On the Identification Protocols of Versions 4 and 6

International Journal of Engineering Science Invention
ISSN (Online): 2319 – 6734, ISSN (Print): 2319 – 6726
www.ijesi.org Volume 3 Issue 10 ǁ October 2014 ǁ PP.18-21
www.ijesi.org 18 | Page
On the Identification Protocols of Versions 4 and 6
Mustafa A. Salman
Ajman University of Science and Technology
ABSTRACT: In this paper, a new method for assigning addresses for the Identification Protocols of version 4
and version 6 have been introduced which makes the addresses space compact and the generation of a new
address by a host is direct with no need for algorithm to check the uniqueness of the new address. The method of
representing addresses of the Identification Protocol of Version 6 is presented to be compatible to that been
used for version 4 which makes it convenient to define a 1-1 injective function from IPv4 space to IPv6 space
and a direct consequence of that the IPv4 space becomes isomorphic to a subspace of the IPv6 space. This
means there is no need for exchange process of addresses between the two versions that is no need for Gateway
Algorithm or any other translation algorithm. The output of these processes is a reduction of the number of used
algorithms by omitting the Duplicate Address Detection Algorithm and the translation technology algorithms
and eases the process of generating new addresses, using a minimum number of bits, to satisfy future demands
for internet devices or objects.
KEY WORDS: object; IPv4; IPv6; identification protocol; Duplicate Address Detection Algorithm; exchange
addresses; 1-1 invertible function.
I. INTRODUCTION
The two Identification Protocols of version 4 (IPv4) and version 6 (IPv6) are the recent protocols that
have been used for the Internet of Things (IoT) and for any network. Identification Protocol (IP) is a
communication protocol that deals with the identification and location of a device or object in the internet or in a
network and a thing in the IoT is an object that is capable of sensing, communicating, and interacting with the
environment ( sensor, computer, source, … etc). The work with The IoT is directed toward having a smart
society that is a society on which every things senses, communicates, and interacts with the environment such as
homes, cars, road, air, science, education, business, communication, … etc [1, 2]. An internet or network that
connect all objects in the world certainly needs a unique address for each object together with other needs such
as privacy, security, coding, ... , etc . Billions of objects exchanging and storing data between them is carried out
by both identification protocols IPv4 and IPv6 although till yet majority of objects deal with the IPv4 but IPv6 is
the identification protocol of the future because of the large capacity that has for addresses. Deployment of IPv4
and IPv6 in IoT faces many challenges, among them, the limited addresses space of IPv4, (32 – dimensional
vector space), while the number of users of the internet and objects connected to the internet is growing rapidly
in billions which is expected to be out of the addresses space of IPv4 soon. Also the generation of new
addresses needs a check for uniqueness which is performed by an algorithm (Duplicate Address Detection
Algorithm) and the addresses exchange between IPv4 and IPv6 identification protocols, needs some translation
algorithms since the recent identification protocols IPv4 and IPv6 are not simultaneously compatible.
II. THE IDENTIFICATION PROTOCOL IPV4
IPv4 was the first identification protocol used, worldwide, in the internet. In September 1981, a version
of IPv4 published to replace earlier one. On May 2014, the IPv4 was responsible for 96% of traffic of internet
worldwide [1, 2, 3], but with the highly increased number of new objects to be connected to the internet, the
IPv4 seemed to be not capable of satisfying all future demands for new objects, since every object must have an
IP address for identification and location.Mathematically, IPv4 can be regarded as a 32-dimensional vector
space over a binary field GF(2). It consists of 32-bit binary sequences, so the number of available addresses will
be ( 232
) which provides approximately 4.3 Billion addresses for objects to be connected to the internet. The 32-
bit sequences of IPv4 is partitioned to four octets, each octet is a binary sequence of eight bits, which is
represented by a decimal number ranging from 0 to 255. An example of such address could be
10011100 01010001 00110000 00001111 which is represented by
156 81 48 15
That is a binary number 10011100 = 156 decimal number and 01010001 = 81 decimal number and so on.
