Algebraic curves have a broad range of application in cryptology: on the one hand, elliptic and hyperelliptic curve cryptosystems are increasingly employed as public-key cryptosystems. On the other hand, cryptanalytical alorithms for attacking cryptosystems utilize algebraic curves. Examples include the elliptic curve method for solving the Factorization Problem (FP) or PollardÄs Rho method for solving the Elliptic Curve Discrete Logarithm Problem (ECDLP). With this thesis, we contribute to both aspects of cryptology. We present algorithmic improvements in the field of cryptography, namely for Hyperelliptic Curve Cryptosystems. In the field of cryptanalysis, we propose different hardware architectures for cryptanalytical algorithms, resulting in a security evaluation of particular symmetric and asymmetric cryptosystems against attacks with special-purpose hardware. Our implementations in software as well as in hardware form the basis for such an analysis und stress the paramount importance of an efficient implementation or arithmetic primitives regarding the overall performance of cryptologic algorithms. In addition, we present the concept and realization of a cost-optimized and reprogrammable code-breaker which is based on contemporary low-cost FPGAs.weiterlesen