2,554 research outputs found
Cryptography from tensor problems
We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler
Length-Based Attacks for Certain Group Based Encryption Rewriting Systems
In this note, we describe a probabilistic attack on public key cryptosystems
based on the word/conjugacy problems for finitely presented groups of the type
proposed recently by Anshel, Anshel and Goldfeld. In such a scheme, one makes
use of the property that in the given group the word problem has a polynomial
time solution, while the conjugacy problem has no known polynomial solution. An
example is the braid group from topology in which the word problem is solvable
in polynomial time while the only known solutions to the conjugacy problem are
exponential. The attack in this paper is based on having a canonical
representative of each string relative to which a length function may be
computed. Hence the term length attack. Such canonical representatives are
known to exist for the braid group
Quantum Fourier sampling, Code Equivalence, and the quantum security of the McEliece and Sidelnikov cryptosystems
The Code Equivalence problem is that of determining whether two given linear
codes are equivalent to each other up to a permutation of the coordinates. This
problem has a direct reduction to a nonabelian hidden subgroup problem (HSP),
suggesting a possible quantum algorithm analogous to Shor's algorithms for
factoring or discrete log. However, we recently showed that in many cases of
interest---including Goppa codes---solving this case of the HSP requires rich,
entangled measurements. Thus, solving these cases of Code Equivalence via
Fourier sampling appears to be out of reach of current families of quantum
algorithms.
Code equivalence is directly related to the security of McEliece-type
cryptosystems in the case where the private code is known to the adversary.
However, for many codes the support splitting algorithm of Sendrier provides a
classical attack in this case. We revisit the claims of our previous article in
the light of these classical attacks, and discuss the particular case of the
Sidelnikov cryptosystem, which is based on Reed-Muller codes
Cryptographical Properties of Ising Spin Systems
The relation between Ising spin systems and public-key cryptography is
investigated using methods of statistical physics. The insight gained from the
analysis is used for devising a matrix-based cryptosystem whereby the
ciphertext comprises products of the original message bits; these are selected
by employing two predetermined randomly-constructed sparse matrices. The
ciphertext is decrypted using methods of belief-propagation. The analyzed
properties of the suggested cryptosystem show robustness against various
attacks and competitive performance to modern cyptographical methods.Comment: 4 pages, 2 figure
MOR Cryptosystem and classical Chevalley groups in odd characteristic
In this paper we study the MOR cryptosystem using finite classical Chevalley
groups over a finite field of odd characteristic. In the process we develop an
algorithm for these Chevalley groups in the same spirit as the row-column
operation for special linear group. We focus our study on orthogonal and
symplectic groups. We find the hardness of the proposed MOR cryptosystem for
these groups
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