Computational aspects of cryptography and cryptanalysis

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.