Download Here - IJPAM

International Journal of Pure and Applied Mathematics
Volume 101 No. 5 2015, 753-760
ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)
url: http://www.ijpam.eu
AP
ijpam.eu
ENCRYPTION OF TIME AND LOCATION FOR ANY EVENT
Karan Kumar Singh
VIT University Chennai Campus
Vandalur, Kelambakkam Road, Chennai, 600048, INDIA
Abstract: In cryptography, encryption is the process of encoding messages in
such a way that eavesdroppers or hackers cannot read it, but that authorized
parties can. In an encryption scheme, the message or information is encrypted
using an encryption algorithm, turning it into an unreadable cipher text. This
is usually done with the use of an encryption key, which specifies how the
message is to be encoded. Any adversary that can see the cipher text should
not be able to determine anything about the original message. An authorized
party, however, is able to decode the cipher text using a decryption algorithm
that usually requires a secret decryption key.
In the mid-1970s, strong encryption emerged from the sole preserve of secretive government agencies into the public domain, and is now employed in
protecting widely-used systems, such as Internet e-commerce, mobile telephone
networks and bank automatic teller machines, secret defense information etc.
This paper contains an algorithm for encrypting time and location for any
particular event to occur. The mechanism uses basic knowledge of angles and
radians and energy sequence in s-p-d-f shells and little knowledge of topography.
AMS Subject Classification: 03B97
Key Words: encryption, topography, grid references
1. Introduction
Encryption can provide a means of securing information. It can also provide
a means of ”message authentication” and also for sharing secret messages between two defense units without getting cracked by terrorists. To safeguard
Received:
March 12, 2015
c 2015 Academic Publications, Ltd.
url: www.acadpubl.eu
754
K.K. Singh
mission systems’ sensitive data, data security specialists must know all options
for encryption and security. Cost-effective and proven, no matter what level of
encryption the application demands.
From a defense perspective, nowadays encryption algorithms are being replaced with open, standards-based algorithms that are less cumbersome to manage in terms of physical controls. We need more advanced encryption techniques
so that out data and security are guarded. This paper concentrates on encrypting location and time details of a missile launch or attack.
Today’s encryption systems do not make use of concepts from physical
sciences. We could have many possible ways of encrypting messages by using
concepts from physics, chemistry and geography. For example:
1. The time of missile launch can be encrypted in such a manner that it will
not look like an encryption and knowledge of trigonometry will be required to
crack it. Also the location of missile launch can be encrypted using knowledge
of topography and the energy level patterns in atoms which will be difficult to
recognize. This difficulty in recognizing the pattern will lead to strong encryption.
2. Certain algorithms can be developed by monitoring the positions of
different constellation and stars and these algorithms can be used to encrypt
locations and in to a very complex and unhackable system.
3. Beauty and symmetry in the fractal pattern,fibonacci series and golden
ratio can also be used to encode data.
As with any fairly new technology, there are advantages and disadvantages
that must be weighed. Less privacy, in the case of the defense Carnivore, is in
the interest of increased national security. No data is one hundred percent safe,
a reality we must accept.
2. Encryption of Location
Location describes the position of a particular area on the earth surface. To
identify the exact location of a particular area on the earths surface, people use
topographical maps. In this paper we present a method to encrypt the location
of an area making use of concepts from topography. The proposed algorithm
uses the following two methods for encrypting data: Energy Sequence in Subshells of atoms and Topography. In the subsections below, these two methods
are explained.
ENCRYPTION OF TIME AND LOCATION FOR ANY EVENT
755
2.1. Energy Sequence in Sub-Shells of Atom
Fig. 1. (a) shows the energy sequence in increasing order, from 1s then
2s,2p,3s,3p,4s,3d,4p,5s and so on. In the algorithm proposed in this paper,
numbers are assigned to the grid squares of the topographical area following
the energy sequence order. This sequence is also called aufbaus principle.
2.2. Topography
Topographical maps provide the graphical representation of objects present on
the surface of the earth. These maps provide the preliminary information about
a terrain. The base map is divided into sections of 4 degree latitude x 4 degree
longitude and designated numbers from 1 to 136.
For Indian Topographic maps, each section is further divided into 16 sections (4 rows by 4 columns), each of 1 degree latitude x 1 degree longitude
(1:250,000), starting with a letter A (North-West corner) and ending on P,
column-wise. These topographic or degree sheets are designated by a number
followed by an alphabet such as 53 C. Degree sheets are further divided into 16
sheets (4 rows by 4 columns), each 15’ latitude x 15’ longitude (1:50,000) and
numbered from 1 to 16 column-wise and are identified as 53 B/3.
Grid references define locations on maps using Cartesian coordinates. Grid
lines on maps define the coordinate system, and are numbered to provide a
unique reference to features. A grid reference locates a unique square region
on the map. Grid systems vary, but the most common is a square grid with
grid lines numbered sequentially from the origin at the bottom left of the map.
