5 research outputs found
Compressing Sets and Multisets of Sequences
This is the accepted manuscript for a paper published in IEEE Transactions on Information Theory, Vol. 61, No. 3, March 2015, doi: 10.1109/TIT.2015.2392093. © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper describes lossless compression algorithms
for multisets of sequences, taking advantage of the
multiset’s unordered structure. Multisets are a generalization of
sets, where members are allowed to occur multiple times. A multiset
can be encoded naïvely by simply storing its elements in some
sequential order, but then information is wasted on the ordering.
We propose a technique that transforms the multiset into an
order-invariant tree representation, and derive an arithmetic
code that optimally compresses the tree. Our method achieves
compression even if the sequences in the multiset are individually
incompressible (such as cryptographic hash sums). The algorithm
is demonstrated practically by compressing collections of SHA-1
hash sums, and multisets of arbitrary, individually encodable
objects.This work was supported in part by the Engineering
and Physical Sciences Research Council under Grant EP/I036575 and in
part by a Google Research Award. This paper was presented at the 2014 Data
Compression Conferenc
Unconditionally secure ciphers with a short key for a source with unknown statistics
We consider the problem of constructing an unconditionally secure cipher with
a short key for the case where the probability distribution of encrypted
messages is unknown. Note that unconditional security means that an adversary
with no computational constraints can obtain only a negligible amount of
information ("leakage") about an encrypted message (without knowing the key).
Here we consider the case of a priori (partially) unknown message source
statistics.
More specifically, the message source probability distribution belongs to a
given family of distributions. We propose an unconditionally secure cipher for
this case. As an example, one can consider constructing a single cipher for
texts written in any of the languages of the European Union. That is, the
message to be encrypted could be written in any of these languages
Integer Set Compression and Statistical Modeling
Compression of integer sets and sequences has been extensively studied for
settings where elements follow a uniform probability distribution. In addition,
methods exist that exploit clustering of elements in order to achieve higher
compression performance. In this work, we address the case where enumeration of
elements may be arbitrary or random, but where statistics is kept in order to
estimate probabilities of elements. We present a recursive subset-size encoding
method that is able to benefit from statistics, explore the effects of
permuting the enumeration order based on element probabilities, and discuss
general properties and possibilities for this class of compression problem