RSA 32-bit Implementation Technique

DOI : 10.23883/IJRTER.2017.3359.UXAIW 279
RSA 32-bit Implementation Technique
Dian Kurnia1
, Haida Dafitri2
, Sugianto3
, Mardiana4
, Andysah Putera Utama Siahaan5
1,5
Faculty of Computer Science, Universitas Pembanguan Panca Budi, Medan, Indonesia
2,4
Department of Informatics, Sekolah Tinggi Teknik Harapan, Medan, Indonesia
3
Department of Information System, Sekolah Tinggi Teknik Harapan, Medan, Indonesia
Abstract - Encryption is a technique that transforms a code from an understandable into an
incomprehensible code. Many methods can be applied to an encryption process. One such method is
RSA. RSA works by appointing on byte values. The value is obtained from character conversion to
ASCII code. This algorithm is based on the multiplication of two relatively large primes. Applications
of the RSA algorithm can be used in data security. This research provides RSA algorithm application
on data security system that can guarantee data confidentiality. RSA algorithm is known as a very
secure algorithm. This algorithm works with the number of bits in the search for prime numbers. The
larger the bits, the less chance of ciphertext can be solved. The weakness of this method is the amount
of ciphertext capacity will be floating in line with the number of prime numbers used. Also, to perform
the process of encryption and decryption, RSA requires a relatively long time than other algorithms.
The advantage of RSA is that complicated ciphertext is solved into plaintext.
Keywords - Cryptography, RSA, Public Key, Prime
I. INTRODUCTION
Data security and confidentiality issues are an important aspect of information systems.
Because of the confidentiality and security of data, it is essential always to be concerned both for
common security, as well as for the privacy of individuals [6]. In this case, it is closely related to how
important the information and data is sent and received by the interested person. Information is no
longer useful if the information is tapped by an irresponsible person. For the data is not known by
parties who are not concerned, then each data owner is always trying to do security with some specific
techniques.
To secure the data, one way can be applied to use cryptography. Cryptography will encrypt the
data before the submission. There are many algorithms for cryptography that can be used. The use of
keys in cryptography is divided into two, symmetrical ones that only use a secret and asymmetric key
that uses a pair of public keys and a secret key. This research uses RSA [1][2]. It was discovered by
Ron Rivest, Adi Shamir, and Leonard Adleman in 1978. RSA stands for the initials of the names of
the three of them. RSA is used because it is the most commonly used asymmetric cryptography
algorithm at present. This algorithm is well known and safe. The length of keys in bits can be set. The
longer bit used, the more difficult to solve. It is because of the difficulty of factoring two huge numbers.
However, the greater the prime used, the longer the decryption process.
II. BASIC CONCEPT
2.1 Cryptography
Cryptography is a science or art of securing a message and done by a cryptographer. While
cryptanalysis is a science and art of solving ciphertext to plaintext. The person doing it is called
cryptanalysis. The word cryptography comes from the Greek word "kryptos" which means to hide and
"graphein" which means to write. Cryptography can be defined as a science that transforms

International Journal of Recent Trends in Engineering & Research (IJRTER)
Volume 03, Issue 07; July - 2017 [ISSN: 2455-1457]
@IJRTER-2017, All Rights Reserved 280
information from understandable forms into incomprehensible forms. Cryptography Algorithm always
consists of two parts, namely encryption, and decryption. Encryption is a process done to convert a
readable message into an unreadable message (ciphertext). Decryption is the opposite of the encryption
process, returning unread messages to unread messages. The encryption and decryption process is
governed by one or more cryptographic keys. In a system where there is a cryptographic algorithm,
plus all possible plaintext, ciphertext and keys are called cryptosystems [5].
2.2 Public-Key
One of the major difficulties of conventional encryption is the need for security to distribute
keys used in a secure state. The next generation technique is a modern cryptography. It is a way to
remove this weakness with an encryption model that does not require a key to be distributed. This
method is known as the "public-key" encryption and was first introduced in 1976. For conventional
encryption, the keys used in the encryption and decryption process are the same. However, this is not
necessary conditions. However, it is possible to construct an algorithm that uses one key for encryption
and decryption. This process requires different keys for encryption and decryption. Furthermore, it is
possible to create an algorithm in which the knowledge of the encryption algorithm and the encryption
key is insufficient to determine the decryption key [3].
The following techniques will be possible:
1. Each of the systems makes a key pair used for encryption and decryption.
2. Each of the systems will publish its public key by installing it in a general register or file, while its
partner is kept as a private key.
3. If the sender wants to record a message to the receiver, it will encrypt its message with the receiver's
public key.
4. When the receiver gets a message from the sender, it will use its private key to encrypt a message
from the sender.
Figure 1. Public-Key cryptography scheme
Figure 1 explains how public-key cryptography works. Both plaintexts are covered by public
and private keys. Several of them use the same key to encrypt and decrypt, but there also use the
different keys. Public-key solves the distribution problem because it does not need a key to share. All
users have access to public keys, and private keys are generated individually by each user, so there is
no need to share private keys between each other. As long as the user keeps the private key well, then
the information sent will always be safe and secure. Any system changing the private key of its partner
public key will replace the old public key. The weakness of public key encryption method, when
compared with the conventional encryption method, is this encryption has the more complex algorithm.
So for comparison the size and price of the hardware. The public key method will result in lower
performance than conventional methods.

