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In this thesis, we analyze performance gain versus the hardware cost for elliptic and hyperelliptic curve cryptosystems, when a certain amount of special hardware is added to the system.For our implementation, we use a typical embedded processor, the ARM 7TDMI.The circuit uses an efficient transformation from the normal basis into a suitable polynomial basis, and performs polynomial multiplication concurrently with polynomial reduction and the back-transformation into the normal basis in an efficient manner.The transformation circuit uses $n 2\mu(n) \mu(2n)$ XOR gates, and has a propagation delay of \lceil \log_2(n)\rceil$, wherein $n$ is the degree of the field extension over $\F_2$, and $\mu(n)$ is a function that is majorized by $n\log_2(n)$.Recently a new class of collision attacks which was originally suggested by Hans Dobbertin has been introduced.

Our major finding is that the new combined analytical and side channel approach reduces the attack effort compared to all other known side channel attacks.

By taking advantage of the birthday paradox, it is possible to cause a collision in an output with as little as 20 measurements.

Each collision will reveal at least 8 bits of the secret key.

Eines dieser neuen Verfahren ist das MOR System, das auf der Schwierigkeit der Berechnung diskreter Logarithmen in der Gruppe der inneren Automorphismen Inn(G) einer nicht-abelschen Gruppe beruht.

Das MOR System wird zunächst vorgestellt und die Schwierigkeit des Problems der Berechnung diskreter Logarithmen in Inn(G) diskutiert.

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