This thesis deals with various computational aspects of theoretical and applied cryptology. The theoretical part of this dissertation studies the hardness and relations of cryptographic assumptions in black-box models of computation (black-box groups and rings). This yields partial answers to two longstanding open questions in cryptographic research: We provide evidence towards the equivalence of the Integer Factorization problem and the RSA problem and against the equivalence of the Discrete Logarithm problem and the Diffie-Hellman problem. The second part of this thesis is concerned with the development of novel and highly efficient hard- and software architectures for cryptographic and cryptanalytic applications. In particular, we present powerful hardware-based attacks on the GSM stream ciphers A5/1 and A5/2 as well as efficient architectures for ECDSA and MQ signature schemes.weiterlesen