Lightweight Cryptography for Distributed PKI Based MANETS

International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.2, March 2018
Lightweight Cryptography for Distributed
PKI Based MANETS
N Chaitanya Kumar, Abdul Basit, Priyadarshi Singh, and V. Ch. Venkaiah
School of Computer and Information Sciences, University of Hyderabad,
Hyderabad-500046, India
Abstract. Because of lack of infrastructure and Central Authority(CA), secure communication is
a challenging job in MANETs. A lightweight security solution is needed in MANET to balance its
nodes resource tightness and mobility feature. The role of CA should be decentralized in MANET
because the network is managed by the nodes themselves without any fixed infrastructure and cen-
tralized authority. In this paper, we created a distributed PUblic Key Infrastructure (PKI) using
Shamir secret sharing mechanism which allows the nodes of the MANET to have a share of its pri-
vate key. The traditional PKI protocols require centralized authority and heavy computing power to
manage public and private keys, thus making them not suitable for MANETs. To establish a secure
communication for the MANET nodes, we proposed a lightweight crypto protocol which requires
limited resources, making it suitable for MANETs.
Keywords: Secret sharing, Lightweight Cryptography, Public key cryptography, MANETS
1 Introduction
MANET known as Mobile ad hoc Network is a self-configuring, a dynamic and
infrastructure-less network of wireless connected mobile nodes [1] [2]. These mobile
nodes move freely. Every node in the network has its own communication range and
other nodes within the range can interact and exchange messages. If any nodes tend
to go from the prescribed range of the MANET, it eventually leads to the failure of
nodes [3]. The computational power of the fixed infrastructure devices are greater
than the nodes i.e, the nodes are less computational because of their restrictions
on the amount of energy utilization. Denial of service, eavesdropping, interception
and routing attacks are major threats to security in MANETS.[4] [5]. The advent of
IOT devices and the wide usage of the electronic devices raised concerns over these
security issues. There are several factors like power dissipation, area and cost that
affect embedded applications which implement a full-fledged cryptographic environ-
ment. Because of these factors the concept of lightweight cryptography emerged.
Less amount of memory space is utilized by lightweight cryptography. As a result of
this, the amount of gate equivalent count is less and eventually leads to an efficient
hardware implementation. Nowadays Public key cryptosystem(PKC) is used widely
in many applications. The main concept of PKC is to provide key exchange services
and digital signatures for authentication purpose. In PKC, the concept of public
DOI: 10.5121/ijcnc.2018.10207 69

International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
key management is to be handled carefully to avoid the wide range of attacks. In
PKC, an authority looks after all the public parameters and generates them and
will provide the details when necessary to a particular user. The authority might
also generate the private keys too. But as it is a third party, there are cases where
the authority might misuse its power, therefore the trusted authority will generate
only partial private key [6]. In our proposal, the nodes of the MANET hold a partial
share of the MANET secret and they use that share to generate a secret key using
Diffie - Hellman key exchange to communicate among them
2 Preliminaries
2.1 Shamir Secret Sharing
Blakley [10] and Shamir [12] are the first to introduce secret sharing techniques. In
general a secret sharing scheme contains a dealer D and a set U = {u1, u2, . . . , un}
of n users. The dealer has a secret s and a share si of which is privately distributed
to user ui, 1 ≤ i ≤ n. A valid subset u ( for : u ⊂ U) of t number of users
holding valid shares can reconstruct the secret s, where t is minimum number of
users or threshold value and (t, n) scheme is called as threshold access structure
[12]. In threshold cryptography, the private key s is shared among n participants
using a (t,n) threshold access structure with the help of a secret sharing scheme,
with each participant ui having a partial share si [13]. For example, in public key
cryptography(PKC), let the public key be pk and the corresponding private key be
s. If a user has encrypted a message using the public key pk then to decrypt the
message, at-least t out of n nodes are needed to decrypt the message.
