The following notes are aimed at computer scientists, i.e., their main goal is not
to explain why such or such things work but to show how they can be implemented.
Factoring Class Polynomials over the Genus Field
Abstract. Primality proving...
Cryptography... As soon as we want to build an elliptic curve with a known order over
a Z/p field using the socalled complex multiplication, we have to find a
root of a class polynomial. Depending on the degree of this polynomial (and on the
size of the prime p), this operation might be very lengthy. More concretely, suppose
we have to find a root of H[12932920](x) (the degree of this polynomial is 832).
Suppose now we can compute a factor of degree 13 more quickly than we can compute the
whole polynomial H[D](x) itself. Of course, it would make the task easier...


Easy and Fast Keydependent Affine Transformation of Square SBoxes
Abstract.
Substitution boxes (Sboxes) are generally the only nonlinear part of a block cipher. Using
keydependent Sboxes rather than static ones might increase the security of a block cipher
but it would take too much time to build a good keydependent Sbox from scratch just before
ciphering or deciphering. What we can do is to transform an existing Sbox, assuming
1) the relevant cryptographic properties of the Sbox are preserved;
2) the execution of the transformation is sufficiently fast.



