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Oberseminar SoSe 2010 Zusammenfassung des Vortrags von A. Stein (Oldenburg)

Ellipic Curves and Cryptography - Some (new) attacks to the elliptic curve discrete logarithm problem

In recent years, elliptic curves have become objects of intense investigation because of their significance to public-key cryptography. The major advantage of ECC is that the cryptographic security is believed to grow exponentially with the length of the input parameters. This implies short parameters, short digital signatures, and fast computations. We provide a survey of elliptic curves over finite fields and their interactions with algorithmic number theory. Our main focus will be the discussion of various interesting attacks to the so-called elliptic curve discrete logarithm problem (ECDLP) and their mathematical background as well as their important impact on public-key cryptography.