ECDH based security model for IoT using ESP8266

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ECDH based Security Model for IoT using
ESP8266
Ravi Kishore Kodali and Ashwitha Naikoti
Department of Electronics and Communication Engineering
National Institute of Technology,Warangal
WARANGAL 506004, INDIA
Abstract-Now a days, Internet of Things (IoT) is the emerg-
ing trend in technology that aims at making our life simpler
using sensors and smart devices. All of them are connected to
the Internet. Because of this it is possible to access and control
them from any place and at any time. The most important
aspect in this networking is communication between the smart
devices. The correctness in the behavior of the devices mostly
depends on its efficiency to send the data properly. Thus
security is very important in IoT implementations. In this
paper Elliptic Curve Diffie-Hellman(ECDH) key exchange
on NIST P-192 curve for secured communication between
ESP8266 modules has been discussed and implemented using
NodeMCU.
I. INTRODUCTION
The idea of Internet of Things is spreading to be part and
parcel of our lives. The devices used in domestic automation,
industry, infrastructure and other smart applications are inter-
connected with the internet. Because of this there will be a
variety of data that is read, assembled and transmitted in an
efficient and secure manner.[2]
To achieve the task of connecting devices ESP8266 is used
which provides embedded Wi-Fi capabilities at lowest cost
with good functionality[8]. It is a system on chip(SOC) which
is self contained and has an integrated TCP/IP protocol stack
to give access to WiFi network. It is a low power technology.
The widespread internet connectivity gives rise to high se-
curity problems such as unauthorized access to the devices,
eavesdropping and threat to privacy. As these interconnected
devices can be accessed and controlled at anytime and from
anywhere, authentication and authorization becomes essential.
The following are the criteria that must be taken into account
while selecting the type of public-key exchange methods. [1]
1) Functionality
2) Security
3) Performance
The difficulty involved in solving the mathematical problem
employed in the public key protocol is very important as it is
the main factor that decides the strength of the cryptography
method used. The hardness of this problem reflects the
execution as it decides the main elements like the sizes of the
domain and key parameters[1]. Elliptic Curve Cryptography
TABLE I
KEY SIZE COMPARISON(I N BITS)
ECC RSA Symmetric Algorithms
163 1024 80
233 2240 112
283 3072 128
409 7680 192
512 15360 256
has taken over RSA in many applicatons beacuse it is very
efficient. The size of the parameters is very much compressed
in Elliptic Curve Cryptograph(ECC) than with RSA and
DL schemes when compared at the same security level.
High speed computations, reduced key sizes and certificates
are the advantages gained by using ECC. Comparison of
key sizes of ECC and RSA is shown in Table 1 [5]. It is
used in applications where power,storage and bandwidth are
constrained.
ECC becomes the best choice for authentication and
authorization of IoT devices because of the storage capacity
of ESP8266. The module has various variants. Each variant
is an improvement over the previous one in terms of the
hardware of the module. ESP8266-01 is the cheapest and it
is has the least features. ESP8266-13 is the most expensive
of them with most features. The various features include
the types of pins, number of GPIO pins, presence of
shield and antenna on the chip, type of chip packaging and
storage capacity. The ESP8266 module requires 3.3V and upto
250mA power supply. It is power efficient and low in cost.[8].
TABLE II
COM PAR ISON O F PRI CES
ESP8266-01 $ 5
Ethernet shield for Arduino $ 60
Zigbee $ 25
Wify shield sparkfun $ 40
Wi-Fi shield for Arduino $ 80
Huzzah Wi-Fi shield by Adafruit $ 40
ESP8266-12 $ 7

II. OVERVIEW OF ELLIPTIC CURVE CRYPTOGRAPHY
Victor Miller and Neal Koblitz selfstandingly proposed
Elliptic Curve Cryptography[3][4]. In these cryptosystems
an elliptic curve is considered on which the members of
the group are defined. The operations between these mem-
bers is also defined on the curve[9]. ECC has been stan-
dardized by organizations such as NIST(National Institute
of Standards Technology)[14], IEEE(Institute of Electrical
and Electronics Engineers)[12], ISO(International Standards
Organization)[13], and ANSI(American National Standards
Institute)[11]. This made it widely commercially accepted.