Shamir’s secret sharing scheme realizes a (t, n) threshold access structures by
means of polynomial interpolation. Let Zq be a finite field with q > n and let s ∈ Zq
be the secret. A polynomial P(x) is taken by the dealer having degree t − 1, here
the actual secret is s which is a constant term of P(x) and all other coefficients
ai for i ∈ 1, 2, 3, . . . , t − 1 are selected from Zq uniformly and independently at
random. That is, P(x) = s + t−1
i=1 ai ∗ xi. Every party or user ui is associated
to a field element bi publicly for i ∈ 1, 2, 3, . . . , n. The different field elements are
associated with different parties or users. The dealer privately sends to party ui the
value [s]i = P(bi), for i = 1, 2, . . . , n.This scheme realizes (t, n) threshold access
structure. The parties agreeing to recover secret s is u1, . . . , ut. The secret s can
be obtained as
t
i=1
[s]i
t
m=0,m=j
xm
xm−xj
. The number of parties less than t cannot
interpret any information regarding the secret s. We used basic Shamir’s secret
sharing to share the key among the MANET nodes, however depending on the
application different variations can also be used like the one proposed by Abdul et.
al. [21] and [11].
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2.2 Elliptic Curve Cryptography [14] and Diffie Hellman Key
Exchange
Elliptic curve cryptosystems were first proposed independently by Neil Koblitz and
Victor Miller in 1985. Elliptic curve cryptography (ECC) is a public key encryp-
tion technique that is based on the algebraic structure of elliptic curves over finite
fields. In comparison to non-Elliptic curve cryptography, Elliptic curve cryptogra-
phy makes use of relatively smaller keys to provide the same level of security. The
discrete logarithmic defined using a group of points on an elliptic curve over a finite
field is the hardest among the remaining groups. The security of a cryptosystem
relies on the hardness of this discrete logarithmic problem. [15].
Elliptic Curve Discrete Logarithm Problem (ECDLP) ECDLP is the prob-
lem of finding the integer s, given a rational point Q on the elliptic curve E and the
value of s*Q. Elliptic curve cryptosystems are dependent on the level of difficulty
of ECDLP. If an attacker can solve the ECDLP then he will be able to break the
system, but ECDLP is much harder than Discrete Logarithm Problem(DLP) in
finite fields. The strongest techniques generally used to solve DLP in finite fields,
like the index calculus method, Shank’s baby step giant step algorithm, the Pohlig
- Hellmann method and Pollard’s ρ method don’t work in solving ECDLP prob-
lem. Most of them work only if the group order is divisible by some large prime.
In 1993, Menezes, Okamoto and Vanstone reduced the ECDLP to DLP on F∗
( qk).
This method works only for supersingular curves i.e curves of the form y2 = x3 +ax
when the characteristic p of Fq ≡ −1(mod 4) and also curves of the form y2 = x3 +b
when p ≡ −1(mod 3) i.e curves for which k is small. This method known as MOV
method is only useful for a small class of elliptic curves but most elliptic curves are
non supersingular.
The Diffie Hellman Key Exchange using ECC Symmetric Encryption of
data requires the transfer of secret key from the sender to receiver without anyone
intercepting the key, which is the most challenging task [8]. Diffie-Hellman algorithm
made the transfer and the generation of similar keys at two ends secretly successful.
The idea of the Diffie-Hellman algorithm was coined by Diffie and Martin Hellman
in the year 1976. The key goal behind the development of this algorithm was not
mere encryption and decryption of data, but it completely revolved around the
generation of a similar private cryptographic key at two ends so that the transferring
of a key.[9]. The algorithm may lag behind due to its speed, but the power of
the algorithm is the ultimate reason behind its popularity among key generation
techniques. The following procedure generates a common secret key between two
parties A and B using ECC.
– A and B agree on a Finite field Fq and an elliptic curve E defined over Fq.
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– They also choose a public random base point P that belongs to E.
– A chooses a random secret integer a, computes a · P ∈ E and sends it to B.
– B chooses a secret random integer b, computes b · B ∈ E and sends it to A.
