Ghada Abdelhady (#289)
Topic of his/her doctorate.
New DES based on Elliptic Curve
AES , block ciphers , complexity theory , cryptanalysis , DES , discrete logarithm problem , elliptic curve cryptosystem , secret-key cryptography , stream ciphers
Year of completion
Elliptic curves (EC) have proved to be a good choice for building asymmetric
encryption system. Also EC has been used to enhance the asymmetric systems
to minimize the secret key such as RSA, Die-Hellman and ElGamal systems.
Although most of the symmetric systems have been broken, we can use EC to
create a new system that has the same properties of the symmetric encryption
systems and at the same time, it has the strength of elliptic curves in encryption.
This work presents a new symmetric algorithm using the Fiestel function and S-
boxes like DES but each stage in this algorithm will be based on the elliptic curves
so we will call it "New DES based on EC".
Without any doubt the Fiestel function is the core of most of symmetric encryp-
tion systems. The symmetric encryption systems are fast and easy to implement
in hardware. Therefore the presented study will try to bring back DES to life by
creating another symmetric system using elliptic curves. Such curves involve ele-
mentary arithmetic operations that make it easy to implement (in either hardware
or software). The proposed system is an analogue to DES i.e. it will be based on
the Fiestel function that includes S-boxes but they will be designed in a different
way using the elliptic curves dened over nite elds that provide an inexhaustible
generation of nite abelian groups.
Our work has been accomplished through three stages that will be explained
in the next chapters. Before starting in building the proposed algorithm, we start
in building the regular DES on MATLAB. The most important points in our
suggested algorithm are: that its key schedule will be generated in a dierent way
from that used in DES. Also the secret key will be increased to more than three
times the key used in the regular DES that will lead to increase the key space of
the new algorithm. Also the block size of our new algorithm will be increased to
double of the block size of the regular DES.
Of course, since the presented system is a new one in the symmetric encryption
systems; this study provides the sucient criteria to measure the eciency of this
new system like the encryption quality measurement, the execution time of the
encryption/decryption algorithms that will lead us to calculate the speed of the
suggested algorithm. Also we will compute the time and space complexity and
apply some statistical analysis on our algorithm.
At the end of this work, we will present a comparison between the regular
DES and the presented new algorithm. A comparison has been conducted for
those encryption algorithms at dierent settings for each algorithm such as the
key size, the key space, block size, speed, security, time and space complexity, and
encryption/decryption execution time.
As AES (Advanced Encryption Standard) and TDES (Triple DES) are the
most widely used symmetric cipher today, so we will compare between the pro-
posed algorithm (new DES based on EC), AES and TDES as benchmarks for our
algorithm. Also we will study some of cryptanalysis techniques like the Strict
Avalanche Criterion (SAC) that is a desirable property of any cryptographic algo-
rithm. Also we will introduce the brute force attack for the suggested algorithm.
Brute force attack is considered as a measure for the quality and the strength of
the cryptographic algorithms.
Building DES algorithm and studying its properties are considered as the base
for the three stages of the suggested algorithm. DES algorithm and its properties
will be discussed in chapter (2) of the thesis.
The rst stage explains the plaintext masking in which we use EC to mask the
plaintext. This step is similar to the algorithm used in ECDLP (Elliptic Curve
Discrete Logarithm Problem) then we will combine DES algorithm and the rst
stage and apply the required criteria to evaluate the resulted encryption system
after adding the rst stage. These items will be discussed in Chapter (3). Also in
this chapter we will demonstrate how to use the elliptic curve equation to generate
the secret key and build the key schedule which is considered the second stage.
Also we will present the performance criteria required to evaluate the resulting
The last stage to accomplish our suggested algorithm is generating the S-boxes
using many elliptic curve equations. That will be presented in Chapter (4). At
the end of this chapter, we will apply the performance criteria required to measure
the efficiency of the whole algorithm. Also we will compare between the proposed
algorithm and AES and TDES according to the criteria mentioned previously. The
last chapter will present a conclusion and the future work.
As a future work, we will be able to get a hybrid system that leverages with the
benefits of symmetric and asymmetric systems i.e. in the future; we can transform
"New DES Based on EC" from a symmetric encryption system to asymmetric
one. Also, we can apply the stages of the new DES algorithm on other symmetric