310 research outputs found
Edit Distance: Sketching, Streaming and Document Exchange
We show that in the document exchange problem, where Alice holds and Bob holds , Alice can send Bob a message of
size bits such that Bob can recover using the
message and his input if the edit distance between and is no more
than , and output "error" otherwise. Both the encoding and decoding can be
done in time . This result significantly
improves the previous communication bounds under polynomial encoding/decoding
time. We also show that in the referee model, where Alice and Bob hold and
respectively, they can compute sketches of and of sizes
bits (the encoding), and send to the referee, who can
then compute the edit distance between and together with all the edit
operations if the edit distance is no more than , and output "error"
otherwise (the decoding). To the best of our knowledge, this is the first
result for sketching edit distance using bits.
Moreover, the encoding phase of our sketching algorithm can be performed by
scanning the input string in one pass. Thus our sketching algorithm also
implies the first streaming algorithm for computing edit distance and all the
edits exactly using bits of space.Comment: Full version of an article to be presented at the 57th Annual IEEE
Symposium on Foundations of Computer Science (FOCS 2016
Lower Bounds for Sparse Recovery
We consider the following k-sparse recovery problem: design an m x n matrix
A, such that for any signal x, given Ax we can efficiently recover x'
satisfying
||x-x'||_1 <= C min_{k-sparse} x"} ||x-x"||_1.
It is known that there exist matrices A with this property that have only O(k
log (n/k)) rows.
In this paper we show that this bound is tight. Our bound holds even for the
more general /randomized/ version of the problem, where A is a random variable
and the recovery algorithm is required to work for any fixed x with constant
probability (over A).Comment: 11 pages. Appeared at SODA 201
Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data
We provide formal definitions and efficient secure techniques for
- turning noisy information into keys usable for any cryptographic
application, and, in particular,
- reliably and securely authenticating biometric data.
Our techniques apply not just to biometric information, but to any keying
material that, unlike traditional cryptographic keys, is (1) not reproducible
precisely and (2) not distributed uniformly. We propose two primitives: a
"fuzzy extractor" reliably extracts nearly uniform randomness R from its input;
the extraction is error-tolerant in the sense that R will be the same even if
the input changes, as long as it remains reasonably close to the original.
Thus, R can be used as a key in a cryptographic application. A "secure sketch"
produces public information about its input w that does not reveal w, and yet
allows exact recovery of w given another value that is close to w. Thus, it can
be used to reliably reproduce error-prone biometric inputs without incurring
the security risk inherent in storing them.
We define the primitives to be both formally secure and versatile,
generalizing much prior work. In addition, we provide nearly optimal
constructions of both primitives for various measures of ``closeness'' of input
data, such as Hamming distance, edit distance, and set difference.Comment: 47 pp., 3 figures. Prelim. version in Eurocrypt 2004, Springer LNCS
3027, pp. 523-540. Differences from version 3: minor edits for grammar,
clarity, and typo
The best of both worlds: Applying secure sketches to cancelable biometrics
AbstractCancelable biometrics and secure sketches have been introduced with the same purpose in mind: to protect the privacy of biometric templates while keeping the ability to match this protected data against a reference. The paradigm beyond cancelable biometrics is to perform an irreversible transformation over images and to make matching over transformed images. On one hand, a drawback of this technique is that for biometrics using a matching algorithm relying on some complex characteristics, such as the ones used for fingerprints, the irreversible transformation tends to break the underlying structure, thus degrading the performance accuracy. On the other hand, for secure sketches, matching is reduced to an error correction and we show here that applying secure sketch error correction to cancelable biometrics allows one to keep good matching performance. Moreover, the security’s advantages of both schemes adds up together
The Mathematics of Information Science
This paper describes a course, The Mathematics of Information Science, which was taught at Towson University in Spring 1998, 1999, and 2000. This course is the junior level interdisciplinary course of the Maryland Collaborative for Teacher Preparation program. The effectiveness of the course in teaching problem solving techniques and abstract mathematical ideas is documented. The students constructed their own knowledge from laboratory experiences involving digital logic circuits. They were subsequently challenged to abstract this knowledge and to find ways to solve progressively more difficult problems using these digital logic circuits. The mathematics of encoding and decoding information constituted the major mathematical content of the course. This course is shown to be effective in introducing prospective elementary and middle school teachers to abstract mathematical ideas and problem solving techniques
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