A Robust Cryptographic System using Neighborhood-Generated Keys

International Journal of Research in Computer Science
eISSN 2249-8265 Volume 2 Issue 5 (2012) pp. 1-9
www.ijorcs.org, A Unit of White Globe Publications
doi: 10.7815/ijorcs.25.2012.041

A ROBUST CRYPTOGRAPHIC SYSTEM USING
NEIGHBORHOOD-GENERATED KEYS
Samuel King Opoku
Computer Science Department, Kumasi Polytechnic, GHANA
Email: samuel.k.opoku@gmail.com

Abstract: The ability to hide information from Authority (CA) – a central control point that everyone
unauthorized individuals has been a prevalent issue trusts [4]. To ensure maximum security, private and
over the years. Countless algorithms such as DES, public keys generated by PKI are periodically
AES and SHA have been developed. These algorithms refreshed as per application by the Trent [3], [4]. Trent
depend on varying key length and key management regenerates the keys and informs the parties
strategies to encrypt and decrypt messages. The size of repeatedly. Each party's public key is distributed to the
the encrypted message is so large that it therefore entire parties and the private key needs to be sent to
consumes and wastes valuable storage space when the party individually via a secure channel. Key
implemented in organizations that store and handle distribution in asymmetry cryptography is much easier.
large volumes of small data. The ability to share the Authentication and non-repudiation are available in
generated keys securely also poses a problem. This asymmetric key distribution. Compromising a private
paper proposes a robust cryptographic algorithm key of a user does not reveal messages encrypted for
which generates its keys from the surroundings and other users in the group. The involvement of Trent in
already-designed coding schemes. The proposed generating keys however affects the privacy issue of
system conserves storage space and processing power. the individuals [3]. Asymmetric cryptography is
The algorithm is implemented and tested using PHP generally computational expensive [4].
and MySQL DBMS.
Asymmetric cryptography is used in Digital
Keywords: Cryptography, DES, AES, SHA, Coding
Signature Standard (DSS), Password authenticated key
Scheme, Key Management, Privacy, Security.
agreement technique and with key distribution
algorithms [1], [3], [5]. Commonly known algorithms
I. INTRODUCTION
that use asymmetric cryptography are Elliptic Curve
Cryptography has been the technique for preventing Cryptosystem (ECC), Rivest-Shamir-Adleman (RSA)
unwanted disclosure of the content of information [6]. Identity-Based Cryptography (IBC) has been the
through encryption. Encryption is therefore the method method developed to eliminate the requirement of
of transforming information into an illegible format. certificate distribution [7] - [9]. IBC brings free pair-
Cryptography involves the use of keys in either wise keys without any interaction between nodes
symmetric or asymmetric way to encrypt messages [1]. requiring lower processing power, storage space and
In symmetric cryptography, the receiver and sender of communication bandwidth. It however requires
an encrypted message have the same key [1], [2] to signature scheme [7]. Protocols based on certificateless
decipher the encrypted message. The commonly public key cryptography (CL-PKC) are preferred since
known algorithms that use symmetric cryptography are they do not need certificates to guarantee the
Data Encryption Standards (DES) and Advanced authenticity of public keys and does not suffer from
Encryption Standard (AES). The problem associated key escrow of identity-based cryptography [3], [5]
with symmetric cryptography is the ability to share the
key securely [2]. Data can be encrypted in three ways [10], [11]:

Asymmetric cryptography, on the other hand, 1. Stream Cipher which works by encrypting single
requires the generation of two keys – public and bits or bytes of information one a time. The
private keys – for data encryption. The public key may technique uses symmetric cryptography methods in
be distributed freely and is used for encrypting data. its process
The private key is given to the intended recipient of 2. Block Cipher which is an encryption technique that
the encrypted data who can decrypt the data securely breaks down and encrypts data into individual
[3]. Traditional asymmetric cryptography widely and blocks. The size of a block is typically 64bits [12].
effectively used in the Internet relies on a Public The DES and AES have used block cipher design in
Key Infrastructure (PKI). The success of PKI depends their applications [2].
on the availability and security of a Certificate

