Triangulation algorithm for non-linear equation systems

The topic of this thesis is a triangulation algorithm and its use in cryptanalysis. First of all we will define a non-linear equation system on which we can apply triangulation algorithm and we will explain what its output is. Then we will demonstrate its application in cryptanalysis, more specificaly during the attack on the Rinjdael cifer. We will illustrate this attack by a search of collision for our hash function, created for this purpose in Davies-Mayer mode using Rijndael cipher This thesis also contains a practical part in which we will demonstrate the search of collision for our hash function mention before

Triangulation algorithm for non-linear equation systems

The topic of this thesis is a triangulation algorithm and its use in cryptanalysis. First of all we will define a non-linear equation system on which we can apply triangulation algorithm and we will explain what its output is. Then we will demonstrate its application in cryptanalysis, more specificaly during the attack on the Rinjdael cifer. We will illustrate this attack by a search of collision for our hash function, created for this purpose in Davies-Mayer mode using Rijndael cipher This thesis also contains a practical part in which we will demonstrate the search of collision for our hash function mention before

Weil differentials

This thesis focuses upon how to calculate local components of Weil differentials of an elliptic function field. Because Weil differentials constitute a one-dimension vector space then one Weil differential is fixed. An algorithm calculating a local component is developed for the fixed one. The first algorithm computes local components of places of degree one. It is based upon elementary properties of local components. The definition of the Weil differential does not say enough about why it is defined in this way and about why it is useful. Thus there is the relationship between the Weil differential and some objects from complex analysis like the Laurent series and the residue. It provides a better understanding of properties of the Weil differential. The result of this thesis are other two algorithms calculating local components of Weil differentials. The algorithms employ the residue.