IPv4 addresses space is embedded in IPv6 space in a natural function in which the first 32 bit (least significant
bit ) will be IPv4 address then followed by a 16 bit of one's and the remaining 80 bit all set to zeroes and that

On The Identification Protocols Of…
sum up to 128 bit, the length of the binary sequence in the IPv6 addresses space. The problem of this injection is
the non-uniform set of sequences of the addresses of IPv4. IPv4 space has two kinds of addresses local and
global, which put more difficulty on exchanging addresses and generating new address because the possibility
of having duplicate addresses.
III. THE IDENTIFICATION PROTOCOL IPV6
The IPv6 was defined by1996, and formally published on December 1998, [8]. IPv6 is a 128-
dimensional vector space over a binary field GF(2). It consists of 128-bit binary sequences, which provide 2128
address of the 128-dimensional space of addresses. Since 210
= 1024 > 103
then this huge number 2128
is
approximately (3.4 x 1038
). That is, IPv6 provides this amount of addresses for objects connected to the internet.
The method of representation of addresses in IPv6 is different than, that used for IPv4.The 128-bit sequence of
the identification protocol, IPv6 is partitioned to eight groups of four hexadecimal digits (128 = 8 x 16). For
example,
2211: 02ab: 00ef: 85a1: 1000: 39cd: 0274: 2160
is one of the representation of 128-bit sequence (address) of IPv6.
In the above representation, each digit is a hexadecimal (4 bits) that is a hexadecimal number "02ab", represents
" 0000 0010 1010 1011" binary number (sequence), and the hexadecimal number " 39cd " is represented by the
binary number "0011 1001 1100 1101, [4, 5, 6]. In general
0 → 0000, 1 → 0001, 2 → 0010, … , 9 → 1001, a → 1010, b → 1011, … , f → 1111.
The identification protocol, IPv6 has features not present in IPv4. Some of these, the host identifier portion of
the 128 bit address is fixed by 64 bit, provide source to destination data transmission across multiple IP network
in a single operation, security was considered in the design, and hosts can configure themselves automatically
when connected to an IPv6 network, and so on [7, 8].
In IPv6, a packet has two parts, a header and payload. The header consists of a fixed portion with minimum
number of functions required for all packets. It contains a source address, destination address, traffic
classification options and the type of payload follows the header, [7, 9, 10].
The headers of IPv4 packets and IPv6 packets are different because the two protocols are not compatible. To
exchange traffic between IPv4 and IPv6, a gateway or translation technology is required such as tunneling
protocol, [4].This is one of the problems that this paper is dealing with.
IPv6 permits any host to generate an IP address and check whether it is unique or not. Checking the uniqueness
of an address is performed by, the Duplicate Address Detection Algorithm. In these processes, the host will send
a message asking for the Link-Layer address of the assumed new IP address. If there is another host using that
address then it will respond, otherwise it will be regarded new IP address, [7, 9, 10]. That is, another problem,
this paper is dealing with.
IV. NEW METHOD FOR ASSIGNING ADDRESSES FOR IPV4 SPACE
As indicated in the above section, generating new address by a host needs to run the Duplicate Address
Detection Algorithm since the set of the IP addresses of the IPv4 is not a compact set. By a uniform set, in this
paper, it meant a set of ascending sequences on which each term is more than the previous one. In other word, it
is a set of increasing sequences. A compact set of sequences, in this paper, means a uniform sequence on which
each term is more than the previous term by 1.
Let A be the set of all the recent addresses of the IPv4, and let (n +1) be the number of these addresses.
Clearly n < 232
Hence A = { vi : vi = ( a31 a30 … a1 a0 ) } , where aj ε {0,1} , i = 0, 1, … , n.
Re-order the elements (32-bit binary sequence) in A, to have a set of ascending elements with respect to the
decimal value of the 32-bit binary numbers of the elements (addresses).
Let B be the produced set of addresses after re-ordering the elements of A in ascending order.
Then B = { ui : ui = ( b31 b30 … b1 b0 ) } , where bj ε {0,1} , i = 0, 1, … , n
Clearly, as binary numbers ui ≤ ui+1 since IPv4 have local and global addresses which may suggest a
possibility of repeated addresses.