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2 Samuel King Opoku

3. Using hash algorithm is another encryption algorithm. The attacker then aims at deducing plaintext
technique. It uses mathematical algorithm to or even better, the key from the ciphertext.
convert large amounts of data into smaller,
compressed size. This technique is used in “One B. Known-Plaintext Attacks:
way encryption” [13] where data is not decrypted Attacker has the plaintext and ciphertext of one or
for viewing. It provides data integrity and more messages. The attacker tries to discover the key
authentication but no confidentiality. The general used to encrypt one of the messages and use the key to
hashing algorithms uses 128-bit hash value, 160-bit decipher and read the other messages. A typical
hash or 256-bit hash value. 128-bit hash values are variation is the Linear Cryptanalysis in which the
produced by Message Digest (MD) algorithms such attacker evaluates the input and output values for each
as MD2, MD4 and MD5. 160-bit hash values are Substitution-box (S-box) [19]. With S-box, each
produced by Secure Hash Algorithms (SHA) such message is being encrypted with the same key [20].
as SHA-1. Various versions of SHA’s with varying The attacker evaluates the probability of input values
hash values have been evolved. These include ending up in a specific combination and assigns these
SHA-256, SHA-384 and SHA-512 which probability values to different keys until one shows a
respectively produce 256-bit, 384-bit and 512-bit continual pattern of having the highest probability
hash values. This method generate large values for
small data and is therefore not appropriate for C. Chosen-Plaintext Attacks:
encrypting large number of small data that need to Attacker has the plaintext but can choose randomly
be stored and retrieved in a database the plaintext to be encrypted to see the corresponding
The figure below summarizes the ciphertext. This gives the attacker, more power and
functionalities of the above algorithms. possibly a deeper understanding of the way the
encryption process works so that they gather more
information about the key being used. Another form of
this attack is the Differential Cryptanalysis (DC). In
DC, the attacker takes two messages of plaintext and
follows the changes that took place to the blocks as
they go through different S-boxes. The differences
identified in the resulting ciphertext values are used to
map probability values to different possible key
values. DC has been used to break several
cryptosystems such as DES and Triple-DES [21], RC4
[22] and AES [23].
D. Chosen-Ciphertext Attacks:
Attacker chooses a ciphertext to be decrypted under
unknown key. The goal is to figure out the key. This is
a harder attack to carry out compared to the previously
mentioned attacks. The attacker needs to have control
of the system that contains the cryptosystem
E. Side-Channel Attacks:
Attacker measures power consumption, radiation
Figure 1: Functionalities of the Various Cryptographic emissions and the time it takes for certain types of data
Algorithms to process. With this information, an attacker can work
backwards by reverse-engineering the process to
In spite of the above algorithms, encrypted uncover an encryption key or sensitive data. A power
messages are usually subjected to attacks. Active attack, an attack to review the amount of heat released,
attackers modify system files, masquerade and change has been successful in uncovering confidential
messages with the aim to discover the key used in the information from smart cards. RSA private keys were
encryption process. Commonly used attacks are [14]- uncovered in 1995 by measuring the relative time
[18]: cryptographic operations took
A. Cipher-Only (also known as Known-Cipher) F. Statistical Attacks:
Attacks:
Attacker identifies statistical weaknesses in
Attacker has ciphertext of several messages that algorithm design for exploitation. For instance, a
have been encrypted using the same encryption Random Number Generation (RNG) may be biased. If

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A Robust Cryptographic System using Neighborhood-Generated Keys 3

keys are taken directly from the output of the RNG, +, =, * and -. Thus CashierID only contains English
then the distribution of keys would also be biased. The uppercase letters and digits. Software designers are
statistical knowledge about the bias could be used to also allowed to include lowercase letters and then

#+.## , where # ∈ Z + and 0 ≤ # ≤ 9
reduce the search time for the keys assign coding scheme values to them.
G. Replay Attack: 5. The amount to be encrypted should be in the format

