBER
Microsoft Research, Silicon Valley
A resource may be abused if its users incur little or no cost. For example, e-mail abuse is rampant
because sending an e-mail has negligible cost for the sender. It has been suggested that such
abuse may be discouraged by introducing an artificial cost in the form of a moderately expensive
computation. Thus, the sender of an e-mail might be required to pay by computing for a few
seconds before the e-mail is accepted. Unfortunately, because of sharp disparities across com-
puter systems, this approach may be ineffective against malicious users with high-end systems,
prohibitively slow for legitimate users with low-end systems, or both. Starting from this obser-
vation, we research moderately hard functions that most recent systems will evaluate at about
the same speed. For this purpose, we rely on memory-bound computations. We describe and
analyze a family of moderately hard, memory-bound functions, and we explain how to use them
for protecting against abuses.
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