  This paper is a short summery of results announced in a previous paper on a
new universal method for Cryptanalysis which uses a Black Box linear algebra
approach to computation of local inversion of nonlinear maps in finite fields.
It is shown that one local inverse $x$ of the map equation $y=F(x)$ can be
computed by using the minimal polynomial of the sequence $y(k)$ defined by
iterates (or recursion) $y(k+1)=F(y(k))$ with $y(0)=y$ when the sequence is
periodic. This is the only solution in the periodic orbit of the map $F$.
Further, when the degree of the minimal polynomial is of polynomial order in
number of bits of the input of $F$ (called low complexity case), the solution
can be computed in polynomial time. The method of computation only uses the
forward computations $F(y)$ for given $y$ which is why this is called a Black
Box approach. Application of this approach is then shown for cryptanalysis of
several maps arising in cryptographic primitives. It is shown how in the low
complexity cases maps defined by block and stream ciphers can be inverted to
find the symmetric key under known plaintext attack. Then it is shown how RSA
map can be inverted to find the plaintext as well as an equivalent private key
to break the RSA algorithm without factoring the modulus. Finally it is shown
that the discrete log computation in finite field and elliptic curves can be
formulated as a local inversion problem and the low complexity cases can be
solved in polynomial time.
