Abstract: In 1978, Rivest, Shamir and Adleman introduced the public-key cryptosystem RSA. Thereafter, it was extended to Lucas sequences and elliptic curves. This thesis analyses the security of these cryptosystems in given contexts. In particular, all major known attacks against RSA-type systems (including some attacks due to the author) are reviewed. We also see how these attacks can be avoided.
Organization: The thesis is available in one compressed file.
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