Free Essay

Submitted By chaitumart

Words 7761

Pages 32

Words 7761

Pages 32

A B.Tech Project Report submitted in fulfilment of the requirements for the Degree of Bachelor of Technology Submitted by K Bharadwaj Sharma 07010219 M Krishna Chaitanya 07010228 Under the Guidance of Dr.Ratnajit Bhattacharjee

Department of Electronics and Electrical Engineering Indian Institute of Technology Guwahati Guwahati-781039, Assam

i

Candidate’s Declaration

I hereby declare that the work which is being reported in this thesis entitled “ On Implementation of Elliptic Curve Cryptography and self-certified public key cryptosystems in Wireless Mesh Networks “ in partial fulfilment of the requirements for the award of the Degree of Bachelor of Technology, submitted in the Department of Electronics and Communication Engineering, Indian Institute of Technology Guwahati, is a record of my own work carried out during my thesis work under the supervision of Dr.Ratnajit Bhattacharjee, Associate Professor, Department of EEE, IIT Guwahati. The matter entitled in this thesis has not been submitted elsewhere for the award of any other degree.

Place: Guwahati Date: 21st April, 2011 This is to certify that the above statement made by the candidate is correct to the best of my knowledge.

April,2011 IIT Guwahati

`

Supervisor: Dr. Ratnajit Bhattacharjee Associate Professor

Dept. of EEE IIT Guwahati

ii

ACKNOWLEDGEMENT

First and foremost, I would like to take this opportunity to express my deepest and sincere gratitude to my thesis supervisor, Dr. Ratnajit Bhattacharjee. I value the freedom he gave me to carry out research in the field of my interest and I sincerely thank him for that. His stimulating suggestions and encouragement helped me in the time of research and writing of this thesis. I am very much thankful to him for his continuos help and support during entire thesis. Finally, I would like to thank my parents, siblings and friends for their immense love and support during my entire student life.

iii

Abstract

We consider wireless mesh networks where the main challenge in design of these networks is their vulnerability to security attacks. As WMN has memory and computational constraints, the traditional schemes for achieving security are not applicable. This report discusses how Elliptic Curve Cryptography (ECC) can be used in providing security features in a Wireless Mesh Networks (WMN). WMN is an architecture which is becoming increasingly popular. It does not have the security features well developed as in WLAN. Since such mesh network contains a large number of wireless transceivers cryptographic protocols which can provide energy efficiency and small key size is a desirable feature. Recently ECC is being investigated as it promises these features. This report then discusses about an efficient Elliptic Curve Cryptography (ECC)based self-certified public key cryptosystem (ECCSCPKC) and why it is considered to be an efficient authentication and key agreement (AKA) scheme to provide fundamental user authentication and transmission confidentiality services in a Wireless Mesh Network. ECCSCPKC is constructed based on elliptic curve cryptosystems (ECC) and the ID-based self-certified public key cryptosystems. It also discusses about related security schemes constructed using proposed ECCSCPKC: the Identification scheme, the session key exchange scheme, the encryption-decryption scheme, the digital signature scheme and the authenticated encryption scheme.

iv

Contents

Abstract ………………………………………………………………………………………………… iv List of figures ………………………………………………………………………………………… 1 List of Tables …………………………………………………………………………………………. 2 1. Introduction ………………………………………………………………………………….. 1.1 Background…………………………………………………………………………… 1.2 Thesis Objective……………………………………………………………………. 1.3 Literature Review…………………………………………………………………. 3 3 6 7

2.

Elliptic Curve Cryptography …………………………………………………………… 2.1 Background…………………………………………………………………………… 2.2 Operations on Elliptic Curves ……………………………………………….. 2.2.1 Point Addition ……………………………………………………………………. 2.2.2 Point Multiplication ……………………………………………………………. 2.3 Elliptic Curve Discrete Logarithm Problem …………………………..

8 8 9 9 9 9

3.

Elliptic Curves ………………………………………………………………………………. 3.1 Elliptic Curves over finite field …………………………………………….. 3.2 Elliptic Curves over prime field ……………………………………………. 3.3 Domain parameters of elliptic curves ………………………………….

11 11 11 12

4.

Benefits of Elliptic Curve Cryptography ……………………………………… 13

v

5.

ECC based schemes ……………………………………………………………………….. 5.1 Elliptic Curve Encryption and Decryption Scheme …………………. 5.2 Elliptic Curve Key Agreement Scheme …………………………………… 5.3 Results and Analysis ………………………………………………………………

15 15 16 16

6.

Elliptic Curve Cryptography – based Self – Certified Public key Cryptosystem (ECCSCPKC) ……………………………………………………………………………………... 21 6.1 Background …………………………………………………………………………….. 21 6.2 Proposed scheme of ECCSCPKC ……………………………………………….. 22

7.

ECCSCPKC based schemes …………………………………………………………………. 7.1 The Identification scheme ……………………………………………………….. 7.2 The session key exchange scheme …………………………………………… 7.2.1 Time-invariant session key exchange ……………………………………. 7.2.2 Time-variant session key exchange ………………………………………. 7.3 The Encryption-Decryption scheme ………………………………………… 7.3.1 Encryption ……………………………………………………………………………. 7.3.2 Decryption …………………………………………………………………………… 7.4 The Digital signature scheme …………………………………………………. 7.4.1 Signature generation …………………………………………………………… 7.4.2 Signature verification ………………………………………………………….

24 24 25 25 25 26 26 26 27 27 27

8.

Analysis of ECCSCPKC …………………………………………………………………….. 8.1 Benefits …………………………………………………………………………………. 8.2 Security features ……………………………………………………………………. 8.2.1 Security of secret keys …………………………………………………………. 8.2.2 Security against active attacks ……………………………………………… 8.2.3 Security of related security schemes ……………………………………. 8.3 Results of the proposed schemes …………………………………………… vi

28 28 28 29 29 30 31

9.

Conclusion and Discussion ……………………………………………………………… 37

Bibliography ……………………………………………………………………………………………. 38

vii

List of figures

1.1 A typical WMN architecture…………………………………………………………………….. 4

2.3 Elliptic Curve showing the operation P + Q = R …………………………………………. 10

5.3 Elliptic group…………………………………………………………………………………………….. 17 5.3 Encryption of a message using elliptic curve …………………………………………….. 18 5.3 Decryption of an encrypted message ……………………………………………………….. 19 5.3 Key Agreement between two users for a shared secret key ……………………… 20

8.3 User registration scheme …………………………………………………………………………. 32 8.3 Identification scheme ………………………………………………………………………………. 33 8.3 Session key exchange scheme …………………………………………………………………. 34 8.3 Encryption/Decryption scheme ……………………………………………………………….. 35 8.3 Digital Signature scheme …………………………………………………………………………. 36

1

List of Tables

Table 1. Comparison of strength of RSA and ECC …………………………………………… 14

2

Chapter 1 Introduction

1.1 Background

Wireless Mesh Network (WMN) is a new wireless networking paradigm. WMN is a promising technology for numerous applications such as broadband home networking, community networks. This technology allows a fast, easy and inexpensive network deployment. It is characterized by dynamic self-organization, self-configuration and self-healing to enable flexible integration, quick deployment, easy maintenance, low costs, high scalability, and reliable services [8]. WMN is a wireless co-operative communication infrastructure between large amounts of individual wireless transceivers .The infrastructure is decentralized, as each node need only transmit as far as the next node. Nodes act as repeaters to transmit data from nearby nodes to nodes that are too far away to reach, resulting in a network that can span large distances. Typical wireless mesh networks consist of mesh routers and mesh clients. Mesh routers, which are static and power-enabled, forms a wireless backbone of the WMNs. Mesh clients access the network through mesh routers. They can also directly mesh with each other. The main constraints in mesh clients are large computations on nodes are slow, as computing power of the processor is small and total energy resource is very limited and it is not desirable for large computations and transmissions. The main challenge in design of these networks is their vulnerability to security attacks [4]. Their security is easily compromised due to the distributed network architecture, the vulnerability of channels and nodes in the shared wireless medium, and the dynamic change of network topology. As WMN has memory and computational constraints, the traditional schemes for achieving security are not applicable. However, Elliptic Curve Cryptography[11] provides energy and 3

computation efficient techniques in implementing cryptographic algorithm, which can be suitable for mesh clients. WMN infrastructure consists of mesh routers and mesh clients, where mesh routers have minimal mobility and form the backbone of WMN. Fig. shows most a typical architecture of WMN in a community network.