The grid numbers on the east-west (horizontal) axis are called eastings, and the
grid numbers on the north-south (vertical) axis are called Northings. Numerical
grid references consist of an even number of digits. Eastings are written before
Northings. Thus in a 6 digit grid reference 123456, the Easting component is
123 and the Northing component is 456.
For example, from Fig. 1. (b), an area lies in the square 1844 where 18
refers to eastings and 44 to northings in four grid reference. However, more
the number of digits added to a grid reference, the more precise the reference
becomes. To locate a specific area, two more digits are added to the four-digit
reference to create a six-digit reference. The additional two digits describe the
position within the 1-kilometre square. A further 10x10 grid within the current
grid square is made for six grid reference. Suppose for this area in figure 2, this
gives the digits 5 and 3 (5 on Eastings) and 3 Northings. These are added to
the four-figure grid reference after the two digits describing the same coordinate
756
K.K. Singh
Figure 1: (a) Energy sequence; (b) sub-divisions in one grid
axis, and thus our six-figure grid reference for the area becomes 185443.
2.3. Algorithm for Encrypting Location
Step 1: The location format is NN’ alphabet/N” (6 grid reference)
Step 2: Now, Take the correct location and reverse the digits of NN’ to form
N’N.
Step 3: According to Topology, the map number is divided into 16 alphabet
grids from A-P as shown in Block 2 and each alphabet is further divided into 16
number grid. Give the numbers to the alphabet grid in analogy to increasing
energy shell as in chemistry. Take the correct alphabet and locate the number
assigned too it on the grid. Now take the number and write the alphabet which
comes at that number in alphabetical order.
Step 4: For finding N”, take the correct N” and replace it with the corresponding assigned number from the alphabet grid as shown in Block 1. And for
six grid reference say AB CD EF; shift the pair forward and the new pattern
will be EF AB CD now reverse the resulting pair giving DC BA FE.
Step 5: Hence the resulting location will be the encrypted location.
1 5 9 13
2 6 10 14
Block 1
3 7 11 15
4 8 12 16
ENCRYPTION OF TIME AND LOCATION FOR ANY EVENT
A1
B3
Block 2
C6
D 10
E2
F5
G9
H 13
I4
J8
K 12
L 15
757
M7
N 11
O 14
P 16
2.4. Strength of the Encryption Algorithm
The strength of encryption lies in the randomness of the concepts used. The
algorithm proposed here links concepts from chemistry with geography which
makes it formidable to determine the pattern. Secondly, the encrypted location
comprises of a disguise feature that hides the actual code with looking like it.
Also the increasing energy subshell pattern does not have any mathematical
equation derived for it making the encryption more powerful and undetectable.
2.5. Weakness of Encryption Algorithm
This algorithm is weak if the numbers N is equal to N’ because for N=N’ the
wrong location will also give the correct N and N’, where the event is going
to happen. Also, the encryption is weak if the given alphabet is P because for
alphabet P the replacement alphabet will be P only.
3. Encryption of Time
The proposed encryption system works for 12 hour clock system where, the
angle between each hour is 30 degree and it is divided into 6 equal parts, as
shown in Fig. 2(a) and (b). Each part shows 5 degree and for each 5 degree
rotation of the hour hand, the minute hand will rotate by 60 degree. Here, we
use the following notation:
AM : A- Angle, Anticlockwise, Acute, M- Midpoint
PM : P- Angle, Clockwise, Obtuse, M- Midpoint
3.1. Algorithm for encrypting time.
Given below is the algorithm for encrypting time:
Step 1) First, take the wrong time T in the form of aa:bb where aa represents
the hour input and bb represents the minute input. The minute input should
be a multiple of 5.
Step 2) Plot it on the clock and measure the angle (Acute or Obtuse angle
according to AM or PM respectively) between hour hand and minute hand.
758
K.K. Singh
Figure 2: (a) Clock showing the angle between each hour; (b) Six subdivisions with each division of 5 degree
Step 3)Find the mid-angle by dividing the angle between hour hand and
minute hand by 2.
Step 4) Rotate the hour hand anticlockwise or clockwise according to AM
or PM respectively.
Step 5) It will give the new time T’ with changed phase of the day (AM to
PM and vice versa).
Step 6) Subtract the old time from the new time without considering the
sign and it will give a new time T”. If T” has value above 60 after decimal then
convert it into the 12 hr time form. (Note: Only subtraction is done because
addition cant be performed, otherwise time will go above 12 in some cases,
multiplication also cant be performed considering zeros. Division will also give
decimal values.)
Step 7)Take the angles between hour and minute hand of T and T’, according to AM or PM and find the average angle.
Step 8) Using approximation convert the angle such that in the ones place we
have either zero or five and the decimal part is removed (for eg. 164.45=160+4.45;
166.55=170-3.45).