Attacker captures some type of data (usually
6. and the Kleene star, +, represents one or more
authenticated information) and resubmits it with the
occurrences. Thus the least amount is 0.00
hope of fooling the receiving device into thinking that
it is legitimate information. Time stamps and sequence B. Key Generation
numbers are countermeasures to replay attacks.
The keys are generated from the fields in the
The strength of a cryptographic mechanism database table. The various elements (dd, mm, yy or
depends on the length of the key and the key yyyy, HH, MM and SS) are manipulated such that the
management strategy used [11]. The length of the key value obtained for any given expression is greater than
is directly proportional to the effectiveness of the zero. Basically, there are two keys generated. These
algorithm and the number of bits in the encrypted are called K1 and K2. K1 is obtained from date and time
message. Thus storage space are usually consumed and elements whereas K2 is obtained from CashierID.
wasted when these algorithms are implemented in
organizations that store and use large volumes of small To obtain the value of K1 from date and time,
data. This paper proposes a robust cryptographic designers are allowed to create their own formulas but
algorithm which generates its keys from the they should keep in mind that their formulas should
surroundings and coding schemes. The proposed satisfy this condition, K1 > 0. A typical generation of

K1 = (dd ∗ mm + SS) ∗ (HH + MM + yy).
system conserves storage space and processing power. K1 which is used throughout this work is given as:
The algorithm is implemented and tested using

With this definition of K1, it implies that ∀𝐾1 , 𝐾1 >
Hypertext Preprocessor (PHP) and MySQL Database

0 and 1 ≤ 𝐾1 ≤ 78011. 𝐾1 = 1 when the date is
Management System (DBMS).

II. CRYPTOGRAPHIC PARAMETERS AND KEYS

However, 𝐾1 = 78011 when the date is 31/12/99 (that
given as 01/01/00 (that is 1st January, 2000) and the
GENERATION time of entry is 00:00:00 (that is 12:00:00 am).
This section describes the various elements required
to generate the keys for the cryptographic system. It is 31st December, 1999) and the time is 23:59:59.
also describes how these keys are obtained from the Since date and time do not remain constant, it implies
database environment. that the same amount encrypted at different periods
will have different K1 values and hence different cipher
A. Obtaining Cryptographic Parameters texts.
The cryptographic system designed in this work is The key, K2, is obtained from the individual

𝐾2 = �(𝐶𝑎𝑠ℎ𝑖𝑒𝑟𝐼𝐷 𝐶𝑜𝑑𝑒𝑑 𝐶ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑠).
based on the following: characters which constitute CashierID so that:
1. The database table which contains the amount to be
encrypted has Date, Time and the Cashier’s
Identification (CashierID) as part of its fields.
These fields may constitute the primary fields of the Each character in CashierID is encoded by
table assigning them numeric values. The flexibility of the
system also gives the designer the choice of values to
2. The Date should be in the format dd-mm-yy or
be assigned to the various characters. However, to
dd/mm/yy. The separator of the date elements is
improve the efficiency of the system, designers are

that ∀dd, 01 ≤ dd ≤ 31; ∀mm, 01 ≤ mm ≤
inconsequential to the efficiency of the system. The
encouraged to assign at least two-digit value (that is a

12 and ∀yy, 00 ≤ yy ≤ 99. Designers can choose
elements (dd, mm, yy) are employed such
value greater than or equal to ten) to each character.

yyyy such that ∀yyyy, 0000 ≤ yyyy ≤ 9999
The table below shows a sample of values assigned to
each encoded character.
instead of yy. Table 1: Sample Coding Scheme for K2 Generation

that ∀HH, 00 ≤ HH ≤ 23; ∀MM, 01 ≤ MM ≤ 59
A →21 J → 30 S → 39 1 → 48
and ∀SS, 00 ≤ SS ≤ 59
3. The Time should be in the format HH:MM:SS and CODING SCHEME FOR GENERATING K2

B → 22 K → 31 T → 40 2 → 49
C → 23 L → 32 U → 41 3 → 50
D → 24 M → 33 V → 42 4 → 51
4. The CashierID consists of uppercase alphanumeric
characters only. There is no such special symbol as