Assign to each 32-bit binary number, the equivalent decimal number as shown below:
00000000 00000000 00000000 00000000 → 0
00000000 00000000 00000000 00000001 → 1
00000000 00000000 00000000 00000010 → 2
00000000 00000000 00000000 00000011 → 3
.
.
11111111 11111111 11111111 11111111 → 232
- 1

Transform the addresses in B to new distinct addresses as follows:
ui → i decimal = 32-bit binary sequence wi . That is
u0 → 0 decimal = 32-bit binary sequence w0 , where
w0 = 00000000 00000000 00000000 00000000
u1 → 1 decimal = 32-bit binary number (sequence) w1, where
w1 = 00000000 00000000 00000000 00000001
u2 → 2 decimal = 32-bit binary sequence w2, where
w2 = 00000000 00000000 00000000 00000010
.
.
un → n decimal = 32-bit binary sequence wn .
Then the new addresses set W = { wi : i = 0, 1, 2, … , n } is a compact set consists of ascending binary
sequences whose numerical values from 0 to n and wi+1 = wi + 1 .
Hence, the set, A, of the recent addresses of the IPv4, has been transformed, to the compact set W.
Since new addresses as binary numbers range from 0 to n as decimal numbers then a new address generated by
host will be the 32-bit sequence whose decimal value, is ( n + 1 ) with no need to check for duplication.
These processes of assigning new addresses, for the recent addresses of the IPv4, done one times only. The
output will be having a compact uniform set of addresses that makes it possible to generate new addresses
easily, without checking for duplication, and all addresses will be global, since all new addresses been given
different addresses in the compact set. Unless IPv4 has exhausted more than half of the space capacity of the
IPv4, the most significant bits will be zeroes.
V. EMBEDDING THE IDENTIFICATION PROTOCOLS IPV4 IN IPV6
The recent representation of IPv6, as mentioned in section 3, is an eight group of four hexadecimal.
This means the 132 bit of the addresses of the IPv6 is partitioned to 8 parts, each part consists of 4 digits and
each digit consists of 4 bits. This is not convenient for compatibility with IPv4.
Since 128 = ( 8 x ( 4 x 4 )) = ( 8 x 16 ) = ( 16 x 8 )
Then, the 132- bit of the IPv6, could be partitioned to 16 octets similar to that used for IPv4. The four least
significant octets will be left for addresses of the IPV4, which will be done by a natural 1 – 1 injective function
as shown below:
Let wi be an address in the compact space of IPv4.
Then wi = c3 c2 c1 c0 , where ci is an octet of number i .
Define an injective function f: IPv4 space → IPv6 space such that
f(wi) = 015 014 013 012 011 010 09 08 07 06 05 04 c3 c2 c1 c0 where 0i is an octet of zeroes.
This is a natural embedding function of IPv4 addresses into IPv6 space. Clearly, the addresses of the IPv4
occupy 32 bit or less and the rest bits will be zero, which suggests that the addresses of IPv6 occupy the
complement of these addresses. This means IP6 may have new 128- bit addresses in the same way of the
addresses of IPv4 but starting from the address whose numerical value is 232
and the second will have the
numerical value 232
+ 1 and so on. Considering the numerical value of addresses of IPv6, the first address h0 will
have 1 in the 33rd
bit and the rest bits will be zero, h1 = h0 +1 , h2 = h1 +1, . . . , hi+1 = hi +1, . . . , hm+1 = hm + 1,
where m+2 is the number of addresses of IPv6. Clearly IPv6 addresses set will be compact and this method of
assigning addresses to both IPv4 and IPv6 will divide them to two portion one for addresses whose numerical
value less than 232
for IPv4 addresses and the other for addresses whose numerical value more than or equal 232
for IPv6 addresses. This results that IPv4 space is an isomorphic to a subspace of the vector space IPv6. That is
the IPv4 subspace, is embedded in the IPv6 space, and then having same pattern. The differentiation between
them depends on the numerical value of the addresses. Hence, the IPv6 will start having addresses starting from
h0 that represents a binary number of 128 bit of zeroes except the 33rd
bit is one as shown below:
015 014 013 012 011 010 09 08 07 06 05 (0000 0001) 03 02 01 00
The successor h1 = h0 + 1 will be
015 014 013 012 011 010 09 08 07 06 05 (0000 0010) 03 02 01 00
And so on.
