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The Random-Query Model and the Memory-Bounded Coupon Collector
We study a new model of space-bounded computation, the random-query model. The model is based on a branching-program over input variables x_1,…,x_n. In each time step, the branching program gets as an input a random index i ∈ {1,…,n}, together with the input variable x_i (rather than querying an input variable of its choice, as in the case of a standard (oblivious) branching program). We motivate the new model in various ways and study time-space tradeoff lower bounds in this model. Our main technical result is a quadratic time-space lower bound for zero-error computations in the random-query model, for XOR, Majority and many other functions. More precisely, a zero-error computation is a computation that stops with high probability and such that conditioning on the event that the computation stopped, the output is correct with probability 1. We prove that for any Boolean function f: {0,1}^n → {0,1}, with sensitivity k, any zero-error computation with time T and space S, satisfies T ⋅ (S+log n) ≥ Ω(n⋅k). We note that the best time-space lower bounds for standard oblivious branching programs are only slightly super linear and improving these bounds is an important long-standing open problem. To prove our results, we study a memory-bounded variant of the coupon-collector problem that seems to us of independent interest and to the best of our knowledge has not been studied before. We consider a zero-error version of the coupon-collector problem. In this problem, the coupon-collector could explicitly choose to stop when he/she is sure with zero-error that all coupons have already been collected. We prove that any zero-error coupon-collector that stops with high probability in time T, and uses space S, satisfies T⋅(S+log n) ≥ Ω(n^2), where n is the number of different coupons
A Lower Bound Technique for Communication in BSP
Communication is a major factor determining the performance of algorithms on
current computing systems; it is therefore valuable to provide tight lower
bounds on the communication complexity of computations. This paper presents a
lower bound technique for the communication complexity in the bulk-synchronous
parallel (BSP) model of a given class of DAG computations. The derived bound is
expressed in terms of the switching potential of a DAG, that is, the number of
permutations that the DAG can realize when viewed as a switching network. The
proposed technique yields tight lower bounds for the fast Fourier transform
(FFT), and for any sorting and permutation network. A stronger bound is also
derived for the periodic balanced sorting network, by applying this technique
to suitable subnetworks. Finally, we demonstrate that the switching potential
captures communication requirements even in computational models different from
BSP, such as the I/O model and the LPRAM
Finding the Median (Obliviously) with Bounded Space
We prove that any oblivious algorithm using space to find the median of a
list of integers from requires time . This bound also applies to the problem of determining whether the median
is odd or even. It is nearly optimal since Chan, following Munro and Raman, has
shown that there is a (randomized) selection algorithm using only
registers, each of which can store an input value or -bit counter,
that makes only passes over the input. The bound also implies
a size lower bound for read-once branching programs computing the low order bit
of the median and implies the analog of for length oblivious branching programs
Time and Space Bounds for Reversible Simulation
We prove a general upper bound on the tradeoff between time and space that
suffices for the reversible simulation of irreversible computation. Previously,
only simulations using exponential time or quadratic space were known.
The tradeoff shows for the first time that we can simultaneously achieve
subexponential time and subquadratic space.
The boundary values are the exponential time with hardly any extra space
required by the Lange-McKenzie-Tapp method and the ()th power time with
square space required by the Bennett method. We also give the first general
lower bound on the extra storage space required by general reversible
simulation. This lower bound is optimal in that it is achieved by some
reversible simulations.Comment: 11 pages LaTeX, Proc ICALP 2001, Lecture Notes in Computer Science,
Vol xxx Springer-Verlag, Berlin, 200
SoK: Cryptographically Protected Database Search
Protected database search systems cryptographically isolate the roles of
reading from, writing to, and administering the database. This separation
limits unnecessary administrator access and protects data in the case of system
breaches. Since protected search was introduced in 2000, the area has grown
rapidly; systems are offered by academia, start-ups, and established companies.
However, there is no best protected search system or set of techniques.
Design of such systems is a balancing act between security, functionality,
performance, and usability. This challenge is made more difficult by ongoing
database specialization, as some users will want the functionality of SQL,
NoSQL, or NewSQL databases. This database evolution will continue, and the
protected search community should be able to quickly provide functionality
consistent with newly invented databases.
At the same time, the community must accurately and clearly characterize the
tradeoffs between different approaches. To address these challenges, we provide
the following contributions:
1) An identification of the important primitive operations across database
paradigms. We find there are a small number of base operations that can be used
and combined to support a large number of database paradigms.
2) An evaluation of the current state of protected search systems in
implementing these base operations. This evaluation describes the main
approaches and tradeoffs for each base operation. Furthermore, it puts
protected search in the context of unprotected search, identifying key gaps in
functionality.
3) An analysis of attacks against protected search for different base
queries.
4) A roadmap and tools for transforming a protected search system into a
protected database, including an open-source performance evaluation platform
and initial user opinions of protected search.Comment: 20 pages, to appear to IEEE Security and Privac
Communication Complexity and Secure Function Evaluation
We suggest two new methodologies for the design of efficient secure
protocols, that differ with respect to their underlying computational models.
In one methodology we utilize the communication complexity tree (or branching
for f and transform it into a secure protocol. In other words, "any function f
that can be computed using communication complexity c can be can be computed
securely using communication complexity that is polynomial in c and a security
parameter". The second methodology uses the circuit computing f, enhanced with
look-up tables as its underlying computational model. It is possible to
simulate any RAM machine in this model with polylogarithmic blowup. Hence it is
possible to start with a computation of f on a RAM machine and transform it
into a secure protocol.
We show many applications of these new methodologies resulting in protocols
efficient either in communication or in computation. In particular, we
exemplify a protocol for the "millionaires problem", where two participants
want to compare their values but reveal no other information. Our protocol is
more efficient than previously known ones in either communication or
computation
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