– A computes the secret key s = a(b·P) and B computes the secret key s = b(a·P).
so they both have the common secret point s.
– If the attacker gets hold of P, a · P, b · P, then there is no easy way to calculate
abP because of ECDLP.
2.3 Lightweight Cryptography
The type of cryptography which deals with the integration of cryptographic prim-
itives, ciphers and various techniques utilizing a small computing power and de-
liver high standards of security is known as lightweight cryptography. To design
lightweight algorithms, the computational complexity and the demands on hard-
ware and other limitations of the device are to be analyzed. In this paper we
considered Tiny Encryption Algorithm (TEA), which is one of the fastest and most
efficient lightweight algorithm.
Tiny Encryption Algorithm(TEA) [7] TEA is a symmetric Feistel type cipher
created by David Wheeler and Roger Needham of Cambridge University, which
come under a specialized class possessing iterated block ciphers. The ciphertext is
generated from the plain text by repeatedly applying the same transformation or
round function. In this form of cipher, there are two stages of encryption process.
The first stage is the application of a round function F on the first part with the
use of a subkey and the output of this stage is XOred with the remaining part. The
above mentioned pattern is followed for each round except the final round where
the swapping is not applied. A double shift operation in TEA results in the mixing
of key and all bits containing the data repeatedly. The 128-bit key K is split into
four 32-bit blocks (K = (K[0], K[1], K[2], K[3]) by using the key shift algorithm.
ENCRYPTION OF TEA [20] A plain text P of 64 bit length will be splitting into
2 equal halves i.e 32 bit each. The encryption of one half is done with the other
half by processing it in 64 rounds. Later this is joined and eventually leads to the
formation of cipher text block( C = Left[64], Right[64]). A 128 bit key K is divided
in to four parts ( K =K[0], K[1], K[2], K[3]).
– A sub key k[i], Left[i-1] and Right[i-1] act as inputs to each round i which are
the output from the previous round.
– The sub keys K[i] are different from K and from each other.
– The constant delta = (
√
5 − 1) ∗ 231 = 0x9E3779B9.
– The round function slightly differs from a classical Fiestel cipher structure in
that integer addition modulo 232 is used instead of exclusive-or as the combining
operator.
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Fig. 1. TEA Encryption Structure
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The structure of TEA encryption algorithm is depicted in ﬁgure 1 and the
symbol denotes integer addition modulo 232. The round function F, consists
of the key addition, bit wise XOR and left and right shift operations. The output
(Left[i+1],Right[i+1]) of the ith cycle of TEA with respect to the input (Left[i],Right[i])
is described as follows :
Left[i + 1] = Left[i] F(Right[i], K[0, 1], delta[i])
Right[i + 1] = Right[i] F(Right[i + 1], k[2, 3], delta[i])
delta[i] = (i + 1)/2 ∗ delta
The round function F, is denoted by
F(M, K[j,k], delta[i]) = ((M 4) K[j]) ⊕ (M delta[i])⊕ ((M 5) K[k]), where
j,k ranges from 1 to 64. The round function structure is same for each round but
takes parameters from the round sub key K[i]. It uses simple key schedule algorithm,
the 128-bit key K is divided into four 32-bit blocks K = K[0],K[1],K[2],K[3]). The
odd rounds used the keys K[0] and K[1] and the even rounds use the keys K[2] and
K[3]. Figure 2 shows the internal details of the ith cycle of TEA.
Fig. 2. General View of TEA in its i-th Cycle
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DECRYPTION OF TEA The decryption process initiates with accepting the ci-
pher text as input followed by the reverse application of the K[i] subkeys. This
process is similar to the encryption process.The Decryption is similar to encryption
which takes cipher text as input and the sub keys K[i] are iapplied in the reverse
order. The intermediate value of the decryption process is equal to the correspond-
ing value of the encryption process with the two halves of the values swapped. For
example, if the output of the ith encryption round is
ELeft[i]||ERight[i] (ELeft[i] concatenated with ERight[i]).