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E → 25 N → 34 W → 43 5 → 52
4 Samuel King Opoku

F → 26 O → 35 X → 44 6 → 53
% (a symbol for arithmetic modulo) and

G → 27 P → 36 Y → 45 7 → 54
+ (a symbol for concatenation) */

H → 28 Q → 37 Z → 46 8 → 55
String str_Cipher2 = Cipher2 + “”;

I → 29 R → 38 0 → 47 9 → 56
if (Length(str_Cipher2) % 2 != 0){
str_Cipher2 = “0” + str_Cipher2;
}
III. ENCRYPTION ALGORITHM str_Cipher2 to Cipher3 using the coding
Step 4. Convert
Given that any amount entered to be stored in a scheme shown in the table below which is

the fractional part. The integer part, 𝐼 𝑝 , is a number
database is formatted as #+.##, the amount can be obtained by grouping str_Cipher2 characters into
divided into two parts. These are the integer part and twos.

such that 𝐼 𝑝 ≥ 0 whereas the fractional part, 𝐹𝑝 , is also
a number which satisfies 00 ≤ 𝐹 𝑝 ≤ 99. Each part of
Table 2: Sample Coding Scheme for Obtaining Cipher3

CODING SCHEME FOR CONVERTING str_Cipher2

00 → + 25 → h 50 → U 75 → ¬
the amount is encrypted differently with different
TO Cipher3

01 → - 26 → I 51 → u 76 → `
procedure to ensure that ciphertext generated is

02 → * 27 → i 52 → V 77 → 1
relatively provable.

03 → ? 28 → J 53 → v 78 → 2
A. Integer Part Encryption

effective steps. Given the keys 𝐾1 and 𝐾2 and the 04 → ! 29 → j 54 → W 79 → 3
05 → , 30 → K 55 → w 80 → 4
The integer part is encrypted using four simple but

06 → [ 31 → k 56 → X 81 → 5
07 → ( 32 → L 57 → x 82 → 6
amount to be encrypted which is denoted as Amt, the

∅ be the size of the data type (like 08 → ] 33 → l 58 → Y 83 → 7
following steps are applied:

09 → ) 34 → M 59 → y 84 → 8
Step 1. Let

10 → A 35 → m 60 → Z 85 → 9
integer, float and double) of the variable

11 → a 36 → N 61 → z 86 → 0
(called Cipher1) used to store the value of

Cipher1 = 𝑛 𝑝 ∗ 𝐾1 ∗ 𝐴𝑚𝑡 ± 𝑚 𝑞 ∗ 𝐾1 12 → B 37 → n 62 → . 87 → ;
13 → b 38 → O 63 → ^
the first step of the encryption process, then

where 𝑛, 𝑝, 𝑚 𝑎𝑛𝑑 𝑞 𝑛 𝑝 and 14 → C 39 → o 64 → < 89 → /
𝑚 represent different coefficients of 𝐾1 which are
88→space

𝑞 15 → c 40 → P 65 → > 90 →
are constants,

16 → D 41 → p 66 → % 91 → |
17 → d 42 → Q 67 → = 92 → {
used to enhance the effectiveness of the algorithm such

18 → E 43 → q 68 → $ 93 → }
∀ 𝑝, 𝑝 ∈ 𝑍 + ≥ 0 and
that:

19 → e 44 → R 69 → £ 94 → “
20 → F 45 → r 70 → _ 95 → ‘
𝑝 < 𝑎𝑏𝑠(𝐼𝑛𝑡𝑒𝑔𝑒𝑟 � � − 1) 21 → f 46 → S 71 → # 96 → €
log ∅−log 𝐾1
log 𝑛
22 → G 47 → s 72 → & 97 → 𝛼
23 → g 48 → T 73 → ~ 98 → 𝛽
24 → H 49 → t 74 → @ 99 → 𝛾
∀ 𝑞, 𝑞 ∈ 𝑍 + ≥ 0 and
where abs denote absolute value=

log ∅ − log 𝐾1
𝑞 < 𝑎𝑏𝑠(𝐼𝑛𝑡𝑒𝑔𝑒𝑟 � � − 1)
This step is employed to conserve storage space

log 𝑛
(where N is the length of str_Cipher2), 𝑁/2 characters
and also to discourage naive editing. The coding