There are many security issues, challenges and requirements of WMNs.The issues of user authentication,acces control as well as transmission confidentiality are extremely fundamental in security.The authentication and key agreement between two entities is the crucial issue. Public key cryptosystems are vulnerable to active attacks,such as attempts to modify a genuine public key by a fake one during key distribution.The most widely adopted solution to this is for a cerification authority(CA) to provide authenticated public keys.The certificate-based approach requires an extra public key issued by cerification authority (CA) after user registration.In this approach,anyone that wants to use a public key for certain subsequent cryptographic application(e.g, key exchange) should independently perform public key verification and subsequent cryptographic application through two separate steps.Another approach to generate authenticated public keys is known as the ID-based public key cryptosystem.This approach employs the user’s identity as his/her public key and hence need no extra public key certificate and 4

no verification of signatures which can reduce amount of storage,communication and computation.Although ID-based approach effectively solves the problem of public key verification for practical usage,its security disadvantage is that CA knows all user’s secret keys after user registration.Therefore,the CA my have the opportunity to masquerade as any legitimate user by generating a valid publickey/secret-key pair for the user without being detected. To resolve the problem of public key verification,a self-certified public key system was proposed in [22].A self-certified public key system has three features: First, the secret key can be determined by the user himself/herself or together by the user and CA, and does not be known to CA. Second,the user can use his/her own secret key to verify the authenticity of the self-certified public key issued by CA, and thus no extra certificate is required.Third, the task of public key verification can be further accomplished with subsequent cryptographic application in a logically single step. Therefore, public key verification of the self-certified approach earns more efficiency in saving the communicational cost and the computational effort as compared to that of the certificate-based approaches. The implemented ECCSCPKC is constructed based on the elliptic curve cryptosystems (ECC) and the ID-based self-certified public key cryptosystems.ECCSCPKC and its related security schemes can gain much efficiency in saving both the communicational cost and the computational effort via simplifying the public key distribution.Also,the cost of system maintanence can be greatly reduced without the need of managing the key directory.Therefore,it is quite suitable for the devices with inadequate memory space,limited computing power and low bandwidth which are features of wireless mesh networks. In this report, we discuss about ECCSCPKC to construct WMN security infrastructure.The implemented scheme is efficient in both communication and computation, resistant to some common attacks (e.g., impersonation and replay), as well as easy to maintain. Then, we discuss about related security schemes constructed using implemented ECCSCPKC: the Identification scheme, the session 5

key exchange scheme, the encryption-decryption scheme, the digital signature scheme and the authenticated encryption scheme.

1.2 Thesis Objective

The main objective of this thesis is to study and analyse how Elliptic Curve Cryptography (ECC) can be used in providing energy and computation efficient techniques in implementing cryptographic algorithms, which can be suitable for wireless mesh networks and implement various security schemes based on ECC. With this in mind, this thesis investigates the following:

i. Compare and analyse the advantages of elliptic curve cryptography compared to other cryptographic schemes. Here we have considered key sizes of various cryptographic schemes for same security strength. ii. Investigate the benefits of elliptic curve cryptography in memory and computationally constrained environments. Here, the key sizes are considered to be of equivalent strength based on Million Instructions per second (MIPS) years needed to recover one key. iii. Implement basic encryption-decryption algorithm and key agreement schemes using Elliptic Curve Cryptography. The security of these schemes depend on the difficulty of elliptic curve discrete logarithm problem(ECDLP). iv. Construct and implement several security schemes using ECC-based selfcertified public key cryptosystems. It is ID-based self-certified public key distribution.

6

1.3 Literature Review

The vulnerability to security attacks has been the main challenge for wireless mesh networks. As WMN has memory and computational constraints, the traditional schemes for achieving security are not applicable. However, Elliptic Curve Cryptography [11] provides energy and computation efficient techniques in implementing cryptographic algorithms. Dr. R.Shanmugalakshmi and M.Prabu [3] have discussed about the comparison between ECC and other cryptography algorithms. ECC is a kind of public key cryptosystem. But it differs in its quicker evolving capacity and by providing attractive and alternative way to researchers of cryptographic algorithm. The security level which is given by others, can be provided even by smaller keys of ECC. Zia Xiangya , Wang Chao [12] have analysed on elliptic curve discrete logarithm problem , on which the security of ECC depends.The main operation involved in ECC is point multiplication and it is computationally infeasible to obtain the scalar Involved between two points. Shamir[20] proposed ID-based public key cryptosystems. In this approach employs the user’s identity as his/her public key, and hence needs no extra public key certificate which can reduce the amount of storage, communication and computation. But its security disadvantage is that certification authority(CA) knows all users secret keys after user registration. In 1991, Girault [21] proposed a self-certified public key system to resolve the problem of public key verification. In this the secret key can be determined by the user himself/herself and does not be known to CA. The user can use his/her own secret key to verify the authenticity of the self-certified public key issued by CA.

7

Chapter 2 Elliptic Curve Cryptography

2.1 Background

Elliptic Curve Cryptography is an approach to public-key cryptography, based on elliptic curves over finite fields. The technique was first proposed individually by Neal Koblitz and Victor Miller in 1985. It differs from RSA in its quicker evolving capacity and by providing attractive and alternative way to researchers of cryptographic algorithm. The security level which is given by RSA, can be provided even by smaller keys of ECC. For example, the 1024 bit security strength of a RSA could be offered by 163 bit security strength of ECC [3].The ECC is based on the Elliptic Curve Discrete Logarithm problem. An elliptic curve is defined by:

Where ‘a’ and ‘b’ take real values. The mathematical operations of ECC is defined over the elliptic curve (1), with 4a3 + 27b2 ≠ 0. Each value of the ‘a’ and ‘b’ gives a different elliptic curve. All points (x, y) which satisfies the above equation plus a point at infinity lies on the elliptic curve. The public key is a point in the curve and the private key is a random number. The public key is obtained by multiplying the private key with the generator point G in the curve. The generator point G, the curve parameters ‘a’ and ‘b’, together with few more constants constitutes the domain parameter of ECC.

y 2 = x 3 + ax + b

(1)

8

2.2 Operations on Elliptic Curves

The addition and multiplication operations on elliptic curves are performed geometrically in a different manner than the arithmetic addition and multiplication operations. 2.2.1 Point Addition If P(XP,YP) and Q(XQ,YQ) are points on the elliptic curve and if - XP ≠ XQ (equally P ≠-Q), then, R(XR, YR) = P+ Q can be defined geometrically. In the case P ≠Q, a line intersecting the curve at the points P and Q must also intersect the curve at a third point -R, and R(XR, YR) is the answer, if P=Q (point doubling),the tangent line is used. X R = s2 - X P - XQ YR = -YP + s(XP - XR) s is the slope of the line through P and Q. (2) (3)

(4) XR = s2 – 2XP YR = -YP + s(XP - XR) (5) 2 And s is the tangent on the point P i.e., s = (3XP + a) / (2YP ) for the case where P=Q. 2.2.2 Point Multiplication A point P on the elliptic curve is multiplied with a scalar k using elliptic curve equation to obtain another point Q on the same elliptic curve by repeated addition.