Then the corresponding input to the (64 − i)th decryption round is
DRight[i]||DLeft[i] (DRight[i] concatenated with DLeft[i]).
Once the last iteration of the encryption process is completed then the two halves
of the output are exchanged, so that the cipher text is ERight[64]||ELeft[64] and
the ﬁnal cipher text C is the output of that round. Figure 3 represents the structure
of the TEA decryption process.
Fig. 3. The structure of TEA decryption process
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3 Proposed System
In our Proposed system, we show how the nodes of MANET can communicate
securely using lightweight cryptography. An additive group G being generated by
some element Q having prime order q, and is hard under the assumption of discrete
logarithmic problem are made public. The public key is given as PK = s ∗ Q. We
use a collision-resistant hash function h : {0, 1}∗ → Zq. All the values G, q, Q, PK
are made public. The nodes exchange the private keys by using the Diffie hell-
man key exchange. Our proposed scheme consists of the phases Initial Setup,
Key Distribution, Computing a secret Key and Secure communication.
3.1 Initial Setup
The very first step is to make the MANET as de-centralized as possible, i.e., the
role of the dealer has to be played by nodes themselves.
Let N be the initial set of k founding nodes in the MANET, t be the threshold
for t ≤ k. Every founding node ni ∈ N chooses a bi-variate polynomial, symmetric
in x, z with the degree of x and z being t−1, where t is the threshold number. Every
node ni ∈ N obtains its partial secret si by implementing Shamir secret sharing
scheme. The protocol also supports new nodes joining the network, by obtaining
their respective partial share. The complete step by step procedure is described in
the next section Key Distribution
3.2 Key Distribution
Every node ni ∈ N which is part of the MANET receives partial share si of the
actual secret s. This is achieved using the following protocol.
1. Every founding node ni ∈ N chooses a bi-variate polynomial Fi(x, z) ∈ Zq[x, z],
symmetric in x, z and the degree of x and z is at most t − 1, where t is the
threshold value. These polynomials implicitly define a polynomial F(x, z) =
Σni∈N Fi(x, z). Let us denote fi,0 = Fi(0, 0) the constant term of polynomial
Fi(x, z) and s =
k
i=1
fi,0 = F(0, 0) the constant term of F(x, z).
2. Every node ni ∈ N computes and secretly sends to all other nodes nj ∈ N the
univariate polynomial Fij(x) = Fi(x, h(nj), along with the value Yi = Fi(0, 0)∗Q
(where Q is the generator of Group G).
3. Finally every node nj has values received from other k-1 nodes and also has
it’s own value Fjj(x, h(nj)) with it. Then every node nj ∈ N computes Sj(x) =
k
j=1
Fij(x) =
k
j=1
Fi(x, h(nj) = F(x, h(nj))
4. Now every node njnN has a share sj = Sj(0) = F(0, h(nj) of implicit MANET
secret s = F(0, 0) and a secret univariate polynomial of its own Si(x).
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5. The public key PK of the MANET is made public by each node in MANET.
This public key is computed by each node in MANET with the help of the
information acquired from the rest of the nodes in the initial setup. The public
key is given as PK = Σi∈N Fi(0) ∗ Q = s ∗ Q
The MANET secret function F(x, z) =
k
i=1
Fi(x, z) and MANET secret key
s = F(0, 0) are safe and hidden as they are implicit and not known to any particular
node. The reconstruction of the secret takes place if any only if minimum of t
nodes possessing the partial secret of the actual MANET secret come together.
Key distribution process is depicted in Figure 4. The shares of the nodes can be
frequently updated by using the concept of proactive secret sharing as discussed in
[19].
3.3 Computing a Secret Key
If the nodes ni, nj ∈ N want to communicate securely then they need a common
secret key, which is used for both encryption and decryption. The nodes follow
the Diﬃe Hellman Key exchange algorithm discussed in section 2.2.2 to compute
the secret key. They use the following protocol: The General Algorithm for Diﬃe
Hellman is as follows:
1. ni and nj choose random numbers a, b ∈ Zq.
