| dc.description.abstract | Koblitz [7, 1987] and independently Miller [10, 1986] suggested the use of
the group of points of an elliptic curve de ned over a nite eld Fq. The
main incentive for this suggestion was based on the fact that the discrete
logarithm problem over this group appeared to be quite hard to solve.
The main objective of this dissertation was to understand how the theory of
elliptic curves is applied in the design of cryptosystems. The rst chapter is
an overview of cryptography - the basic fundamental aspects and de nitions
that would be used in later sections. Chapter two is about the theory of
elliptic curves - from the Weierstrass equations to elliptic curves over nite
elds.
In chapter three, we discuss about the applications of the theory of elliptic
curves in public key cryptography before nally discussing about the bilinear
pairings and the MOV attack on the elliptic curve discrete logarithm
problem. | en |
