|
Organizers |
A Note on Elliptic Curve Based Transformations in Symmetric-Key Cryptography
by
Michele Elia
Politecnico di Torino - Italy
Coauthors: Guglielmo Morgari (Telsy Elettronica - Torino - Italy)
The addition group structure of super-singular elliptic curves
E(F) over a Galois field F=GF(2m)
is used to define a function Q which may be profitably
used in symmetric-key cryptography.
The value u of Q(x) is defined as the abscissa of a point-sum
Q(u, v)=P(X(x), Y(x))+kK(a, b) on
E(F) for all x Î F, where
K(a, b) is a fixed point on E(F),
k is an integer, and P(X(x), Y(x)) is a point on
E(F) which can be inexpensively computed as a
function of x.
A thorough analysis of Q(x) as a function of k, a, and
b shows that many properties of these functions have cryptographic
appeal.
Some examples of applications to symmetric-key encryption are thus
presented, and their cryptographic characteristics investigated.
Date received: October 5, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # carm-15.