Q= kP= P+P+....+P. (k times addition)[14]

2.3 Elliptic Curve Discrete Logarithm Problem

The security of ECC depends on the difficulty of Elliptic Curve Discrete Logarithm Problem. Let P and Q be two points on an elliptic curve such that kP = Q, where k is a scalar. Given P and Q, it is computationally infeasible to obtain k, if k is sufficiently large. k is the discrete logarithm of Q to the base P. 9

Hence the main operation involved in ECC is point multiplication i.e. multiplication of a scalar k with any point P on the curve to obtain another point Q on the curve[12][13].

Figure 2: Elliptic curve showing the operation P+Q = R

10

Chapter 3 Elliptic Curves

3.1 Elliptic Curves over Finite fields

The elliptic curve [2] operations defined above are on real numbers. Operations over the real numbers are slow and inaccurate due to round-off error. Cryptographic operations need to be faster and accurate. To make operations on elliptic curve accurate and more efficient, the curve cryptography is defined over finite fields. • Prime field ������������������������ and • Binary field F2������������ The field is chosen with finitely large number of points suited for cryptographic operations. The operations in these sections are defined on affine coordinate system. Affine coordinate system is the normal coordinate system that we are familiar with in which each point in the coordinate system is represented by the vector (x, y). An elliptic group over the Prime Field[1] Ep(a, b) is obtained by computing ������������ 2 mod p = x 3 + ax + b mod p for 0 ≤ x < p. The constants a and b are non negative integers smaller than the prime number p and must satisfy the condition: 4a3 + 27b2 mod p ≠ 0. Here the elements of the finite field are integers between 0 and p – 1. The prime number p is chosen such that there is finitely large number of points on the elliptic curve to make the cryptosystem secure. The graph for this elliptic curve equation is not a smooth curve. Hence the geometrical explanation of point 11

3.2 Elliptic Curves on Prime Field Fp

addition and doubling as in real numbers will not work here. However, the algebraic rules for point addition and point doubling can be adapted for elliptic curves over Fp. For each value of x, one needs to determine whether or not in it a quadratic residue. If it is the case, then there are two values in the elliptic group. If not, then the point is not in the elliptic group Ep(a, b). For addition to be well defined for any two points, we need to include an extra zero point 0, which does not satisfy the elliptic curve equation. 0 is taken to be a point of the curve. The order of the curve is the number of distinct points on the curve, including the zero point .

3.3 Domain parameters for EC over Prime field Fp

The domain parameters[2] for Elliptic curve over Fp are p, a, b, G and n. p is the prime number defined for finite field Fp. a and b are the parameters defining the curve y 2 mod p= x 3 + ax + b mod p. G is the generator point (xG , yG ), a point on the elliptic curve chosen for cryptographic operations. n is the order of the elliptic curve. The scalar for point multiplication is chosen as a number between 0 and n – 1[1].

12

Chapter 4 Benefits of ECC

ECC has same security strength as other cryptographic schemes for a smaller key size. The benefits of this higher-strength per-bit are • Higher speeds • Lower power consumption • Bandwidth savings • Storage efficiencies and • Smaller Certificates The result is that ECC is especially well suited for constrained environments. ECC’s inverse operation gets harder, faster[10] against increasing key length than do the inverse operations in Diffie-Hellman and RSA. Moreover as security requirements increase, ECC can be implemented with much smaller key size compared to other cryptographic schemes. The advantage ECC has over RSA is that the basic operation in ECC is point addition, which is known to be computationally very expensive. This is one of the reasons why it is very unlikely that a general sub-exponential attack on ECC will be discovered. On the other hand, RSA already has a known sub-exponential attack which works in general [5]. Table below compares the key sizes needed for equivalent strength security in ECC with RSA. Given the best known algorithms to factor integers for RSA and compute elliptic curve logarithms for ECC, the key sizes are considered to be of equivalent strength based on Million Instructions per second(MIPS) years needed to recover one key. It can be observed that as the requirement of security strength increases ECC key size becomes much smaller compared to RSA.

13

Time to break in RSA key ECC key RSA/ECC key MIPS years size size size 104 512 106 5:1 1020 1078 1011 108 768 132 6:1 1024 2048 21000 160 210 600 7:1 10 : 1 35 : 1

Source: NIST Guidelines for Public Key Sizes with Equivalent Security Levels

Table 1: Comparision of strength of RSA and ECC

Security is not the only attractive feature of elliptic curve cryptography. Elliptic curve cryptosystems also are more computationally efficient than the RSA and Diffie-Hellman. Although elliptic curve arithmetic is slightly more complex per bit than either RSA or DH arithmetic, the added strength per bit more than makes up for any extra compute time. Closely related to the key size of different public key systems is the channel overhead required to perform key exchanges and digital signatures on a communication link. The key sizes for public key in Table (above) is also roughly the number of bits that need to be transmitted each way over a communications channel for a key exchange. In channel-constrained environments, elliptic curves offer a much better solution Diffie-Hellman and RSA [9].

14

Chapter 5 ECC based Schemes - Algorithms

We have implemented encryption-decryption and key agreement schemes using Elliptic Curve Cryptography. These schemes have been implemented using the following algorithms.

5.1 Elliptic Curve Encryption and Decryption Algorithm

Elliptic curve cryptography can be used to encrypt plaintext messages, M, into cipher texts. The plaintext message M is encoded into a point PM form the finite set of points in the elliptic group, Ep(a, b). The first step consists in choosing a generator point, G ∈ Ep(a, b), such that the smallest value of n such that nG = O is a very large prime number. The elliptic group Ep(a, b) and the generator point G are made public. Each user selects a private key, nA < n and computes the public key PA as: PA = nA G. To encrypt the message point PM for Bob (B), Alice (A) choses a random integer k and compute the cipher text pair of points PC using Bob’s public key PB : PC = [(kG), (PM + kPB )] (6) After receiving the cipher text pair of points, PC , Bob multiplies the first point, (kG) with his private key, nB , and then adds the result to the second point in the cipher text pair of points, (PM + kPB ): (PM + kPB ) − [nB (kG)] = (PM + knB G) − [nB (kG)] = PM (7)

which is the plaintext point, corresponding to the plaintext message M. Only Bob, knowing the private key, nB , can remove , nB (kG) from the second point of the cipher text pair of point, i.e. (PM + kPB ), and hence retrieve the plaintext information PM [7]. 15

5.2 ECC key agreement Algorithm

It is a key agreement protocol that allows two parties to establish a shared secret key that can be used for private key algorithms. Both parties exchange some public information to each other. Using this public data and their own private data these parties calculate the shared secret. Any third party, who doesn’t have access to the private details of each device, will not be able to calculate the shared secret from the available public information. For generating a shared secret between A and B using ECDH, both have to agree up on Elliptic Curve domain parameters. Both end have a key pair consisting of a private key d and a public key Q = d * G (G is the generator point). Let (dA , Q A ) be the private key - public key pair of A and (dB , Q B ) be the private key - public key pair of B. • • • • The end A computes K = (xK , yK ) = dA * Q B . The end B computes L = (xL , yL ) = dB * Q A . Since dA Q B = dA dB G = dB dA G = dB Q A . Therefore K = L. Hence K is the shared secret key.

Since it is practically impossible to find the private key dA or dB from the public key K or L, it is not possible to obtain the shared secret for a third party[2].

5.3 Results and Analysis

The finite field generated for elliptic curve in (1) with a=1 and b=1 choosing the prime number p = 263.Points on the curve i.e., the group elements are given in the following figure.It can be noted that the size of elliptic curve is 259 which is the number of points in the elliptic group.

16

Fig.3 The field generated for elliptic curve in (1).

