Abstract: In this paper we propose two first non-generic constructions
of multisignature scheme based on coding theory. The
first system make use of the CFS signature scheme and is secure
in random oracle while the second scheme is based on the KKS
construction and is a few times. The security of our construction relies
on a difficult problems in coding theory: The Syndrome Decoding
problem which has been proved NP-complete [4].
Abstract: An optimal solution for a large number of constraint
satisfaction problems can be found using the technique of
substitution and elimination of variables analogous to the technique
that is used to solve systems of equations. A decision function
f(A)=max(A2) is used to determine which variables to eliminate. The
algorithm can be expressed in six lines and is remarkable in both its
simplicity and its ability to find an optimal solution. However it is
inefficient in that it needs to square the updated A matrix after each
variable elimination. To overcome this inefficiency the algorithm is
analyzed and it is shown that the A matrix only needs to be squared
once at the first step of the algorithm and then incrementally updated
for subsequent steps, resulting in significant improvement and an
algorithm complexity of O(n3).