Abstract:
DES was published by the United States' National Bureau of
Standards in January 1977 as an algorithm to be used for
unclassified data. The algorithm had been used in banks for
funds transfer security [2]. DES encryption was broken in
1999 by Electronics Frontiers Organization. This resulted in
NIST issuing a new directive that year so Triple DES that is
three consecutive applications of DES was appeared but as
DES became unsecured, researchers proposed a variety of
alternative designs, which started to appear in the late 1980s
and early 1990s: examples include RC5, Blowfish and IDEA.
Most of these designs kept the 64-bit block size of DES; DES
itself can be adapted and reused in more secure schemes [3].
In 2001, after an international competition, NIST selected a
new cipher, the Advanced Encryption Standard (AES), as a
replacement. The algorithm which was selected as the AES
was submitted by its designers under the name Rijndael. Other
finalists in the NIST AES competition included RC6 and
Twofish.
In our study, we will go back to the past and try to bring
back DES to life by using elliptic curves which are considered
the simplest possible curves after lines and conics. Elliptic
curves over finite fields provide an inexhaustible supply of
finite abelian groups. Such curves involve elementary