∀ 𝑚, 𝑛; 𝑚, 𝑛 ∈ 𝑍 + ≥ 1.
scheme ensures that instead of storing N characters

are stored. Users of the system who are attackers are
discouraged from editing str_Cipher2 elements which
The size of Cipher1 depends on the size of its data are numbers only with the view that the numbers
type. Thus for large values, designers are encouraged correspond to the correct amount. Encoding individual

= Cipher1 + 𝐾2
to use double data type instead of integer or even float digits in str_Cipher2 without grouping them gives ten
(10) ways to determine the digits that constitute
Step 2. Cipher2
str_Cipher2.
Step 3. Count the number of characters in Cipher2. If
the total number of characters is not even then However, grouping the digits into twos gives
pad Cipher2 with a zero. This is done by using hundred (100) ways to determine any paired number
the algorithm blow: which relatively increases the efficiency of the system.
If the digits in str_Cipher2 are rotated or rearranged,
/* converts Cipher2 to string using

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there are 10𝑁 ways (where 𝑁 is the length of the Let 𝑝 = 0 and 𝑞 = 0 then 𝑛 𝑝 = 1 𝑎𝑛𝑑 𝑚 𝑞 = 1.
then using individual digits without grouping them, = 356

str_Cipher2 or the total number of characters in Given that Amt = 50,
str_Cipher2) to determine the digits in Cipher2 from
Cipher3. The complexity of the algorithm in terms of Cipher1 = K1 * Amt + K1
decrypting time is O(n). = 8701 * 50 + 8701

grouped into twos, there are 100𝑁(𝑁/2) ways of
However, when the digits in str_Cipher2 are = 443751
Cipher2 = Cipher1 + K2
determining the digits in Cipher2 from Cipher3. The = 443751 + 356

time is O(n2 ). The primary challenge of grouping the
complexity of the algorithm in terms of decrypting = 444107.

digits in str_Cipher2 into twos is the inclusion of non- The length of Cipher2 is six which is even. Hence
English characters. The number of characters for a padding is ignored
Standard English keyboard is ninety-seven (97) and Grouping Cipher2 into twos without rearranging
thus there are three (3) other character groups that need them, we have 44, 41 and 07. Thus Cipher3 is obtained
to be handled. In this work, Greek letters were chosen as:
and this required additional system configuration to
handle Greek letters Cipher3 = Encode (Grouped Cipher2)
= Encode (44, 41, 07)
B. Fractional Part Encryption
using coding scheme in Table 2 so that 44→R, 41→p
The fractional part is encrypted using coding and 07→(
scheme in Table 2. The keys K1 and K2 are not used in
encrypting the fractional part of the amount. The = Rp(
fractional part of the amount is encrypted differently to The fractional part, 00, is encoded using coding
frustrate attackers. Thus, the encoded fractional part scheme in Table 2 to get Cipher4. Thus
forms Cipher4 and the resulting Ciphertext obtained
from encrypting the integer part and the fractional part Cipher4 = Encode (Fractional Part)
of the amount is given by: = Encode (00)
=+
Ciphertext = Cipher4Cipher3
Finally, the encrypted amount (called Ciphertext)
C. Demonstration of Encryption Algorithm which is stored in the database is obtained as:
To illustrate the encryption algorithm, consider an Ciphertext = Cipher4Cipher3
amount of GHS 50.00 paid on 21st May, 2012 at = +Rp(
15:50:08 received by a cashier with CasherID
CE840716, using Table 1 and Table 2, the keys are IV. DECRYPTION ALGORITHM
computed as:
The algorithm for decrypting a Ciphertext requires
For K1: seven (7) steps which also involve data integrity
Using yy format of the year, it implies dd=21, checking. The description is used to decrypt +Rp(

p = 0, and q = 0 then np = 1 and mq = 1.
Thus K1 is computed as:
mm=5, yy=12, HH=15, MM=50 and SS = 8. which was encrypted in section III above given that

