Software Protection and Simulation on Oblivious RAMs.
Rafail Ostrovsky
Abstract: Software protection is one of the most important issues concerning computer practice. There exist many heuristics and ad-hoc methods for protection, but the problem as a whole has not received the theoretical treatment it deserves. In this paper we provide theoretical treatment of software protection. We reduce the problem of software protection to the problem of efficient simulation on oblivious RAM.
A machine is oblivious if the sequence in which it accesses memory locations is equivalent for any two inputs with the same running time. For example, an oblivious Turing Machine is one for which the movement of the heads on the tapes is identical for each computation. (Thus, it is independent of the actual input.) What is the slowdown in the running time of any machine, if it is required to be oblivious? In 1979 Pippenger and Fischer showed how a two-tape oblivious Turing Machine can simulate, on-line, a one-tape Turing Machine, with a logarithmic slowdown in the running time. We show an analogue result for the random-access machine (RAM) model of computation. In particular, we show how to do an on-line simulation of an arbitrary RAM input by a probabilistic oblivious RAM with a poly-logarithmic slowdown in the running time. On the other hand, we show that a logarithmic slowdown is a lower bound. Our proof yields a technique of efficiently hiding (through randomization) the access pattern into any composite data-structure which has many practical applications.
comment: M.I.T. Ph.D. Thesis, 1992. Preliminary version appeared as a single-author paper in Proceedings of 22nd annual ACM Symposium on Theory of Computing (STOC-90) pp. 514-523.
Fetch PostScript file of the
Ostrovsky Ph.D. thesis
or fetch PDF file of the
Ostrovsky Ph.D. thesis
Journal version (which combines my thesis with Oded Goldreich previous
historical paper on the same subject) appeared in JACM
Vol. 43, No. 3, May 1996, pp.431-473.
You can also get this version, with a somewhat different, shorter
proof of bucket re-shufflng method of section 5.5:
[postscript],
[pdf].
| Back to Publications List |