Step 9) Plot T” (from step 7) on the clock and find the angle between
hour and minute hand according to AM or PM. Now subtract it from the
approximated average angle and double the resulting angle.
Step 10) Now rotate the hour hand of T” by the resulting angle from step
11 according to AM or PM and it will give a new time T”’. Now add or subtract
the remaining angle (after approximation) from step 10 to T”’ and it will give
the final time T””.
ENCRYPTION OF TIME AND LOCATION FOR ANY EVENT
759
3.2. Strength of Encryption Algorithm
The illustrated algorithm make use of angles and basic arithmetic in a typical
manner. The concepts used in algorithm is basically rotation of clock hands
and uses knowledge of the angles between the clock hours which are totally
fundamental. But these concepts are used in a complex manner making it
difficult to crack. The strength lies in the algorithm irreversibility (it also has
its drawbacks, explained in weakness) and disguise feature as it does not look
like a code, which makes the encryption strong.
3.3. Weakness of Encryption Algorithm
The illustrated encryption of time cannot be reversed back. In the algorithm,
first wrong time is provided which gives the correct time. So, for deciding
the wrong time according to the correct time of the event we have to make an
analysis chart which will contain the correct times with respect to every possible
wrong times. Secondly, due to the complication of calculations the minutes in
the wrong time taken, is limited to multiples of five.
4. Illustrations
4.1. Illustrations of Location Algorithm
We now illustrate the algorithm given in section 2.3. Suppose we wish to encrypt
the location: 56 H/12 364587
Step 1) Reverse the first 2 numbers which gives 65
Step 2) Locate H on grid and take the number assigned to it and replace it
with the alphabet which comes at that number in alphabetical order here, H is
assigned 13 so it will be replaced by 13th alphabet i.e. M.
Step 3): Take the correct N” i.e. 12 and replace it with the corresponding
number from the alphabet grid. Here, it is 15.
Step 4) For 6 grid reference, after shifting it will be 873645 and after reversing it will be 546378. Hence the encrypted location will be 65 M/15 546378.
4.2. Illustration of Time Algorithm
We now illustrate the algorithm given in section 3.1. Suppose we wish to encrypt
the time: 9:30 AM
760
K.K. Singh
Step 1): T = 9:30
Step 2): Here the angle between hour hand and minute hand is 105 degree.
The mid-angle is 52.5 degree. Therefore rotate the hour hand by 52.5 degree
in anti-clockwise direction.
Step 3) The minute hand will rotate by 630 degree in anti-clockwise direction
as: 52.50/5=10.50, 10.5 * 60 = 630
Step 4) Therefore after rotating the minute hand in anti-clockwise direction
by 630 degree. The T’ will come out to be 7:45 PM.
Step 5) Do T’-T neglecting the sign and the convert the resulting angle to
proper time form 07:45-09:30=1:85 which will convert to 2:25 for AM or PM
add up the digits of T and T’ find the greatest and use that for T”. Here it is
0+7+4+5 is greater than 0+9+3+0, hence T”=2:25 PM
Step 6) Find the angle between hour and minute hand of T and T’ according
to AM or PM. Next take the average. For T =105; T’ = 322.50; Average is
213.75
Step 7) Approximate the time T”, Here 213.75 will be 210 + 3.75 and 3:75
will convert into proper time form as 4:15 therefore 213.750 will be 210 + 4:15
Step 8) Plot T” on the clock and find the angle between hour and minute
hand according to AM or PM. Here, 02:25 PM angle will be 282.5.
Step 9) Subtract the approximate average angle from the new angle and
double the resulting angle. Here (282.5-210)*2 = 145 degree.
Step 10) Now rotate the time T” with 145 degree according to AM or PM.
New time T”’ will be 7:15 PM.
Step 11) Now add the remaining minute time from the approximation to
T”’ and the final time will be T””. Here, 15 + 4:15 = 19 min and 15 sec.
Therefore, final time T””= 7 hour 19 min and 15 sec PM.
5. Acknowledgements
I would like to acknowledge Dr. Kalyani Desikan, Dean, School of Advanced
Sciences, VIT Chennai for her guidance and support.
References
[1] wikipedia.org/Encryption,Grid Reference.
[2] images- www.tutorvista.com,blog.ordnancesurvey.co.uk,www.mathsisfun.com.
ENCRYPTION OF TIME AND LOCATION FOR ANY EVENT
761
[3] nptel.iitm.ac.in/courses/web-courses-contents/IITROORKEE/SURVEYING
[4] defensesystems.com/articles/2013/01/15/cyber-defense-dataencryption.aspx
[5] education.illinois.edu/wp/netfiles.uiuc.edu/alhiggin/www/privacyencryption.html
[6] www.cwcdefense.com/technology/encryption.html
762