Clearly, the above embedding function and the new addresses for both IPv4 and IPv6 will results that there will
be no need for exchanges traffic between IPv4 and IPv6 since IPv4 became a subspace of IPv6 space. Also no
need for gateway, tunneling protocol, or any other exchange algorithms. Addresses of the IPv6, will have some
non- zero bits in the fifth octets or successors of the fifth, while addresses of IPv4 will be limited to the 32 or
less least significant bits. If IPv4 is not exhausted, then a new addresses will be assigned as f(wn+1) which is the
successor of the last one f(wn) otherwise a new address will be assigned hm+2 and so on. Having compact spaces
for both IPv4 and IPv6 will reduces the number of bits that used for addresses. In [11, 12], the eight least

significant octets (64 bit) left for addresses of IPv6 is shown too much and a 51-bit sequence is sufficient for all
addresses needed in future, in the most exaggeration case, up to year 2100. Regarding this, a 51- bit is more than
enough, for addresses up to year 2100, and this will leave 51 – 32 = 19 bit for recent and new addresses of IPv6.
Also a 64 – 51 = 13 bit left for error detection and error correction codes or any other requirement for addresses
sequences.
VI. CONCLUSION
This paper studied the recent identity protocols IPv4 and IPv6 and suggested a new method for
assigning addresses for both IPv4 and IPv6 in such a way that, a new address, directly produced with no
requirement of checking for duplication. This is because the produced sets of addresses of both IPv4 space and
IPv6 space are compact and this will ease these processes. A different method of representation of addresses of
IPv6, convenient to the representation of addresses of IPv4 was introduced which suggest a direct invertible 1 –
1 injective function from IPv4 space into the IPv6 space. The output of this is a direct generation of addresses
with no need for Duplicate Address Detection Algorithm and no need for exchanging traffic between IPv4 and
IPv6 since IPv4 will be a subspace of IPv6 space. It means no need for Gateway, or translation technology such
as tunneling algorithms or others. Also the new method for assigning addresses will produce, a compact sets of
addresses for both IPv4 and IPv6 that occupy no more than 51 bit up to the year 2100 which leave at least 13 bit
for other uses such as error correction or detection codes.
REFERENCES
[1] D.Evance, "The Internet of Things, How the next Evolution of the Internet is changing everything", CISCO white paper(2011).
[2] P. Hartwell, "Methodology, The Internet of Things, How the next Evolution of the Internet is changing everything", CISCO
white paper(2011).
[3] L. Atzori, A. Lera, M.Giacomo , The Internet of Things: A survey , DIEE, Comp NW 4247 (2010)
[4] D. Borman, S. Deering, R. Hinden," IPv6 Jumbograms", RFC 2675 (Aug 1999)
[5] David Frost, "Ipv6 traffic volumes going backwards". iTWire, (20 Apr 2011)
[6] Google, " statistics about Ipv6", https://www.google.com/intl/en/ipv6/statistics.html,(2014).
[7] Google, "Google IPv6 Conference 2008: What will the IPv6 Internet look like?".
[8] D. Borman, S. Deering, R. Hinden," IPv6 Jumbograms", RFC 2675 (Aug 1999)
[9] S. Deering , "Host extensions for IP multicasting",RFC 1112, (Aug1989)
[10] S. Deering, R. Hinden," Internet Protocol, Version 6 (IPv6) Specification", RFC 2460(1998)
[11] R. Hinden, S. Deering, "IP Version 6 Addressing Architecture", RFC 4291, (Feb 2006)
[12] M.A. Salman, On Identification of Internet of Things, (2014), International Journal of Sciences: Basic and Applied Research
(IJSBAR) (2014) Volume 18, No 1, pp 59-62
[13] United Nations Projections, " World Population", en.wikipedia.org/wiki/World_population, (2010).

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