17

Fig.4 Encryption of a message using elliptic curve with above domain parameters

18

Fig.5 Decryption of the encrypted message

19

Fig.6 The key agreement between two users for generating a shared secret key using ECC.

20

Chapter 6 Elliptic Curve Cryptography-based selfcertified public key Cryptosystem (ECCSCPKC)

6.1 Background

In earlier sections, we have discussed ECCSCPKC scheme. In the current section and two subsequent sections, we discuss the implementation of such schemes. Minor modifications of the original proposal are also been made. Operational procedures of the implemented ECCSCPKC are divided in to two phases: system setup and user registration. At the system setup phase, certification authority(CA) defines system parameters and generates a secret/public key pair that will be used to generate self-certified public keys for the registering users dueing the registration phase, the registering user prepares an identitity information (example: username, IP address or other personal related information), randomly chooses a master key,and then submits the identity information and the master key (protected by a zero-knowledge proof) to CA for public key generation.The zero-knowledge proof (ZKP) can be easily established by an ECC function where computing elliptic curve discrete logarithm over ﬁnite ﬁeld is computationally infeasible [15,16,17]. With the usage of a ZKP originated by the registering user, CA does not know the user’s master key during user registration and hence has no opportunity to masquerade as that user in later time.According to the submitted identity information and the protected master key,CA will return as elf-certiﬁed public key and a witness for the public key to the registering user.Thereafter,the registering user can use his/her master key to derive a secret key from the witness issued by CA.Meanwhile, he/she can use the derived secret key to verify the authenticity of the public key issued by CA.Here, the derived secret key and 21

the self-certiﬁed public key can be used as the decryption/encryption or the signature generation/veriﬁcation key-pair in the subsequent cipher text generation or digital signature application.

6.2 Implemented scheme of ECCSCPKC

The system setup and user registration phases of the implemented ECCSCPKC[18] are described in detail in the following:

The system setup phase

CA deﬁnes system parameters as follows: (1) p: a ﬁeld size,where p is typically either an odd prime or a power of 2 in general applications, and its length is about 160bits. (2) An elliptic curve E over Fp: E: y2= x3+ ax + b, where the two ﬁeld elements a,b ϶ Fp and 4a3+27b2 ≠ 0(mod p), and all the points (x,y),x ϶ Fp, y ϶ Fp,on E form the set of E(Fp) containing a point O called the point at inﬁnity. (3) B: a base point of order n over E(Fp),where n is a large prime (160bits) and the number of Fp-rational points on E denoted by #E(Fp), is divisible by n. (4) sSA: CA’s secret key, where sSA ϶ [2,n -2]. (5) PSA:CA’s public key, where PSA = sSA.B (“.” Means the multiplication of a number and an elliptic curve point). (6) h( ): a one-way hash function that accepts a variable length input and produces a ﬁxed length output value j,where j ϶ [2, n - 2] and its length is 160bits. The one-way hash function h should satisfy the properties [10] that given h(x),it is computationally infeasible to ﬁnd x1≠ x such that h(x1)= h(x), meanwhile , h(x1) ≠ h(x) if and only if x1≠ x . After that , CA publishes E, B, p, n, PSA and h,while keeping sSA secret.

The user registration phase

Suppose that a user Ui wants to register with CA.The procedure for user registration is stated below: Step1.Ui executes the following tasks: 22

(1.1)Select an identity information,denotedby Ii. (1.2)Randomly choose an integer xi ϶ [2, n -2] as the master key. (1.3)Compute (8) V i = h(xi||Ii). B. (1.4)Submit {Ii,Vi} to CA. Step2. CA executes the following tasks: (2.1)Randomly choose a time-variant integer ki ϶ [2, n - 2]. (2.2)Compute a public key Pi and its witness wi for Ui, where Pi = V i + ( ki – h( Ii ) . B = ( Pix , Piy ), wi = ki + sSA . ( Pi + h( Ii ) ) . (2.3) Return {Pi,wi} to Ui. Step3.Ui then executes thefollowing tasks: (3.1)Derive a secret key si as si = wi + h( xi ||Ii ) . (3.2) Verify the authenticity of Pi by testing if si . B = Pi + h ( Ii ) . B + [ ( Pix + h( Ii )) ] . PSA . (12) (11) (9) (10)

At the user registration stage ,the registering user uses a hashed-based ECC function,which acts as ZKP, to protect his/her master key xi during transmission. One may notice that diﬀerent registering users mayc hoose the same xi as their master keys, however ,they donot evenknow that they possess the same master key. From eq. (11), it can be seen that the derived secret key si is cooperatively determined by Ui (contributing the master key xi) and CA (contributing the witness wi); however, CA does not know si during the user registration phase. The secret key si (derivedby Ui)and the public key Pi (issued by CA) satisfy Eq. (12).

23

Chapter 7 ECCSCPKC based schemes

7.1 The identiﬁcation scheme

Alice proves to Bob her identity with the help of the identiﬁcation scheme as follows: Step1. Alice sends toBob her identiﬁcation information Ia and public key Pa. Step2. Bob computes Va = Pa + h( Ia ) . B + [ ( Pax + h( Ia ) ) ] . PSA . Step3. Alice randomly chooses an integer ra ϶ [2,n - 2] to compute T a = ra . B And then transmits Ta to Bob. Step4. Bob randomly chooses an integer x ϶ [2,n - 2], and returns it to Alice. Step5. Alice uses her secret key sa to compute ya = r a + s a . x and sends it to Bob. Step6. Bob veriﬁes Alice’s identity by testing if ya . B -x . V a = T a 24 (16) (15) (14) (13)

If the correspondence holds, then Bob accepts the identity Alice claims; otherwise, he rejects her claim. The prover Alice can convince the veriﬁer Bob of her identity by using Eq. (16).

7.2 The session key exchange schemes

The session key exchange schemes between Alice and Bob, including the timeinvariant and time-variant session key exchange.The time-invariant session key exchange means that the session key generated for each session is always unchanged; however, the time-variant one indicates that the session key generated for each session is always distinct. 7.2.1 Time-invariant session key exchange (1)Alice sends her identity information Ia and public key Pa to Bob. (2)Bob returns his identity information Ib and public key Pb to Alice. (3)Alice computes the session key(SK) shared with Bob as follows: (17) V b = Pb + h( Ib ) . B + [ Pax + h( Ia ) ] . PSA SK = sb . V a = ( sa sb ) . B (4)Bob computes the SK shared with Alice as follows: V a = Pa + h ( Ia ) . B + [ Pax + h( Ia ) ] . PSA SK = sb . Va = ( sb sa ) . B 7.2.2 Time-variant session key exchange (1)Alice randomly chooses an integer xa ϶ [2, n - 2] to compute Ta = x a . B , (21) and sends Ia,Pa and Ta to Bob. (2)Bob also randomly chooses an integer xb ϶ [2, n - 2]to compute Tb = x b . B , 25 (22) (19) (20) (18)

And returns Ib,Pb, and Tb to Alice. (3)Alice computes the session key (SK) shared with Bob as follows: V b = Pb + h( Ib ) . B + [ Pbx + h( Ib ) ] . PSA SK = xa . Vb + sa . T b = ( xa sb ) . B + ( sa xb ) . B (4)Bob computes the session key (SK) shared with Alice as follows: V a = Pa + h( Ia ) . B + [ Pax + h( Ia ) ] . PSA SK = xb . Va + sb . T a = ( xb sa ) . B + ( sb xa ) . B (25) (26) (23) (24)

