1,841 research outputs found
Short expressions of permutations as products and cryptanalysis of the Algebraic Eraser
On March 2004, Anshel, Anshel, Goldfeld, and Lemieux introduced the
\emph{Algebraic Eraser} scheme for key agreement over an insecure channel,
using a novel hybrid of infinite and finite noncommutative groups. They also
introduced the \emph{Colored Burau Key Agreement Protocol (CBKAP)}, a concrete
realization of this scheme.
We present general, efficient heuristic algorithms, which extract the shared
key out of the public information provided by CBKAP. These algorithms are,
according to heuristic reasoning and according to massive experiments,
successful for all sizes of the security parameters, assuming that the keys are
chosen with standard distributions.
Our methods come from probabilistic group theory (permutation group actions
and expander graphs). In particular, we provide a simple algorithm for finding
short expressions of permutations in , as products of given random
permutations. Heuristically, our algorithm gives expressions of length
, in time and space . Moreover, this is provable from
\emph{the Minimal Cycle Conjecture}, a simply stated hypothesis concerning the
uniform distribution on . Experiments show that the constants in these
estimations are small. This is the first practical algorithm for this problem
for .
Remark: \emph{Algebraic Eraser} is a trademark of SecureRF. The variant of
CBKAP actually implemented by SecureRF uses proprietary distributions, and thus
our results do not imply its vulnerability. See also arXiv:abs/12020598Comment: Final version, accepted to Advances in Applied Mathematics. Title
slightly change
ESTABLISHED WAYS TO ATTACK EVEN THE BEST ENCRYPTION ALGORITHM
Which solution is the best â public key or private key encryption? This question cannot have a very rigorous, logical and definitive answer, so that the matter be forever settled :). The question supposes that the two methods could be compared on completely the same indicators â well, from my point of view, the comparison is not very relevant. Encryption specialists have demonstrated that the sizes of public key encrypted messages are much bigger than the encrypted message using private key algorithms. From this point of view, we can say that private key algorithms are more efficient than their newer counterparts. Looking at the issue through the eyeglass of the security level, the public key encryption have a great advantage of the private key variants, their level of protection, in the most pessimistic scenarios, being at least 35 time higher. As a general rule, each type of algorithm has managed to find its own market niche where could be applicable as a best solution and be more efficient than the other encryption model.Encryption, decryption, key, cryptanalysis, brute-force, linear, differential, algebra
Deciphering a novel image cipher based on mixed transformed Logistic maps
Since John von Neumann suggested utilizing Logistic map as a random number
generator in 1947, a great number of encryption schemes based on Logistic map
and/or its variants have been proposed. This paper re-evaluates the security of
an image cipher based on transformed logistic maps and proves that the image
cipher can be deciphered efficiently under two different conditions: 1) two
pairs of known plain-images and the corresponding cipher-images with
computational complexity of ; 2) two pairs of chosen plain-images
and the corresponding cipher-images with computational complexity of ,
where is the number of pixels in the plain-image. In contrast, the required
condition in the previous deciphering method is eighty-seven pairs of chosen
plain-images and the corresponding cipher-images with computational complexity
of . In addition, three other security flaws existing in most
Logistic-map-based ciphers are also reported.Comment: 10 pages, 2 figure
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