2. ni sends a point A = a ∗ Q (where Q is the generator of Group G) and nj sends
B = b ∗ Q to ni
3. ni computes a point R = a∗B = a∗b∗Q and nj computes R = b∗A = a∗b∗Q.
4. Both ni and nj have same secret point R = E(Rx, Ry) where RxandRy represent
x and y coordinate of the point R. The secret key sk is computed as sk =
Rx + Ry.
3.4 Secure Communication
Once the nodes ni, nj ∈ N have a common secret key sk then they communicate
securely using TEA algorithm discussed in section 2.3.1.
4 Example
The MANET setup is similar to Chaitanya et al. discussed in [18].
– Setup
– Let the intial set of nodes N = {N1, N2, N3, N4}
No. of Nodes = l = 4
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Fig. 4. Key Distribution process
78

– Public Parmeters :
An additive group G is selected with the prime order q = 83.
- The curve used is E(F83) : y2 = x3 + 1
- The Generator is Q = E(38,50)
- Let t = 3.
– A collision resistant hash function - HTR
– Each node selects a random bivariate polynomial in GF(83)
N1 = 3x2z + 3z2x + 8xz + 5z + 5x + 5
N2 = 5x2z + 5z2x + 3xz + 8z + 8x + 9
N3 = 8x2z + 8z2x + 5xz + 3z + 3x + 6
N4 = 2x2z + 2z2x + 4xz + 8z + 8x + 4
– The polynomial implicitly deﬁned by all the nodes is
F(x,z) = N1 + N2 + N3 + N4
= 18x2z + 18xz2 + 20xz + 24x + 24z + 24
– The MANET secret s F(0,0) = 24.
– Each node secretly sends to each of other founding nodes the univariate poly-
nomial Fij = Fi(x, h(Nj)).
– The hash function used is given below:
def HTR(id,p):
h = int(hashlib.sha224(str(id)).hexdigest(),16)
val = mod(h,p)
return val
– The hash values of the nodes are
hn1 = HTR( Node1 , k) = 21
hn2 = HTR( Node2 , k) = 57
hn3 = HTR( Node3 , k) = 63
hn4 = HTR( Node4 , k) = 31
– Share Distribution
– Each node sends the following values to other Nodes :
– N1 also includes Y1 = 5 * Q = (18,43)
N11 = 63x2 + 2x + 27
N12 = 5x2 − x + 41
N13 = 23x2 + 49x + 71
N14 = 10x2 + 65x + 77
N21 = 22x2 + 35x + 11
N22 = 36x2 + 73x + 50
N23 = 66x2 + 39x + 15
N24 = 72x2 + 9x + 8
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N31 = 2x2 + 67x + 69
N32 = 41x2 + 52x + 11
N33 = 6x2 + 32x + 29
N34 = −x2 + 44x + 16
N41 = 42x2 + 61x + 6
N42 = 31x2 + 11x + 45
N43 = 43x2 + 64x + 10
N44 = 62x2 + 62x + 3
– Then from the received values all the nodes calculate their secret univariate
polynomial.
– S1(x) = 46x2 − x + 30
– S2(x) = 30x2 + 52x + 64
– S3(x) = −28 ∗ x2 + 18 ∗ x − 41
– S4(x) = −23 ∗ x2 + 14 ∗ x + 21
– The public key, PK = s * Q
= 24 * E(38,50) = E(11,81)
– PK should also be equal to Y1 + Y2 + Y3 + Y4
=E(18,43)+E(57,41)+E(68,64)+E(48,55)
= E(11,81)
– Each node computes its share from Si(0).
The shares of the nodes are
S1 = 30, S2 = 64, S3 = 42, S4 = 21
– If n1 and n2 wants to communicate securely then they compute a common secret
key using their shares.
– n1 sends S1 ∗ Q = 30 ∗ E(38, 50) = E(35, 31) to n2.
– n2 sends S2 ∗ Q = 64 ∗ E(38, 50) = E(50, 70) to n1.
