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Improving Network Security Using Elliptic Curve Cryptosystem
CHAPTER THREE -- [Total Page(s) 8]
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CHAPTER THREE
3.0 METHODOLOGY
3.1 BACKGROUND OF ELLIPTIC CURVE CRYPROGRAPHY
Elliptic curve cryptography provides a methodology for obtaining high-speed, efficient, and scalable implementations of network security protocols. The security of these protocols depends on the difficulty of computing elliptic curve discrete logarithm in the elliptic curve group.
The group operations utilize the arithmetic of points which are elements of the set of solutions of an elliptic curve equation defined over a finite field. The arithmetic of elliptic curve operations depend on the arithmetic on the underlying finite field. The standards suggest the use of GF (p) and GF (2k). Elliptic curves used in cryptography are typically defined over two types of finite fields: the fields of odd characteristics GF(p), where p > 3 is a large prime number and the fields of characteristics two GF(2m) called binary fields . We define our elliptic curve over the field of odd characteristics, If the set of all pairs of affine coordinates (x, y) for x, y ∈ Fq form the affine plane Fq × Fq , the locus of points in the affine plane whose coordinates satisfy is a case of an elliptic curve with a point at infinity O , where characteristic p > 3 and a, b ∈ Fp are constants such that 4a3 + 27b3 =_ & y2 = x3 + ax + b
General equation of Elliptic curve
Other work on the security and implementation of elliptic curve cryptosystems (ECC) was reported by Menezes, Menezes, Okamoto and Vanstone. Some public-key cryptosystems using hyper-elliptic curves were proposed. Hyper-elliptic curve cryptosystems were proposed by Koblitz, but little research has since been done regarding their security and practicality.
ECC can be used for providing the following security services:
1. Confidentiality,
2. Authentication,
3. Data integrity,
4. Non-repudiation,
5. Authenticated key exchange.
The progress in factorization and parallel processing leads to the need of larger and larger keys for public-key cryptosystems. But, the growth of keys length will do these cryptosystems slower than before. The use of ECC allows the increasing of security. In the same time, ECC decreases the overloading. ECC security consists in the difficulty to calculate logarithms in discrete fields (discrete logarithms problem): being given A (an element from a finite field) and Ax, it is practically impossible to calculate x when A is big enough. Actually, there are several cryptosystems which are based on discrete logarithms problem in multiplicative group Z*p. But these cryptosystems can be also defined in any other finite group, as the group of points of an elliptic curve. The elliptic curves are suitable in applications where:
1. The computing power is limited (intelligent cards, wireless devices, PC boards);
2. Memory size on integrated circuit is limited; a great speed of computing is necessary;
3. Digital signing and its verification are used intensively;
4. Signed messages have to be transmitted or memorized;
5. Digital bandwidth is limited (mobile communications, certain computer networks).
3. 2 ADVANTAGES OF ECC
1. Increased security: cryptographic resistance per bit is much greater than those of any public-key cryptosystem known at present time;
2. Substantial economies in calculus and memory needs in comparison with other cryptosystems;
3. Great encryption and signing speed both in software and hardware implementation;
4. ECC are ideal for small size hardware implementation (as intelligent cards)
5. Encryption and signing can be done in separate stages.
The intense research done on public-key cryptosystems, based on elliptic curves, demonstrated that ECC are suitable for the vast majority of existing applications.
An ECC with 160-bit key offers a security level equivalent with that offered by a cryptosystem based on a 1024-bit Zp field .Because of this, ECC provide a feasible method of implementation for a high level Security System on a PC card, on an intelligent card or on a mobile communications device.
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ABSRACT - [ Total Page(s): 1 ]ABSTRACTSecuring a network wired or wireless for network administrator has been a big challenges for network administrators in the present day of Internet usage. This project presents ECDSA Cryptosystem as a solution to the problem been faced by network administrators and Engineers. The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA) with the attractiveness that there is no sub exponential algorithm known to solve the ell ... Continue reading---
TABLE OF CONTENTS - [ Total Page(s): 1 ]TABLE OF CONTENTTittle Page Declaration Certification Dedication Acknowledgements Abstract Tables of contents Table of Content1.0 CHAPTER ONE (INTRODUCTION)1.1 BACKGROUND TO THE WORK 1.2 PROBLEM DEFINITION 1.3 PROJECT JUSTIFICATION 1.4 OBJECTIVES 2.0 CHAPTER TWO (LITERATURE REVIEW)2.1 NETWORK SECURITY 2.2 CHARACTERISTICS OF NETWORK SECURITY 2.3 MAIN THREATS TO NETWORK S ... Continue reading---
CHAPTER ONE - [ Total Page(s): 2 ]CHAPTER ONE1.0 INTRODUCTION1.1 BACKGROUND TO THE WORKThe fast development of the modern Internet technology and information technology cause the individual, enterprise, school and government department joining the Internet, Which cause more illegal users to attack and destroy the network by using the fake websites, fake mail, Trojan horse and backdoor virus at the same time. The target of the attacks and intrusion on the network are computers, so once the intruders succeed, it will c ... Continue reading---
CHAPTER TWO - [ Total Page(s): 11 ]Simple packet filters selectively controls the flow of packets in/out of a network or between networks. Control is based and enforced through a series of rules. These rules are based on information stored in the IP and TCP/UDP/ICMP headers.Rule criteria can be based on the following characteristics of the IP packet:➢ Source and/or destination addresses➢ Protocol including TCP, UDP, ICMP, or all IP➢ TCP or UDP source and/or destination ports➢ ICMP messa ... Continue reading---
CHAPTER FOUR - [ Total Page(s): 10 ]Step 3: verifying the signatureAt this stage the program try to verify the signature weather it’s correct or not. It will display VALID or INVALID to ascertain the validity.Result:The result above what gotten using Secp256kr1 algorithm as shown above, the private and public key was gotten based on previous work inculcated into the database for the key generation and FRANCIS was used as the message string in other to get a signature value. ... Continue reading---
CHAPTER FIVE - [ Total Page(s): 1 ]CHAPTER FIVESUMMARY, CONCLUSION, AND RECOMMENDATIONElliptic Curve Digital Signature Algorithm (ECDSA) which is one of the variants of Elliptic Curve Cryptography (ECC) proposed as an alternative to established public key systems such as Digital Signature Algorithm (DSA) and Rivest Shamir Adleman (RSA), have recently gained a lot of attention in industry and academia.The main reason for the attractiveness of ECDSA is the fact that there is no sub exponential algorith known to solve the elliptic c ... Continue reading---