K1 = (dd ∗ mm + SS) ∗ (HH + MM + yy) Step 1. Splitthe Ciphertext into two groups, mainly, T1
and T2 with T1 containing only the first character
= (21 * 5 + 8) * (15 + 50 +12) of the Ciphertext and T2 containing the
= 113 * 77 remaining characters of the Ciphertext. The
= 8701
algorithm below demonstrates how splitting is
accomplished in Java:

Using the coding scheme in Table 1, it implies C →
For K2:

23, E → 25, 8 → 55, 4 → 51, 0 → 47, 7 → 54, 1 → 48
T1 = Ciphertext.substring (0, 1);

and 6 → 53. Thus K2 is computed as
T2 = Ciphertext.substring (1);

K 2 = ∑(CE840716)
Step 2. Decode T1 by reversing the coded scheme in
Table 2. For example, let T1 = +. The value that
= (23 + 25 + 55 + 51 + 47 + 54 + 48 + 53) corresponds to T1 = + is 00. Thus Plain(+) = 00

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6 Samuel King Opoku

Step 3. Decode T2 using the reverse coded scheme in letters as well. The figure below demonstrates how this
Table 2. Thus using Rp( as an example, R→44, can be done.
p→41 and (→07. Thus Plaintext1(T2) = 444107
Step 4. Compute K2 from the CashierID value of the
CashierID field using coded scheme in Table 1.
Deduct K2 from Plaintext1(T2). Using the
example above with K2 = 356. It implies that
Plaintext2(T2) = 444107 – 356
= 443751
Step 5. Compute K1 using date and time values from the
date and time fields respectively in the database.
Use K1 to find the Plaintext of the integer part
as:
Plaintext(integer part) = (plaintext2(T2) – K1) / K1.
Using the example above such that K1 = 8701, it
implies that
Plaintext(integer part) = (443751 - 8701) / 8701
= 50
Step 6. The division part of the computation of
Plaintext(integer part) which is shown as:
Plaintext(integer part) = (plaintext2(T2) – K1) / K1 Figure 3: Table Creation
is used to check data integrity. If the division results in
a real value instead of integer, then the value in the Working with web design tools to create web pages
database has been changed and an alarm needs to be be client side like HyperText Markup Language
raised. Otherwise go to step 7. (HTML) or server side scripting language like
Hypertext Preprocessor (PHP) requires language
Step 7. This
is the final stage where the fractional part modification as well. The figure below illustrates the
and the integer part are put together. language setting of a web page.
Thus
Amount = Plaintext(integer).Plain(T1).
Hence using the above example, the amount is
calculated as 50.00

V. SYSTEM IMPLEMENTATION AND
ALGORITHM TESTING
The system is implemented and tested via the
development of an accounting system. The accounting
system is used to collect school fees and also manages
the financial system of the institution. The introduction
of the Greek letters requires system setting
modification. In creating a database using MySQL
Database Management System, the language setting
needs to be changed. The figure below demonstrates
how to set the language of the database so as to accept Figure 4: Web Page Language Setting
Greek letters. The name of the database is smsystem. The system is designed to use K1 and K2 formulas
that are described under section II of this paper. The
system is implemented such that:
1. There are fifteen different coding schemes from
which K2 can be obtained.
Figure 2: Database Creation
2. There are fifteen different coding schemes for
A typical table is also created such that the obtaining Cipher3 from str_Cipher2.
language it accepts is also altered to accept Greek

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𝑛 𝑝 ∗ 𝐾1 ∗ 𝐴𝑚𝑡 ± 𝑚 𝑞 ∗ 𝐾1 such that ∀ 𝑛 , 𝑚; 𝑛 ≠
𝑚 and 𝑚, 𝑛 ∈ {1, 2, 3, 4, … , 50} and 𝑛 𝑝 ≠ 𝑚 𝑞 =
3. Cipher1 is obtained from K1 using the formula: 35
36 do