7.3 The encryption/decryption scheme

The notations used in this scheme explained are: M : a message to be encrypted, Uj: encrypter, Ui: decrypter. 7.3.1 Encryption (1)Uj ﬁrst transforms M in to a point (mx,my) on the Ellipticcurve E [4] (2)Uj randomly chooses an integer w ϶ [2,n - 2], and computes Vi, C1, and C2 as follows: (27) V i = Pi + h( Ii ) . B + [ Pix + h( Ii ) ] . PSA C1 = w . B (28) (29) C2 = M + w . V I (3) Uj transmits cipher text C1 and C2 to Ui 7.3.2 Decryption (1) Ui obtains cipher text C1 and C2 from a public channel (2) Ui computes the following to recover M: C2 - si . C1 = M + w . Vi- ( wsi ) . B = M + ( wsi ) . B- ( wsi ) . B = M

(30)

26

7.4 The digital signature scheme

The notations used in this scheme explained are: M : a message to be signed, Ua: signer, Ub: veriﬁer. 7.4.1 Signature generation (1) Ua randomly chooses a time-variant integer k ϶ [2,n - 2], and computes (31) k .B = (Xa,Ya) (2) Ua computes r = Xa (32) (33) (3) Ua computes s = k + sa . h( M || r) (4) Ua transmits the signature (r, s) and M to Ub 7.4.2 Signature veriﬁcation (1) Ub computes Va = Pa + h( Ia ) . B + [ Pax + h(Ia )] . PSA and s . B - Va . h( M || r ) = k . B + ( sa h( M || r ) ).B – ( sa .B ).h( M || r ) = k . B = ( x1 , y1 ) (2) If x1 = r holds, then the signature is valid.

(34) (35)

27

Chapter 8 Analysis of ECCSCPKC

8.1 Benefits of ECCSCPKC

ECCSCPKC possess the following advantages: 1. When verifying the validity of public key, it does not need to spend extra much time to verify the signature in the digital certificate used in the certificate-based public key cryptosystem. 2. Both distributing a session key and verifying the validity of public key can be concurrently achieved in a logically single step. 3. Verifying both a signature and the validity of public key can be concurrently accomplished in a logically single step. 4. Both decrypting a cipher correctly and verifying the validity of public key can be concurrently finished in a logically single step. 5. Since the implemented methods are combined with ID-based and ECC public key cryptosystems, they can reduce computation cost greatly. Thus, it reduces the cost of system maintenance as it does not need to manage key directory .It can gain much efficiency in saving both the communicational cost and computational effort, because they can simplify public key distribution.

8.2 Security Analysis

The security of the implemented ECCSCPKC and related security schemes is based on the following two well-known cryptographic assumptions: Elliptic curve discrete logarithm(ECDL) assumption which is stated in section 2.3. 28

One-way hash function (OWHF) assumption: Let h be a one-way hash function. Given h(M) ,it is computationally infeasible to ﬁnd M [5].Furthermore, given M, h(M) and h(M’), it is computationally infeasible to obtain M’. For theoretical analysis, sometimes it is assumed that ﬁnding two diﬀerent values M and M’ such that h(M)= h(M’) is computationally infeasible [19]. 8.2.1 Security of secret keys The secret keys used in the implemented ECCSCPKC include CA’s secret key, users master keys, and users derived(personal) secret keys. Revealing CA’s secret key. CA’s secret key sSA and the corresponding public key PSA, which are deﬁned at the system setup phase, are only used for public key generation at the user registration phase. It is obvious that directly computing sSA from PSA is based on the intractability of solving the ECDL problem. At the user registration phase, sSA is protected by the time-variant parameter ki whose security is based on the intractability of solving the ECDL problem. Therefore, under the ECDL assumption, it is computationally infeasible to reveal sSA from all available public information. Revealing any registering user’s master key. As one can see that the registering user’s master key xi is protected by ZKP, whose security is based on the intractability of the ECDL and the OWHF problems .Even in the worst case that a user’s derived secret key si has compromised due tos ome unpredictable human factors, e.g., accidentally present to a unauthorized person, the user’s master key xi is still protected under the OWHF assumption. Revealing any registering user’s derived secret key. During the user registration phase, the registering user’s derived secret key si is protected by the master key xi that is protected under the OWHF and the ECDL assumptions as discussed above. 8.2.2 Security against active attacks Consider the scenario of an active attack that an adversary attempt to re-register his/her identity information already registered by an existing user with CA in such a way that CA will generate another validself-certiﬁed public key for the 29

masqueraded user. If this attack is successful, then the adversary can universally impersonate that user in the subsequent cryptographi capplications, since he/she possesses the corresponding secret key associated to there generated public key. This active attack can be easily detected or eliminated if a log ﬁle that stores all registered users identity is used. Each time a registering request is accepted, CA should check the submitted identity information with the entries in the log ﬁle to ﬁnd out the re-registration attempt. Consider the scenario of another active attack that an adversary attempts to generate a pair of valid secret/publickey ( si’ , Pi’ ) for a non-existing user with a forged identity information Ii’ without the assistance of CA. In such a case, the secret/public key pair (si’ , Pi’ ) and the forged identity Ii’ should satisfy Eq. (5) otherwise, they cannot be applied to the subsequent cryptographic applications without being detected. However, inorder to plot this active attack successfully, adversary will face the intractability of solving the ECDL problem and reversing the adopted one-way hashfunction h. From the above discussions, it can be seen that under the ECDL and the OWHF assumptions, the implemented ECCSCPKC can eﬀectively with stand the above active attacks that are originated either by re-registering any registered identity information or by creating a forged identity for any non-existinguser. 8.2.3 Security of related security schemes Secure identiﬁcation scheme.As the prover Alice can convince the verifier Bob of her identity an adversary with the forged Ii’ and Pi’ cannot pass the veriﬁcation procedure of the identiﬁcation scheme implemented. Secure session key exchange. Although an attacker can get Pi and Ii from the public channel, he/she cannot derive each user’s secret key as discussed in section 8.2.1. Thus , he/she cannot also obtain the session key shared between any two users. Secure encryption/decryption scheme. If anattacker wants to derive message M from the cipher text C1 and C2,then he/she will encounter the intractability of solving the ECDL problem. Moreover, due to the fact that the integer w is randomly chosen in the encryption scheme each time, it is hard to compute 30

message M from the massively collected cipher text C1’s and C2’s. Secure digital signature scheme. Consider the scenario that an adversary attempts to reveal a user’s derived secret key si from an intercepted signature(r, s) generated by that user. It can be seen that one can solve the derived secret key si from s = k + si .h(M || r) (mod n) only if he/she knows the time-variant variable k in advance.However,the time-variant variable k is protected by the ECDL assumption Therefore, for a given message M, an adversary will face the intractability of solving the ECDL problem to forge a validsignature of M by the name of any user without knowing the user’s derived secret key. Secure authenticated encryption scheme. An adversary cannot get a user’s derived secret key si from an intercepted ciphertext (R, s) generated by that user,because he/she can solve si from s = w - si . Rx( mod n ) only if he/she obtains the variable w in advance. However, the variable w is also protected by the ECDL assumption.

8.3 Results and Discussion of the implemented schemes

These are the results achieved with the elliptic group used for ECC .It also shows clearly the debugging of the programs of each of the scheme steps wise. First, we present the user registration scheme.After both Alice and Bob registers, they need to identify each other.Thus, we present the identification scheme.After identifying each other, they exchange their session keys.After exchanging their session keys, Alice sends Bob an encrypted message and Bob decrypts back the message.We also implemented the Digital Signature Algorithm, which Alice uses to digitally sign his message.