A. Prime Field
A prime field is variant of finite field or galois field GF(p)
where p is a prime number. A prime field denoted by Fp
comprises of integers modulo pwith the results of all the
operations such as addition and multiplication also belonging
to the same field. It is a finite field of order p. All the elements
belonging to this field are 0,1,2, ......., p −1
B. Elliptic Curves
Choose psuch that it is a prime number, and let Fpdenote
the prime field. An elliptic curve Eis defined over Fp. All the
points on this curve belong to the defined prime field. These
points satisfy the equation given below. Here the pair (x,y)
represent the cartesian coordinates of a point on the curve.
y2=x3+ax +b(1)
a,b are also the elements of the prime field Fp. They must
satisfy the condition 4a3+ 27b26= 0 (mod p).
C. Domain Parameters
Other than the curve parameters the parties involved must
agree on some other parameters for secure communication in
ECC. These parameters are known as domain parameters. A
suitable elliptic curve over a prime field is chosen. This gives
rise to a set of parameters called domain parameters[10].
They are summarized as following
1) pis the prime number which is chosen for defining the
prime field.
2) a, b are the two parameters in the curve equation on
which the shape of the curve depends
3) Gis the Base point or Generator point which is a point
on the elliptic curve over Fpselected for performing the
elliptic curve operations
4) nis called the order of a point Don the elliptic curve. It
is the smallest integer such that nD = 0. The operation
performed for calculating nD is called point operation
and is discussed in the later parts of this paper.
5) his the cofactor of the curve
D. NIST p-192
A set of elliptic curves were recommended for the benefit
of the Federal Government. All the curves which are proposed
over a prime field have unity cofactor and the curve equation
is given by E: y2=x3−3x+bmod p. Curves were proposed
for 192, 224, 256, 384, and 521 bits. In this paper NIST
p-192 is used[6][14].
•p=6277101735386680763835789423207666416083908
700390324961279
•a=6277101735386680763835789423207666416083908
700390324961276
•b=0x64210519e59c80e70fa7e9ab72243049feb8deecc14
6b9b1
•Gx=0x188da80eb03090f67cbf20eb43a18800f4ff0afd82
ff1012
•Gy=0x07192b95ffc8da78631011ed6b24cdd573f977a11
e794811
•n=0xffffffffffffffffffffffff99def836146bc9b1b4d22831
E. Finite Field Arithmetic
1) Inversion: Inverse of a nonzero element xwhich be-
longs the finite field Fp, denoted by x−1mod pis an other
unique element mwhich also belongs to the same finite field
Fpsuch that mx=1 mod p. It is efficiently computed by using
extended euclidean algorithm[7].
The modular inversion is calculated by first finding the
greatest common divisor of x and p. The following algorithm
is used for finding the greatest common divisor. The values
returned by the algorithm is the gcd of the two numbers x,p
and the also the values of c,y such that cx+py=gcd(x,p).
Algorithm 1 Extended Euclidean Algorithm
1: procedure EUCLID(x, p)⊲g=gcd of x and p and c,y
such that cx+py=gcd(x,p)
2: a←x
3: b←p
4: u1←1
5: v1←0
6: u2←0
7: v2←1
8: while a6= 0 do
9: q← ⌊b/a⌋
10: t←b−qa
Suppose that p is a prime number and xǫ[1,p-1], and hence
greatest common divisor of x and p is 1. If the above extended
euclidean algorithm is used we get t=1 in this case. The
integer u1, and v1satisfy au1+pv1=1. When a modulus over
p operation is performed on this equation we get pv1mod

11: k←u2−qu1
12: l←v2−qv1
13: b←a
14: a←t
15: u2←u1
16: u1←k
17: v2←v1
18: v1←l
19: end while
20: gcd ←b
21: c←u2
22: y←v2
23: return gcd, c, y
24: end procedure
p= 0. Hence au1=1 mod p and thus u1is the inverse of ain
the prime field.