1. Also ∀ 𝑝, 𝑞; 𝑝, 𝑞 ∈ {0,1, 2, 3, 4} and 𝑝 ≠ 𝑞 = 0
37 new_W = Math.round (Math.random() * 15)
38 while (new_W < 1)
39
The system is implemented so that either n, m, p, q 40 //compare values
or the coding schemes used are changed periodically to 41 if (new_P == Prev_P and new_Q == Prev_Q and
increase the effectiveness of the system. Whenever the 42 new_N == Prev_N and new_M Prev_M and
43 new_Z == Prev_Z and new_W == Prev_W)
parameters are changed, all the encrypted amount in
44 Go to line 09
the system’s database are updated based on the new 45 else
values of the cryptographic parameters. A table called 46 for all encrypted amount
smsystem_specifications is created which has only one 47 decipher each amount using Prev_np, Prev_mq,
field, namely smsystem_settings. The field contains 48 Prev_Z and Prev_W
the string in the order p,q,m,n,z,w where p, q, m and n 49 encrypt each amount again using new_np,
are the respective values of the constants p, q, m and n 50 new_mq, new_Z and new_W
used as the current cryptographic parameters. z is the 51 end for
number of the coding scheme used for obtaining K2. 52 end if
The coding schemes are numbered 1 to 15. w is the 53 Stop
number of the coding scheme used for converting
str_Cipher2 to Cipher3. The coding schemes are VI. ANALYSIS OF THE IMPLEMENTED SYSTEM
numbered 1 to 15. These coding schemes are hidden
A. Strengths of the System
from users and they are hard-coded. The algorithm
below illustrates how the system determines the next The strengths of the system are analyzed as follow:
cryptographic parameters:
1. Encryption uses multiplication and addition which
01 Start prevent the occurrence of fraction in its

The resulting value of the division, (plaintext2(T2) ±
02 Load Prev_P, Prev_Q, Prev_M, computation. However, decryption uses division.
03 Load Prev_N, Prev_Z, Prev_W
04 mq*K1) / (np*K1), should always be an integer. The
05 //computing old parameters system has a simple way of checking data integrity.
06 Compute Prev_np and Prev_mq If a value is changed, the outcome of its decryption
07
shall not be integer but real.
08 //computing new parameter
09 do 2. Unlike the widely known algorithms which are
10 new_P = Math.round (Math.random() * 4) made up of at least sixteen characters occupying
11 while (new_P < 0) device storage space that can be used for storing
12 other important information, this design has a

maximum of � � ∈ Z + ciphertext
length of Amount + 5
13 do minimum of three ciphertext characters and a
2
14 new_Q = Math.round (Math.random() * 4)

seventeen characters and 𝑝 = 𝑞 = 0.
15 while (new_Q < 0)
16 characters given that CashierID contains three to
17 if (new_P == 0 and new_Q == 0)
18 Go to line 09
19 3. Keys are generated from the surroundings, that is
20 do other fields in the same database table. The field
21 new_N = Math.round (Math.random() * 50) values form part of the record. Without generating
22 while (new_N < 1) different keys which are sometimes stored
23 alongside the ciphertext conserves space and
24 do controls processing power.
25 new_M = Math.round (Math.random() * 50)
26 while (new_M < 1)
4. The manipulative or computational part of the

For instance, the format for computing K1 can be
27 algorithm can be change anytime without affecting
28 Compute new_np and new_mq the efficiency and effectiveness of the algorithm.
29 if (new_np == 1 and new_mq == 1 )
30 Go to line 20 changed so as the coding schemes.
31
32 do B. Limitations of the System
33 new_Z = Math.round (Math.random() * 15) The system also has limitations and they are
34 while (new_Z < 1)
discussed as follow:

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8 Samuel King Opoku

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How to cite
Samuel King Opoku, "A Robust Cryptographic System using Neighborhood-Generated Keys". International
Journal of Research in Computer Science, 2 (5): pp. 1-9, September 2012. doi:10.7815/ijorcs.25.2012.041

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A Robust Cryptographic System using Neighborhood-Generated Keys

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