31

Fig.7 The user registration scheme

32

Fig.8 Identification Scheme

33

Fig.9 Session Key exchange Scheme

34

Fig.10 Encryption/Decryption Scheme

35

Fig.11 Digital Signature Scheme

36

Chapter 9 Conclusion and Discussion

In this report, we have discussed about ECC and how it provides greater security and more efficient performance for a far smaller key size than other public key cryptographic techniques. We have implemented the encryption-decryption and key agreement schemes using Elliptic Curve Cryptography. Then, we have discussed the problem of public key verification in WMN ,and implemented a self-certified public key system based on ECC, ECCSCPKC[22]. Based on the results for simplifying public key distribution, the implemented ECCSCPKC and its related security schemes can gain much eﬃciency in saving both the communicational cost and the computational eﬀort,so it is quite suitable to be used for the devices with inadequatememoryspace, limited computing power and low network bandwidth in wireless environments, like the smartcard, mobile phone, personal digital assistant(PDA), etc which are members of WMNs. Also, since the implemented ECCSCPKC does not need to manage the key directory, the cost of system maintenance can be greatly reduced. The security analysis discussed that the implemented ECCSCPKC can withstand potential active attacks and protect CA’s secret key, users master keys, and usersderived(personal) secret keys in eﬀect.All of the implemented security schemes are secure enough, based on the intractability of the ECDL and the OWHF problems.

37

Bibliography

[1] Certicom , http://www.certicom.com/index.php?action=ecc_tutorial,home [2] M. S. Anoop, Elliptic Curve Cryptography - An Implementation Guide, January 2007.

[3] R. Shanmugalakshmi, and M.Prabu, “Research Issues on Elliptic Curve Cryptography and Its applications”, in IJCSNS. International Journal of Computer Science and Network Security,. VOL.9 No.6, June 2009 [4] M.S. Siddiqui and C. Seon, "Security Issues in Wireless Mesh Networks", in Proc. MUE, 2007, pp.717-722.. [5] Vivek Kapoor, Vivek Sonny Abraham and Ramesh Singh, “Elliptic Curve Cryptography”, ACM Ubiquity, Vol. 9, No. 20, May 2008. [6] Fuwen Liu, “A Tutorial on Elliptic Curve Cryptography(ECC)”. [7] V. Vijayalakshmi and Dr. T.G. Palanivelu, ”Secure Localization Using Elliptic Curve Cryptography in Wireless Sensor Networks”, IJCSNS International Journal of Computer Science and Network Security, VOL.8 No.6, June 2008. [8] Ian F. Akyildiz, Xudong Wang and Weilin Wang, “Wireless mesh networks: a survey“ Journal Computer Networks: The International Journal of Computer and Telecommunications Networking Volume 47 Issue 4, March, 2005. [9] National Security Agency, http://www.nsa.gov/business/programs/elliptic_curve.shtml . [10] Design & Reuse, cryptography.html. http://www.design-reuse.com/articles/7409/ecc-holds-key-to-next-gen-

[11] L. Batina, N. Mentens, K. Sakiyama, B. Preneel, and I. Verbauwhede, "Low-cost Elliptic Curve Cryptography for Wireless Sensor Networks" in 3rd European Workshop on Security and Privacy in Ad hoc and Sensor Networks, 2006. [12] Jia Xiangya, Wang Chao. “The Application of Elliptic Curve Cryptosystem in Wireless Communication”, 2005 IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communication, 2005. [13] Kristin Lauter, “The Advantage of Elliptic Curve Cryptography For Wireless Security”, IEEE Wireless Communications, Microsoft Corporation, 2004. [14] Darrel Hankerson, Julio Lopez Hernandez, Alfred Menezes, “Software Implementation of Elliptic Curve Cryptography over Binary Fields”, Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems, 2000.

38

[15]

A. Jurisic, A.J. Menezes, “Elliptic curves and cryptography”, Dr. Dobb_ s Journal (1997) 26–35. 48 (17) (1987) 203–

[16] N. Koblitz, “Elliptic curve cryptosystems”, Mathematics of Computation 209. [17]

J. Sliverman, “The Arithmetic of Elliptic Curves”, Springer-Verlag, New York, 1986.

[18] W. Tsaur, “Several Security Schemes Constructed Using ECC-Based Self Certified Public Key Cryptosystems,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 447-464, 2005. [19] B. Schneier,” Applied Cryptography, second ed.”, John Wiley, New York, 1996.

[20] A. Shamir, “Identity-based cryptosystems and signature schemes, in: Advances in Cryptology”, Proceedings of CRYPTO_84LNCS, vol. 7, Springer-Verlag, New York, 1985, pp. 47–53. [21] M. Girault, “Self-certified public keys, in: Advances in Cryptology” Proceedings of EUROCRYPT 91LNCS, vol. 547, Springer-Verlag, New York, 1992, pp. 490–497.

[22] Woei-Jiunn Tsaur, “Several security schemes constructed using ECC-based self-certified public key cryptosystems” Applied Mathematics and Computation 168 (2005) 447–464

39…...

Premium Essay

...systems, assembly language, and parallel computer architectures. Operating Systems: Design and Implementation, 2nd edition This popular text on operating systems, co-authored with Albert S. Woodhull, is the only book covering both the principles of operating systems and their application to a real system. All the traditional operating systems topics are covered in detail. In addition, the principles are carefully illustrated with MINIX, a free POSIX-based UNIX-like operating system for personal computers. Each book contains a free CD-ROM containing the complete MINIX system, including all the source code. The source code is listed in an appendix to the book and explained in detail in the text. About the Author Andrew S. Tanenbaum has an S.B. degree from M.I.T. and a Ph.D. from the University of California at Berkeley. He is currently a Professor of Computer Science at the Vrije Universiteit in Amsterdam, The Netherlands, where he heads the Computer Systems Group. He is also Dean of the Advanced School for Computing and Imaging, an interuniversity graduate school doing research on advanced parallel, distributed, and imaging systems. Nevertheless, he is trying very hard to avoid turning into a bureaucrat. In the past, he has done research on compilers, operating systems, networking, and local-area distributed systems. His current research focuses primarily on the design and implementation of wide-area distributed systems that scales to a billion users. This research, being......

Words: 292171 - Pages: 1169

Free Essay

...ALL… § Let me clear up a misconception § RSA public/private key encryption is THE leader, in terms of security. For all practical purposes, it is impossible to crack a RSA algorithm. § PGP (Pretty Good Privacy) is probably the best implementation of RSA. It is now owned by Symantec. § Other free products (which do not tightly integrate into email, for example) are available § Understand that PKI is NOT the same thing as public key encryption Fundamentals of Information Systems Security © 2012 Jones and Bartlett Learning, LLC www.jblearning.com Page 5 Fundamentals of Information Systems Security © 2012 Jones and Bartlett Learning, LLC www.jblearning.com Page 6 Public Key Infrastructure (PKI) is a set of hardware, software, people, policies, and procedures needed to create, manage, distribute, use, store, and revoke digital certificates. In cryptography, a PKI is an arrangement that binds public keys with respective user identities by means of a certificate authority (CA). The user identity must be unique within each CA domain. The binding is established through the registration and issuance process, which, depending on the level of assurance the binding has, may be carried out by software at a CA, or under human supervision. The VA (Verification Authority) checks authentication. The PKI role that assures this binding is called the Registration Authority (RA). For each user, the user identity, the public key, their binding, validity conditions and......

Words: 1799 - Pages: 8

Free Essay

...Routing in Wireless Sensor Networks: application on Fire Detection Abstract: this paper is about fire detection in building using a modified APTEEN routing protocol. Here we design a system called iFireControl which is a smart detection system for buildings, which is more water efficient than many current systems, while keeping its robustness. introduction A Wireless Sensor network (WSN) consists of spatially distributed autonomous sensors to monitor physical or environmental conditions, such as temperature, sound, vibration, pressure, motion or pollutants and to cooperatively pass their data through the network to a main location. The more modern networks are bi-directional, also enabling control of sensors activity. The development of wireless sensor networks was motivated by military applications such as battlefield surveillance; nowadays such networks are used in many industrial and consumer applications, such as industrial process monitoring and control, machine health monitoring, Agriculture, Area Monitoring, Smart Home Monitoring, Seismic Monitoring etc. Wireless Sensor Networks provide a bridge between the real physical and virtual worlds; allow the ability to observe the previously unobservable at a fine resolution over large spatio-temporal scales. The WSN is built of “nodes” from a few to several hundreds or even thousands, where each node is connected to one (or sometimes several) sensors. Each such sensor network node has typically several parts: a...

