4,058 research outputs found
Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security
We present information-theoretic definitions and results for analyzing
symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when
perfect secrecy is not attained. We adopt two lines of analysis, one based on
lossless source coding, and another akin to rate-distortion theory. We start by
presenting a new information-theoretic metric for security, called symbol
secrecy, and derive associated fundamental bounds. We then introduce
list-source codes (LSCs), which are a general framework for mapping a key
length (entropy) to a list size that an eavesdropper has to resolve in order to
recover a secret message. We provide explicit constructions of LSCs, and
demonstrate that, when the source is uniformly distributed, the highest level
of symbol secrecy for a fixed key length can be achieved through a construction
based on minimum-distance separable (MDS) codes. Using an analysis related to
rate-distortion theory, we then show how symbol secrecy can be used to
determine the probability that an eavesdropper correctly reconstructs functions
of the original plaintext. We illustrate how these bounds can be applied to
characterize security properties of symmetric-key encryption schemes, and, in
particular, extend security claims based on symbol secrecy to a functional
setting.Comment: Submitted to IEEE Transactions on Information Theor
Order-Revealing Encryption and the Hardness of Private Learning
An order-revealing encryption scheme gives a public procedure by which two
ciphertexts can be compared to reveal the ordering of their underlying
plaintexts. We show how to use order-revealing encryption to separate
computationally efficient PAC learning from efficient -differentially private PAC learning. That is, we construct a concept
class that is efficiently PAC learnable, but for which every efficient learner
fails to be differentially private. This answers a question of Kasiviswanathan
et al. (FOCS '08, SIAM J. Comput. '11).
To prove our result, we give a generic transformation from an order-revealing
encryption scheme into one with strongly correct comparison, which enables the
consistent comparison of ciphertexts that are not obtained as the valid
encryption of any message. We believe this construction may be of independent
interest.Comment: 28 page
A Talk on Quantum Cryptography, or How Alice Outwits Eve
Alice and Bob wish to communicate without the archvillainess Eve
eavesdropping on their conversation. Alice, decides to take two college
courses, one in cryptography, the other in quantum mechanics. During the
courses, she discovers she can use what she has just learned to devise a
cryptographic communication system that automatically detects whether or not
Eve is up to her villainous eavesdropping. Some of the topics discussed are
Heisenberg's Uncertainty Principle, the Vernam cipher, the BB84 and B92
cryptographic protocols. The talk ends with a discussion of some of Eve's
possible eavesdropping strategies, opaque eavesdropping, translucent
eavesdropping, and translucent eavesdropping with entanglement.Comment: 31 pages, 8 figures. Revised version of a paper published in "Coding
Theory, and Cryptography: From Geheimscheimschreiber and Enigma to Quantum
Theory," (edited by David Joyner), Springer-Verlag, 1999 (pp. 144-174). To be
published with the permission of Springer-Verlag in an AMS PSAPM Short Course
volume entitled "Quantum Computation.
Using Echo State Networks for Cryptography
Echo state networks are simple recurrent neural networks that are easy to
implement and train. Despite their simplicity, they show a form of memory and
can predict or regenerate sequences of data. We make use of this property to
realize a novel neural cryptography scheme. The key idea is to assume that
Alice and Bob share a copy of an echo state network. If Alice trains her copy
to memorize a message, she can communicate the trained part of the network to
Bob who plugs it into his copy to regenerate the message. Considering a
byte-level representation of in- and output, the technique applies to arbitrary
types of data (texts, images, audio files, etc.) and practical experiments
reveal it to satisfy the fundamental cryptographic properties of diffusion and
confusion.Comment: 8 pages, ICANN 201
Lists that are smaller than their parts: A coding approach to tunable secrecy
We present a new information-theoretic definition and associated results,
based on list decoding in a source coding setting. We begin by presenting
list-source codes, which naturally map a key length (entropy) to list size. We
then show that such codes can be analyzed in the context of a novel
information-theoretic metric, \epsilon-symbol secrecy, that encompasses both
the one-time pad and traditional rate-based asymptotic metrics, but, like most
cryptographic constructs, can be applied in non-asymptotic settings. We derive
fundamental bounds for \epsilon-symbol secrecy and demonstrate how these bounds
can be achieved with MDS codes when the source is uniformly distributed. We
discuss applications and implementation issues of our codes.Comment: Allerton 2012, 8 page
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