This paper analyzes the complexity of the conjugacy search problem (CSP) in polycyclic and matrix groups. Produces polynomial-time solutions and reductions to discrete logarithm problems, with concrete cryptanalysis algorithms for nonabelian group-based key exchange schemes.

This paper provides a cryptanalysis of a key exchange protocol based on a decomposition problem in the twisted group algebras of the dihedral group over a finite field. The attack runs in polynomial time and succeeds with probability at least 90 percent.

This paper presents a deterministic algorithm for solving the discrete logarithm problem in a semigroup. It also gives an analysis of the success rates of the existing probabilistic algorithms, which were so far only conjectured or stated loosely.

This work defines and explores their properties, with special focus on the minimum size of their basis sets. Applications are presented in areas like cyclic projective planes, cyclic codes, and the theory of k-normal elements.

This paper provides an effective criterion to find all higher moments of the density of a subset of a finite-dimensional free module over the ring of algebraic integers of a number field. The method is demonstrated for Eisenstein polynomials and shifted Eisenstein polynomials.

This paper focuses on constructing collisions in algebraic hash functions that generalize the Zémor and Tillich-Zémor constructions. It introduces deterministic methods using triangular and diagonal message patterns and analyzes structural weaknesses.

This paper provides a number theoretic framework for constructing LDPC codes with large girth, based on permutation matrices. It relates the criteria for the existence of cycles of a certain length with the concept of Sidon sets to obtain LDPC codes with a certain girth.

This paper formulates a general lower bound for the number of $k$-normal elements in a finite field, assuming they exist. It further derives existence conditions for $k$-normal elements and normal elements in with a non-maximal but high multiplicative order.

This paper explores the computational hardness of conjugacy search in several nonabelian group platforms. It demonstrates some reductions to discrete logarithms or systems of linear modular equations.

This doctoral thesis explores the use of algebraic methods in asymmetric cryptography, presenting new algorithms, cryptographic constructions, and structural cryptanalyses. It covers group-based cryptographic primitives, normal and k-normal elements in finite fields, and attacks on nonabelian protocols. The work unifies theoretical insights with practical relevance in cryptographic design and evaluation.

This Master’s thesis presents an in-depth study of quadratic number fields, focusing on their structure, discriminants, units, and ideal class groups. It explores foundational algebraic number theory results and includes illustrative computations and applications.