Words: 4845 - Pages: 20

Premium Essay

...81 vi aUDiTinG anD aSSUranCE S T U D Y T E X T ThE GEnEral aUDiTinG EnvironmEnT 1 CHAPTER ONE THE GENERAL AUDIT ENVIRONMENT S T U D Y T E X T S T S TDUYD Y E T E X T U T X T 2 aUDiTinG anD aSSUranCE S T U D Y T E X T ThE GEnEral aUDiTinG EnvironmEnT 3 CHAPTER 1 THE GENERAL AUDiT ENViRONMENT CHAPTER OBjECTiVES: • • • • • • • • • by the end of this chapter, you are expected to have a general understanding of the following. Definition of Auditing Distinction between auditing and accounting objects of an audit What is true and fair? Benefits of an audit to a public limited company Types of audits Users of audited reports Stages of an audit by the end of this chapter, you are expected to have a general understanding of the general audit environment by being able to distinguish between auditing and accounting, the objects of an audit, types of audits, stages of an audit and the benefits KEY TERMS Audit This is the independent investigation into the quality of published accounting information. EXAM CONTEXT This topic gives you an introduction into the auditing. it covers the basic aspects of auditing and will be tested in conjunction with the topics covered later on this book. iNDUSTRY CONTEXT audits are conducted for most businesses especially where there is separation of ownership from management. at the end of an audit the auditor is expected to give a report to provide some form of assuarance to the users of financial statements. An audit therefore is......

Words: 96495 - Pages: 386

Premium Essay

...Technical Writing Project Cover Sheet Capstone Proposal Project Name: Wireless Home Network Student Name: Degree Program: Information Technology Mentor Name: Signature Block Table of Contents Capstone Proposal Summary 1 Review of Other Work 2 Rationale and Systems Analysis 3 Project Goals and Objectives 5 Project Timeline and Milestones 6 Project Deliverables 8 References 10 Appendix 1: Competency Matrix 11 1 Capstone Proposal Summary This project is going to entail upgrading and installing new components to an existing wireless home network. This is a two story home with attic and basement. Inside this home, there are 8 rooms. A living area, an office area, kitchen, laundry room, 1 ½ bathrooms and 3 bedrooms. Following an interview and on site evaluation to assess what the current needs are, along with the direction of technology in the future. The new network needed to be focused on wireless connectivity of their various devices, which included smart phones, tablets and laptops. There also needed to be easy access for guests who wanted to connect to the wireless network for their own tablets, smart phones and laptops. Currently, the home has DSL internet service, with a basic wireless G router. The DSL service was adequate for the current network setup, but with more and more online content, they were having a problem with lag between devices. The current......

Words: 2803 - Pages: 12

Free Essay

...A wireless mesh network is any wireless network where data is transmitted using mesh networking. That is, where nodes don't just send and receive data, but also serve as a relay for other nodes and each node collaborates in propagating data on the network. A wireless mesh network can be thought of as a collection of nodes where each mesh node is also a router. Compare this to a WiFi access point where service can be provided only within reach of the signal and when it is turned off, the connection is gone. Mesh nodes work differently by rerouting data to another hop which it is connected to, bypassing the empty area where a node might be off. Techopedia explains Wireless Mesh Network (WMN) The concept of mesh networking can be applied to both physical and wireless networking, but it's much more commmon for wireless networks given the cabling costs that would be required to implement as a physical topology. A key difference here is that mesh nodes work in a cooperative gain scheme where the more nodes that are active, the greater the bandwidth available Consider this analogy in traditional networking: when cars (data) coming from a wide road comes to a small bridge they all have to slow down to wait in line. To increase the number of cars going through, you need to make a bigger bridge (add bandwidth) which is then wasted in times of less traffic. In mesh networking, imagine people coming to a river, where in order to continue each person drops a rock to make a......

Words: 1896 - Pages: 8

Free Essay

...June 2013 Implementation and Evaluation of Wireless Mesh Networks on MANET Routing Protocols Shashi Bhushan1,Anil Saroliya2 ,Vijander Singh3 Research Scholar, Computer Science, Amity University, Jaipur, India 1 Assistant Professor, Computer Science, Amity University, Jaipur, India 2 Senior Lecturer, Computer Science, Amity University, Jaipur, India 3 Abstract—Wireless Mesh Network (WMN) is a kind of network which is made up of Mesh router and Mesh clients where Mesh router having lesser mobility and form the heart of WMNs. In this paper, Wireless Mesh Network over MANET implemented using routing protocols such as AODV, DSR. In this work NS-2.34 simulator is used for simulations. Various measurements and calculations were figure out in this work like throughput, Average end-end delay, PDR, NRL and Routing packets in Random way point mobility model. WMN have features such as self configuration, self healing and low cost of equipment. This work specifically aims to study the performance of routing protocols in a wireless mesh network, where static mesh routers and mobile clients participate together to implement networks functionality such as routing and packet forwarding in different mobility scenarios Keywords- Ad hoc Network, Routing Protocols, Wireless Mesh Network, Performance, Throughput, PDR, NRL and Routing packets in Random way point mobility model, Simulation on Network simulator NS-2, AODV,DSR , Routing Overhead. I. INTRODUCTION A Mobile Ad-hoc network (MANET)......

Words: 4335 - Pages: 18

Premium Essay

...passwords. One essential aspect for secure communications is that of cryptography, which is the focus of this chapter. But it is important to note that while cryptography is necessary for secure communications, it is not by itself sufficient. The reader is advised, then, that the topics covered in this chapter only describe the first of many steps necessary for better security in any number of situations. This paper has two major purposes. The first is to define some of the terms and concepts behind basic cryptographic methods, and to offer a way to compare the myriad cryptographic schemes in use today. The second is to provide some real examples of cryptography in use today. I would like to say at the outset that this paper is very focused on terms, concepts, and schemes in current use and is not a treatise of the whole field. No mention is made here about pre-computerized crypto schemes, the difference between a substitution and transposition cipher, cryptanalysis, or other history. Interested readers should check out some of the books in the references section below for detailed — and interesting! — background information. 2. THE PURPOSE OF CRYPTOGRAPHY Cryptography is the science of writing in secret code and is an ancient art; the first documented use of cryptography in writing dates back to circa 1900 B.C. when an Egyptian scribe used non-standard hieroglyphs in an inscription. Some experts argue that cryptography appeared spontaneously sometime after writing was......

Words: 7926 - Pages: 32

Premium Essay

...Wireless Networks & Network Security ISSC 340 Professor Vijay Venkatesh James Lange 08/13/2013 Wireless Networks are somewhat new technology in comparison to the know-how that makes them possible. The knowledge regarding wireless technology goes back about 200 years. One of the first individuals deserving recognition for today’s wireless networks is a scientist, inventor and politician named Benjamin Franklin. In 1747 he had built a model that showed how electricity could move through the air unaided by any type of wiring. In the early 1750’s Mr. Franklin started experimenting with electricity and the rest is history. Franklin was under the belief that lightening was an electrical current. So with the famous kite and key experiment he proved to himself and others that he was right. His fascination with electricity led him to later experiments with an electrical tube given to him by a friend. A second individual that played a part in today’s wireless technology is Hans Christian Oersted. In 1819 he had found that a compass needle had movement if it was presented with electrical current. This relationship between the needle and the electricity is an essential part of electromagnetism. It is said that this discovery by Oersted happened completely by chance. While preparing for one of his lectures he was setting up some of his equipment. The compass and battery were in close proximity to each other and the needle moved from magnetic north whenever the switch to......