Algorithm 2 Inversion in Fpusing Extended Euclidean Algo-
rithm
1: procedure INVERSION(x, p)⊲Inversion of xǫ[1,p-1]
mod p
2: a←x
3: b←p
4: u1←1
5: u2←0
6: while u6= 0 do
7: q← ⌊b/a⌋
8: t←b−qa
9: k←u2−qu1
10: b←a
11: a←t
12: u2←u1
13: u1←k
14: end while
15: return u1⊲ x−1mod p
16: end procedure
2) Point Addition and Point Doubling: Point addition
is the method in which two points M and N on an elliptic
curve are added to get another point which is also on the
same elliptic curve over a prime field Fp.
Fig.1 explains the concept of point addition on an elliptic
curve as defined before. To find the sum of two points M and
N draw a line joining M and N and also to cut the elliptic
curve. A perpendicular is dropped from this point to meet the
elliptic curve at S. This point S gives the sum M+N [15].
Point doubling is method of adding a point M to the same
point to obtain a point S on the elliptic curve over a prime
field Fp.
Let M be the point on which the point doubling has to
be performed. Draw a tangent at this point M. This tangent
meets the elliptic curve. Drop a perpendicular from this point.
Fig. 1. Addition:M+N=S
This perpendicular meets the elliptic curve at S. This S is the
desired point which is obtained by doubling of the point M
[15]. Fig.2 shows how doubling is done.
Fig. 2. Doubling:M+M=S
The concept of adding two points on the curve defines the
following point operations on the elliptic curve.
1) Identity: M+∞=∞+M = M for a point M on the elliptic
curve over the prime field
2) Negative of point M: If M = (x,y) then the negative of
M is given by -M = (x,-y). This is also a point on the
elliptic curve over the prime field.
3) Point Addition: Let the two points to be added on the
curve be M=(xm,ym) and N=(xn,yn). Then the sum
S=M+N is given by (xs,ys) such that
xs=(yn−ym
xn−xm)n-xm-xnmod p
ys=(yn−ym
xn−xm)(xm-xs) - ymmod p
Here (yn−ym
xn−xm)is the slope of the line joining M
and N on the curve.
4) Point Doubling: Let P=(x1,y1) be the point on the
elliptic curve which has to be doubled. Then S=2M =
(xs,ys), where
xs=(3xm
2+a
2ym)2- 2xmmod p
ys=(3xm
2+a
2ym)(xm-xs) - ymmod p

3) Point Multiplication: This is also known as Scalar
Multiplication. It involves calculation of bM, here bbelongs
to the prime field and Mis a point on the elliptic curve
defined over the same prime field Fp. This operation is done
by repeated doubling and adding of the point on the curve
till the point is multiplied for the required number of times.
The following algorithm is followed for the implementation
of scalar point multiplication on an elliptic curve. Binary Left
to Right method is used.
Algorithm 3 Point Multiplication
1: procedure SCALAR MUL(b= (bk−1, ......b2, b1)2, M ǫ
E(Fp)
2: R← ∞
3: for i=k-1 to 0 do
4: R←2R
5: If bi= 1 then R←R+M
6: end for
7: return R
8: end procedure
F. Generation of key using Elliptic Curve
Let the defined elliptic curve be denoted by E. It is defined
over a prime field Fp. Let Tbe a point on such an elliptic
curve E(Fp), and T must have a prime order n[1].
Algorithm 4 Key Generation on an Elliptic Curve
1: procedure KEY(p, E , G, n)
2: P rivate ←[1, n −1] ⊲a value in the interval is
chosen
3: P ublic ←kT ⊲ Point Multiplication
4: return P ublic, P ri vate
5: end procedure
A number is selected randomly such that it belongs to
the prime field. This number is called the private key. It is
multiplied to the base point or the generator point. The result
of this point multiplication is the public key.