Things to watch out for in Public-Key encryption such as:
1. The algorithm used for encryption and decryption with the key pair, one for encryption one for
decryption.
2. The sender and receiver must have a matching pair of keys.
3. One of the keys must be kept secret.
4. It is not possible or very impractical to translate encrypted information.
5. Knowledge of the algorithm and sample of the encrypted word is insufficient to determine the key.
2.3 RSA
RSA is one example of cryptography that applies the concept of the public-key cryptosystem
[4]. In the RSA algorithm, there are three main steps such as key generation, encryption, and decryption.
The keys to RSA include two keys, public key, and private key. The public key is used to perform
encryption and can be known by others. While the private key is kept secret and used to perform
decryption. RSA has several attributes indicate the input and output parameters [7][8]. The following
figure shows the process of RSA algorithm.
Figure 2. A flowchart illustrating the RSA algorithm

There are seven aspects we have to understand before trying to hack the RSA secret key such as:
1. P and Q : private
2. N = P . Q : public
3. φ(N) = (P - 1)(Q - 1) : private
4. E (encryption key) : public
5. D (decryption key) : private
6. M (plaintext) : private
7. C (ciphertext) : public
RSA uses two kinds of keys, public and private. A public key is a prime number which is shared
and unclassified. Both users can know the key, and anybody can get as well. A private key is a key
which is not shared or it is classified. Both users who keep the key must keep it secretly. The sender
and user hope nobody gets those values. N is got from P times Q. RSA uses the Euler function. It is a
function that is used in mathematical calculations. Euler function is a function that is used in
mathematical calculations on the RSA algorithm. It defines φ(N) for N ≥ 1 indicates the number of
positive integers < N relatively prime to N. Two numbers "A" and "B" are relatively prime if GCD(A,
B) = 1. The value of “E” and “D” are used to encrypt and decrypt. The “M” and “C” are the plaintext
and ciphertext byte arrays.
III. EVALUATION
The following illustration will discuss the RSA algorithm implementation which consists of
encryption and description process. For example, the sender sends a message to the recipient. The
process is done starting from the formation of the key, encryption and then the results are described
again the steps are as follows:
Table 1. Key Generation
Variable Value
P 9661
Q 48781
N 471273241
φ 471214800
Table 1 shows the key capture. Taken two small prime numbers of 5 and 11. N is derived from the
multiplication of both primes, N = 55; While Totien is 40.
Table 2. The Encryption Key and GCD
E GCD
459226353 3
459226354 2
459226355 35
459226356 12
459226357 1
459226358 2
459226359 9
459226360 40
459226361 1
459226362 42
459226363 1
459226364 4

Furthermore, in Table 2 will be selected value of E which has a value of GCD = 1. There are
several possible values to choose from because some have GCD = 1 viewed from the table. In this
experiment, we will choose the value E = 459226363, because GCD (459226363, 471214800) = 1.
Then we will find the value of the private key by using the algorithm and obtained that D = 459226363-
1
mod 471214800 = 307475827. Thus, the public key is (N, E) = (471273241, 459226363) and the
secret key is D = 307475827.
Table 3. The complete parameters of RSA
Variable Value
P 9661
Q 48781
N 471273241
T 471214800
E 459226363
D 307475827
The calculations below will illustrate the encryption and decryption process of the RSA algorithm.
Encryption Process:
E1 = 144459226363
𝑚𝑜𝑑 471273241
= 174408074
E2 = 102459226363
𝑚𝑜𝑑 471273241
= 118193768
E3 = 235459226363
𝑚𝑜𝑑 471273241
= 443990101
E4 = 218459226363
𝑚𝑜𝑑 471273241
= 409440301
E5 = 121459226363
𝑚𝑜𝑑 471273241
= 474605588
E6 = 2459226363
𝑚𝑜𝑑 471273241
= 445186215
Decryption Process:
D1 = 174408074307475827
𝑚𝑜𝑑 471273241
= 144
D2 = 118193768307475827
𝑚𝑜𝑑 471273241
= 102
D3 = 443990101307475827
𝑚𝑜𝑑 471273241
= 235
D4 = 409440301307475827
𝑚𝑜𝑑 471273241
= 218
E5 = 474605588307475827
𝑚𝑜𝑑 471273241
= 121
E6 = 445186215307475827
𝑚𝑜𝑑 471273241
= 2

Table 4. RSA Encryption & Decryptioon
ASCII Encryption Decryption
144 174408074 144
102 118193768 102
235 443990101 235
218 409440301 218
121 474605588 121
2 445186215 2
From the above example, it can be seen that the data before the encryption is the same as the
data after the decryption as shown in Table 4. The RCA cryptosystem makes our data more secure
from people who want to steal the data. In the example above the author used a 32-bit prime number.
To improve the security of data should use a bigger prime number and it is hard to factorize.
IV. CONCLUSION
Secrets and data security should be a top priority so that the data we want to send is only
accepted by the person who has been appointed as the recipient of the information. By using RSA
Algorithm, a system capable of ensuring data confidentiality can be established. From a technical point
of view, RSA has easy and simple encryption. However, seeing the size of the prime used, once
encrypted is a very difficult thing to return to the plaintext without knowing the prime number. In the
process of creating public keys and private keys, there are several factors to consider, namely the size
of the key, the determination of the p and q values to be difficult to crack, and the possible weaknesses
that can be known when the data is encrypted. The RSA algorithm's security is based on the difficulty
of factoring large numbers into their prime factors. RSA is very superior to security but very weak of
speed.
REFERENCES
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International Journal of Computer Science, vol. 8, no. 6, pp. 242-247, 2011.
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[3] N. Hegde dan P. Deepthi, “Pollard RHO Algorithm for Integer Factorization and Discrete Logarithm Problem,”
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Technology, vol. 37, no. 1, pp. 15-18, 2016.
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Engineering Trends and Technology, vol. 39, no. 3, pp. 168-172, 2016.
[6] E. Hariyanto dan R. Rahim, “Arnold’s Cat Map Algorithm in Digital Image Encryption,” International Journal of
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