– Both n1 and n2 computes the same secret point. At n1, 30∗E(50, 70) = E(6, 47)
at n2,64 ∗ E(35, 31) = E(6, 47).
– Now both n1 and n2 have a secret key 53, which they use for encryption and
decryption.
– If n1 wants to send a message ”hello” to n2 using TEA, then it sends the cipher
text [’0x95c88604’, ’0x1745f2d7’].
– Then n2 decrypts the cipher text to message ”hello” using the key 53.
5 Security Analysis
The TEA algorithm is prone to key equivalence attack as discussed below:Key
equivalence Attack:This attack on TEA is done by using Known plain/cipher text
pairs of any unknown key (K). The general idea of the attack is that the key in TEA
80

is divided into four 32 bits (key=K[0], K[1],K[2],K[3]) and for one half of the plain
text K[0],K[1] are used and K[2],K[3] for another half. So, if we find the value of K[0]
then we can find K[1] (same with other half) becauseR[i + 1] = L[i] + (((R[i] <<
4)+K[0])⊕((R[i] >> 5)+K[1])⊕(R[i]+Delta))). As all values are known we need to
guess the value of K[0] starting from zero.and calculate k[1] for the first and second
plain text/cipher text pairs. If the these two values do not match then increment
the value of K[0] and proceed form the beginning. If they match then verify whether
this guess of K[0] is correct by checking K[1] for other plain text/cipher text pairs.
If the value of K[1] matched every time then this is the correct guess for K[0] and
the key is found. But we can avoid this attack in MANETs by adopting proactive
secret sharing techniques, where the nodes periodically update their shares thus
not giving enough time to the attacker to find the equivalent keys.
6 Conclusion
In this paper, we proposed the use of lightweight cryptography algorithm in MANETs.
As MANETs have less computation power, they can not use traditional cryptogra-
phy algorithms because of heavy computations. In our MANET setup, first all the
nodes have a share of MANET private key and they use this share to generate a
secret key using Diffie Hellman key exchange. Then they use the secret key with
the TEA algorithm to encrypt/decrypt messages. We also discussed that the gen-
eral key equivalence attack of TEA can be avoided by adopting to proactive secret
sharing.
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Authors
N Chaitanya Kumar received M.Tech from JNTU Hyderabad, and he did Bach-
elor degree in computer science. Currently, he is pursuing his PhD in Computer
Science from the University of Hyderabad. His research interests include Informa-
tion security, Cryptography in MANET.
82

Abdul Basit received Master of computer application from Jamia Hamdard Uni-
versity New Delhi. He did Bachelor of Science in Information technology from SMU
Gangtok. Currently, he is pursuing his PhD in Computer Science from the Univer-
sity of Hyderabad. His research interests include Information security, Cryptogra-
phy, and Cyber security.
Priyadarshi Singh received M.Tech from IIT(ISM) Dhanbad. He did Bachelor
degree in Information Technology. Currently, he is pursuing his PhD in Computer
Science from the University of Hyderabad. His research interests include Cryptog-
raphy, Public key infrastructure.
V. Ch. Venkaiah obtained his PhD in 1988 from the Indian Institute of Science
(IISc), Bangalore in the area of scientiﬁc computing. He worked for several or-
ganisations including the Central Research Laboratory of Bharat Electronics, Tata
Elxsi India Pvt. Ltd., Motorola India Electronics Limited, all in Bangalore. He then
moved onto academics and served IIT, Delhi, IIIT, Hyderabad, and C R Rao Ad-
vanced Institute of Mathematics, Statistics, and Computer Science. He is currently
serving the Hyderabad Central University. He is a vivid researcher. He designed
algorithms for linear programming, subspace rotation and direction of arrival es-
timation, graph coloring, matrix symmetriser, integer factorisation, cryptography,
knapsack problem, etc.
83

Lightweight Cryptography for Distributed PKI Based MANETS

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Lightweight Cryptography for Distributed PKI Based MANETS