Diffie-Hellman Key Exchange: Elliptic Curve Diffie-
Hellman is a protocol used for key agreement that lets two
entities to generate a secret key that will be used for operations
involving the private key. The public key generated by one
individual is shared with the other. Elliptic curve operations are
used for generating the secret key. We consider that Alice and
Bob agree on a common key exchange protocol for exchanging
data. Assumption is made that they had no former contact and
the mode of communication available between them through
the channel is only public. Both of them exchange some public
data or public key with each other. Each of them have a private
key which is used to generate the shared key called the public
key. Both the individuals agree on same domain parameters.
The following steps are followed in this protocol.
Fig. 3. ECDH Key Exchange
1) Alice and Bob choose a common elliptic curve E over
a prime field Fp. They also comport on a base point
GǫE(Fp) so that the subgroup generated by G has
larger group cardinality. This decides the strength of the
method involved.[16]
2) Alice chooses an integer a. This is a secret key and is
not shared with anyone. This is the private key of Alice.
It then performs point multiplication and calculates the
public key Ta=aG, and sends Tato Bob.
3) Bob also selects an integer bwhich becomes his private
key, calculates Tb=bG by point multiplication, and sends
Tbto Alice.
4) Alice computes aTb=abT. This is done by point multi-
plication of the secret key of Alice with shared key of
Bob.
5) Bob performs point multiplication between private key
of Bob and public key of Alice and computes bTa=abT.
The sole data that an eavesdropper can get is about the
elliptic curve E, the finite field Fpand the points G, aG, bG.
It is difficult to calculate the shared secret with only this
information.
III. IMPLEMENTATION AND RESULT
In this paper C++ and BigNumber library in PlatformIO are
used for implementing the Elliptic Curve Diffie Hellman key
exchange. PlatformIO is a platform for IoT development. It
is an open source environment. Many platforms are integrated
into a single environment . It has many libraries for different
platforms like Arduino and MBED. It supports more than 200

development boards along with more than 15 development
platforms and 10 frameworks [19].
ESP8266 has a 32-bit Microcontroller running at 80Mhz. It
has 64KB of instruction RAM and 96KB of data RAM. The
program uses 234,729 bytes of program storage space out of
1,044,464 bytes available on the device.
Result:
Private key of Alice :
341412176158773296680689535904373303553510963046922
2112985
Public key of Alice :
(51816790119107273625873865765880617692097015020142
35969924, 513330497489513344820104154938773242975435
9696581635037518)
Private key of Bob :
480532747230177780107036951687423660415839337411488
0750942
Public key of Bob :
(45193790228990435009008901963536601048026242162644
06525237,502733345526102735485459503590296654734073
4185987094146271)
Verification at Alice (aTb) :
(35413485630412598676400949136684953820106314253240
11641407, 558107221409987501935543495657067732254330
2415357593860274)
Verification at Bob (bTa) :
(35413485630412598676400949136684953820106314253240
11641407, 558107221409987501935543495657067732254330
2415357593860274)
After the key exchange, verification is done by both
Alice and Bob. The computations by both the individuals
result in the same point on the curve E. This authenticates
the connection established between them.
IV. CONCLUSION
Elliptic Curve Diffie Hellman(ECDH) key agreement
scheme which is one of the variants of Elliptic Curve Cryp-
tography forms the basis for security authentication. This has
grabbed the attention of the industry in recent times because
of its advantages over RSA and AES. Many improvements can
be made in securing the communication using this agreement
protocol. Implementing such an algorithm on a potential
device like ESP8266 adds to the advantage. With the IoT
going to be the next Industrial Revolution, secure and low-
cost WiFi device plays a vital role. This can be used in many
applications such as Mesh networks, Home automation, Smart
power meters, Wearable devices, Security ID tags and Sensor
networks.
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