919 research outputs found
MV3: A new word based stream cipher using rapid mixing and revolving buffers
MV3 is a new word based stream cipher for encrypting long streams of data. A
direct adaptation of a byte based cipher such as RC4 into a 32- or 64-bit word
version will obviously need vast amounts of memory. This scaling issue
necessitates a look for new components and principles, as well as mathematical
analysis to justify their use. Our approach, like RC4's, is based on rapidly
mixing random walks on directed graphs (that is, walks which reach a random
state quickly, from any starting point). We begin with some well understood
walks, and then introduce nonlinearity in their steps in order to improve
security and show long term statistical correlations are negligible. To
minimize the short term correlations, as well as to deter attacks using
equations involving successive outputs, we provide a method for sequencing the
outputs derived from the walk using three revolving buffers. The cipher is fast
-- it runs at a speed of less than 5 cycles per byte on a Pentium IV processor.
A word based cipher needs to output more bits per step, which exposes more
correlations for attacks. Moreover we seek simplicity of construction and
transparent analysis. To meet these requirements, we use a larger state and
claim security corresponding to only a fraction of it. Our design is for an
adequately secure word-based cipher; our very preliminary estimate puts the
security close to exhaustive search for keys of size < 256 bits.Comment: 27 pages, shortened version will appear in "Topics in Cryptology -
CT-RSA 2007
Authenticated tree parity machine key exchange
The synchronisation of Tree Parity Machines (TPMs), has proven to provide a
valuable alternative concept for secure symmetric key exchange. Yet, from a
cryptographer's point of view, authentication is at least as important as a
secure exchange of keys. Adding an authentication via hashing e.g. is
straightforward but with no relation to Neural Cryptography. We consequently
formulate an authenticated key exchange within this concept. Another
alternative, integrating a Zero-Knowledge protocol into the synchronisation, is
also presented. A Man-In-The-Middle attack and even all currently known
attacks, that are based on using identically structured TPMs and
synchronisation as well, can so be averted. This in turn has practical
consequences on using the trajectory in weight space. Both suggestions have the
advantage of not affecting the previously observed physics of this interacting
system at all.Comment: This work directly relates to cond-mat/0202112 (see also
http://arxiv.org/find/cond-mat/1/au:+Kinzel/0/1/0/all/0/1
Efficient Quantum Pseudorandomness
Randomness is both a useful way to model natural systems and a useful tool
for engineered systems, e.g. in computation, communication and control. Fully
random transformations require exponential time for either classical or quantum
systems, but in many case pseudorandom operations can emulate certain
properties of truly random ones. Indeed in the classical realm there is by now
a well-developed theory of such pseudorandom operations. However the
construction of such objects turns out to be much harder in the quantum case.
Here we show that random quantum circuits are a powerful source of quantum
pseudorandomness. This gives the for the first time a polynomialtime
construction of quantum unitary designs, which can replace fully random
operations in most applications, and shows that generic quantum dynamics cannot
be distinguished from truly random processes. We discuss applications of our
result to quantum information science, cryptography and to understanding
self-equilibration of closed quantum dynamics.Comment: 6 pages, 1 figure. Short version of http://arxiv.org/abs/1208.069
Post-Quantum Key Exchange Protocols
If an eavesdropper Eve is equipped with quantum computers, she can easily
break the public key exchange protocols used today. In this paper we will
discuss the post-quantum Diffie-Hellman key exchange and private key exchange
protocols.Comment: 11 pages, 2 figures. Submitted to SPIE DSS 2006; v2 citation typos
fixed; v3 appendix typos correcte
Collision Times in Multicolor Urn Models and Sequential Graph Coloring With Applications to Discrete Logarithms
Consider an urn model where at each step one of colors is sampled
according to some probability distribution and a ball of that color is placed
in an urn. The distribution of assigning balls to urns may depend on the color
of the ball. Collisions occur when a ball is placed in an urn which already
contains a ball of different color. Equivalently, this can be viewed as
sequentially coloring a complete -partite graph wherein a collision
corresponds to the appearance of a monochromatic edge. Using a Poisson
embedding technique, the limiting distribution of the first collision time is
determined and the possible limits are explicitly described. Joint distribution
of successive collision times and multi-fold collision times are also derived.
The results can be used to obtain the limiting distributions of running times
in various birthday problem based algorithms for solving the discrete logarithm
problem, generalizing previous results which only consider expected running
times. Asymptotic distributions of the time of appearance of a monochromatic
edge are also obtained for other graphs.Comment: Minor revision. 35 pages, 2 figures. To appear in Annals of Applied
Probabilit
Complexity Theory
Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes
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