3 research outputs found
Authentication With a Guessing Adversary
In this paper, we consider the authentication problem where a candidate
measurement presented by an unidentified user is compared to a previously
stored measurement of the legitimate user, the enrollment, with respect to a
certain distortion criteria for authentication. An adversary wishes to
impersonate the legitimate user by guessing the enrollment until the system
authenticates him. For this setting, we study the minimum number of required
guesses (on average) by the adversary for a successful impersonation attack and
find the complete characterization of the asymptotic exponent of this metric,
referred to as the deception exponent. Our result is a direct application of
the results of the Guessing problem by Arikan and Merhav [19]. Paralleling the
work in [19] we also extend this result to the case where the adversary may
have access to additional side information correlated to the enrollment data.
The paper is a revised version of a submission to IEEE WIFS 2015, with the
referencing to the paper [19] clarified compared with the conference version.Comment: 6 pages, 1 figure, revised IEEE WIFS 2015 submissio
The Minimal Compression Rate for Similarity Identification
Traditionally, data compression deals with the problem of concisely
representing a data source, e.g. a sequence of letters, for the purpose of
eventual reproduction (either exact or approximate). In this work we are
interested in the case where the goal is to answer similarity queries about the
compressed sequence, i.e. to identify whether or not the original sequence is
similar to a given query sequence. We study the fundamental tradeoff between
the compression rate and the reliability of the queries performed on compressed
data. For i.i.d. sequences, we characterize the minimal compression rate that
allows query answers, that are reliable in the sense of having a vanishing
false-positive probability, when false negatives are not allowed. The result is
partially based on a previous work by Ahlswede et al., and the inherently
typical subset lemma plays a key role in the converse proof. We then
characterize the compression rate achievable by schemes that use lossy source
codes as a building block, and show that such schemes are, in general,
suboptimal. Finally, we tackle the problem of evaluating the minimal
compression rate, by converting the problem to a sequence of convex programs
that can be solved efficiently.Comment: 45 pages, 6 figures. Submitted to IEEE Transactions on Information
Theor
Quadratic Similarity Queries on Compressed Data 1
The problem of performing similarity queries on compressed data is considered. We study the fundamental tradeoff between compression rate, sequence length, and reliability of queries performed on compressed data. For a Gaussian source and quadratic similarity criterion, we show that queries can be answered reliably if and only if the compression rate exceeds a given threshold β the identification rate β which we explicitly characterize. When compression is performed at a rate greater than the identification rate, responses to queries on the compressed data can be made exponentially reliable. We give a complete characterization of this exponent, which is analogous to the error and excess-distortion exponents in channel and source coding, respectively. For a general source, we prove that the identification rate is at most that of a Gaussian source with the same variance. Therefore, as with classical compression, the Gaussian source requires the largest compression rate. Moreover, a scheme is described that attains this maximal rate for any source distribution. I