Words: 3213 - Pages: 13

Premium Essay

...Some Problems in Symmetric and Asymmetric Cryptography A thesis submitted for the partial fulfillment of the degree of Doctor of Philosophy in Mathematics By SANTOSH KUMAR YADAV Under the supervision of Prof. Sunder Lal and Prof. S. C. Arora DEPARTMENT OF MATHEMATICS DR. B. R. AMBEDKAR UNIVERSITY, AGRA (FORMERLY AGRA UNIVERSITY) 2010 *Sanskrit verse dating back to the pre-Christian era Dedicated to my Teachers, Friends, Students and Family Members DECLARATION I do hereby declare that the present research work has been carried out by me under the supervision of Prof. Sunder Lal and Prof. S. C. Arora. This work has not been submitted elsewhere for any other degree, diploma, fellowship or any other similar title. Santosh Kumar Yadav Research Scholar CERTIFICATE This is to certify that the thesis entitled “Some Problems in Symmetric and Asymmetric Cryptography” submitted to Dr. B.R.Ambedkar University, Agra for the degree of Doctor of Philosophy by Mr. Santosh Kumar Yadav, is a bonafide record of research work done by him under our supervision. To the best of our knowledge, this thesis has not previously formed the basis for the award to any candidate of any degree, diploma, fellowship or any other similar title and the work has not been submitted to any university or institution, for the award of any other degree. S. C. ARORA SUNDER LAL (Co-supervisor) (Supervisor) Professor Professor of Mathematics, and Department of Mathematics Pro-Vice......

Words: 37424 - Pages: 150

Free Essay

...SECURE ROUTING IN WIRELESS SENSOR NETWORKS By [Name] The Name of the Class (Course) Professor (Tutor): The Name of the School (University): The City and State The Date: Abstract. Wireless sensor networks (WSANs) are a group of sensors and actors that are linked by a wireless medium for the purpose of performing distributed sensing and action on a given task. This involves the sensors collecting information about the surrounding physical environment and sending the information to the actors which take the decisions and perform some needed action basing on the information received from the sensors about the surrounding environment. These sensor networks are sometimes referred to as wireless sensor and actuator networks. They monitor physical or environmental conditions such as sound, pressure, temperature among others and send the collected data to the required location. Effective sensing and acting requires a distributed local coordination methods and mechanism among the sensors and the actors in addition to this, sensor data should be valid in order for right and timely actions to be performed. This paper describes secure routing in wireless sensor networks and outlines its threats on security. Keywords: Wireless sensor and actor networks; Actuators; Ad hoc networks; Sybil attack; Real-time communication; Sinkhole; Routing; MAC; adversary. Introduction With the recent rapid improvement on technology, many networking technologies have been created to make...

Words: 5106 - Pages: 21

Premium Essay

...A Low-Cost Eﬃcient Wireless Architecture for Rural Network Connectivity 1 Introduction Many rural regions around the world, especially in developing regions, do not have good connectivity solutions which are economically viable. As a result, many of these regions remain disconnected from both the rest of the world and from progress in general. In this proposal, I will describe the design of WiFi-based Rural Extensions (WiRE), a new wireless network architecture that can provide connectivity to rural regions at extremely low costs. The WiRE architecture is tailored for the typical rural landscape in several developing regions, in which the population is spread across small but scattered rural regions (less than 1-2 sq kms) within 100-200 kms of the city. WiRE is designed to be a wireless distribution network that extends connectivity from the city to each village. The WiRE architecture has largely been inspired by my prior work on WiFi-based Long Distance (WiLD) Networks [42, 62, 35, 54, 64, 34], a low cost point-to-point network connectivity solution that provides very high bandwidth (typically 6− 10 Mbps) over very long-distances. While prior work on WiLD networks [48, 5, 42, 62, 35] has made signiﬁcant progress in the design of highperformance MAC layer solutions, we still lack a vision of how to design a comprehensive, low-cost, rural connectivity architecture that can eﬃciently support a wide-range of applications. It is this goal that I wish to......

Words: 10544 - Pages: 43

Free Essay

...RUNNING HEAD: Wireless network trends Wireless Network Trends Prepared by: Rossell Powell Professor Yana Todorova ISSC321 I002 Win 12 American Public University 02-25-2012 Networking abilities in households is an important feature as an increasing number of students attend school online and still others work from home. With this increase, an increase in the number of computers in the household increases and all are dependent upon one Internet source. There are advantages and disadvantages to household network set-ups ( Dubendorf, V. A. (2003) The advantages in the ability to form a home network are numerous. The three main advantages to home networking are: sharing a single Internet connection among multiple computers, sharing files among computers, and using a printer or other device connected to another computer. Another advantage is that less wiring is needed when additional computers have wireless capabilities (Freeze, J. T. 2000). “The addition of wireless capabilities to these gateway devices gives the user the convenience of taking a computer anywhere in the house, and not have to worry about running wires through walls and crawl spaces and attics to connect computers in various parts of the house” .While the student is doing homework, the parent can continue to do work online and access their e-mails. Security issues are the biggest disadvantage to home networking. From , there are at least four types of security issues that exist. The first is...

Words: 1005 - Pages: 5

Free Essay

...WIRELESS LOCAL AREA NETWORK: SECURITY ISSUES AND COUNTERMEASURES IN ORGANISATION Nor Rasyidah Binti Haminudin2011634444M. Sc. (Information Technology)Faculty Of Computer And Mathematical SciencesUniversity Technology MARA, Malaysianorrasyidah.haminudin@gmail.com | | | ABSTRACT Every organisation today is looking to implement Wireless Local Area Network (WLAN) infrastructure to improve its communication capabilities by providing access anywhere for employees, and more importantly, convenient access for customers and other users. WLAN provides users many benefits such as portability, flexibility, reduced hardware need and lower installation cost. Without a doubt, the benefits of WLAN enhance an organisation’s overall productivity. However, WLAN is not without its own security problems. WLAN infrastructures that are not secured would actually affect the security posture of the LAN environment as well. Having an unsecured WLAN can result in a loss of service, or can be used as a staging area to launch attacks against other networks. The significant challenges faced today in securing wireless LANs are maintaining privacy, data confidentiality, and preventing unauthorized access using proper access control mechanisms. This paper will mainly focus on the wireless access points (APs) as devices that act as a central transmitter and receiver or WLAN radio signals. It will begin by introducing the concept of WLAN. The introductory section gives brief information on the WLAN...

Words: 3541 - Pages: 15

Premium Essay

...WIRE LESS MESS NETWORK WITH HRPU ABSTRACT A Wireless mesh network is a mesh network created through the connection of wireless access points installed at each network user’s locale. Each user is also a provider, forwarding data at next node. The networking infrastructure is decentralized and simplified because each node need only transmit as far as the next node. Wireless mesh networking could allow people living in the remote areas and small businesses operating in rural neighborhoods to connect their networks together for affordable Internet connections. Here we discuss a hybrid routing algorithm for wireless mesh networks. In HRPU, the mesh portal periodically broadcasts a mesh update message, which allows all nodes to have a route towards the mesh portal stored semi permanently in their routing table. Whenever a node has data to be sent to backbone network, it sends the data without any route establishment delay using the route to the mesh portal. In HRPU the mesh portals and mesh points are intelligent which further improves the performance. INTRODUCTION The Beginning: Wireless Mesh Networking (WMN) was developed as a quick way to set-up wireless networks during military operations. Since then it has grown considerably in popularity based on its advantages in both metropolitan and rural applications. WMNs are being applied as Hot Zones, which cover a broad area, such as a downtown city district. By 2010, municipal Wi-Fi networks will cover over......

Words: 4177 - Pages: 17