On the trace based public key cryptosystems over finite fields

Download
index.pdf
2013
Ashraf, Muhammad
Show full item record
200
views
92
downloads
In this thesis, the trace based Public Key Cryptosystems (PKC) are explored from theoretical and implementation point of view. We will introduce cryptographic protocols for the ones they are not discussed yet. We introduce improved trace based exponentiation algorithm for fifth degree recursive relation. The Discrete Log Problem (DLP), that is computing $x$, given $y=\alpha^x$ and $<\alpha>=G\subset \F_q^*$, based Public Key Cryptosystems (PKC) are being studied since late 1970's. Such development of PKC was possible because of the trapdoor function $f:\Z_\ell\rightarrow G=<\alpha>\subset \F_q^*$, $f(m)=\alpha^m$, is a group homomorphism. Due to this fact, we have Diffie Hellman (DH) type key exchange, ElGamal type message encryption, and Nyberg Rueppel type digital signature protocols. The cryptosystems based on the trapdoor $f(m)=\alpha^m$ are well understood and complete. However, there is another trapdoor function $f:\Z_\ell\rightarrow G$, $f(m)\rightarrow Tr(\alpha^m)$, where $G=<\alpha>\subset \F_{q^k}^*,\; k\ge 2$, which needs more attention from cryptographic protocols point of view. There are some works for a more efficient algorithm to compute $f(m)=Tr(\alpha^m)$ and not wondering about the protocols. There are also some works dealing with an efficient algorithm to compute $Tr(\alpha^m)$ as well as discussing the cryptographic protocols. In this thesis these works are studied along with introduction of some protocols which are not discussed earlier and trace based exponentiation for fifth degree recursive relation is improved.
Public key cryptography., Finite element method., Exponential functions., Digital signatures.
http://etd.lib.metu.edu.tr/upload/12616104/index.pdf
https://hdl.handle.net/11511/22836
Graduate School of Applied Mathematics, Thesis

Suggestions

On lattice based digital signature schemes
Javani, Farid; Akyıldız, Ersan; Department of Cryptography (2014)
Lattice based cryptography is one of the few hopes for secure public key cryptography in post quantum era since there is no known polynomial time quantum algorithm that can solve hard lattice problems. But despite this precious property, for a cryptographic construction which is designed based on a hard lattice problem, to be secure, required time and space is not efficient. This has led to introduction of structured lattices that need less time and space; indeed the only existing standard on lattice based ...
An Analysis on efficient polynomial multiplication algorithms for cryptographic purposes
İlter, Murat Burhan; Cenk, Murat; Department of Cryptography (2016)
The idea of Public Key Cryptography showed up after the studies conducted by W. Diffie and M. Hellman in 1976. In the light of these works, RSA, the first Public Key Cryptography algorithm, came into play. In this algorithm, modular exponentiation is highly costly. In addition to this, key sizes of public key cryptography algorithms has become longer in order to ensure the security as the time passes. For these reasons, the speed of algorithms is relatively slower when it is compared to the speed of ones in...
New methods for public key cryptosystems based on XTR
AKLEYLEK, SEDAT; KIRLAR, Barış Bülent (2015-12-01)
In this paper, we propose novel deterministic and probabilistic public key cryptographic schemes based on an effective and compact subgroup trace representation cryptosystem to handle with the problem of secure and efficient communication between the server and resource-constrained device. The proposed schemes use the hardness of the Trace-discrete logarithmic like problem. We also show that the deterministic version of the proposed scheme is a one-way trapdoor, and the probabilistic version of the proposed...
Marked-string accepting observers for the hierarchical and decentralized control of discrete event systems
Schmidt, Klaus Verner (2006-12-01)
The paper extends previous work, where we develop a control theory for nonblocking hierarchical control of decentralized discrete event systems (DES). The results are based on two technical conditions for the hierarchical abstraction: it has to be (i) locally nonblocking and (ii) marked string accepting. In this paper, we investigate the systematic construction of the hierarchical abstraction. Starting from an initial natural projection which need not fulfill (i) and (ii), we provide an algorithm to compute...
A Control System Architecture for Control of Non-Affine in Control, Open-Loop Unstable Underactuated Systems
Marangoz, Alp; Kutay, Ali Türker (2017-07-25)
In this paper, a control system architecture for control of non-affine in control, open-loop unstable underactuated system is discussed. Passivization of the unactuated (internal) system dynamics achieved through perturbation of trajectories of the actuated states, which are calculated through adaptive dynamic inversion technique, based on Tikhonov's theorem. Performance of the controller is shown through simulation of two open-loop unstable and locally uncontrollable example problems.
Citation Formats
M. Ashraf, “On the trace based public key cryptosystems over finite fields,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.
METU IIS - Integrated Information Service open@metu.edu.tr