Isabelle D&eacute;ch&egrave;ne (University of Ottawa) <br><br><BR>

<b>Uses of generalized Jacobians in cryptography</b> <BR><BR><BR>
 
Generalized Jacobians are natural candidates 
to use in discrete logarithm (DL) based
cryptography since they include the multiplicative 
group of finite fields, algebraic
tori, elliptic curves as well as Jacobians of hyperelliptic curves.
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This thus led to the study of the simplest nontrivial generalized 
Jacobians of an
elliptic curve, which is an extension (of algebraic 
groups) of the elliptic curve by
the multiplicative group. We will first take a 
look at the arithmetic in these
generalized Jacobians. With explicit 
equations at hand, we then study its discrete
logarithm problem (DLP), which is at the heart of the security of DL-based
cryptosystems.

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No prior knowledge of cryptography will be assumed.