This document presents an improved asymmetric key encryption algorithm using MATLAB. It begins with an introduction to asymmetric key cryptography and the RSA cryptosystem. It then describes a modified RSA algorithm using multiple public and private keys to increase security. Next, it explains how to implement RSA using the Chinese Remainder Theorem to reduce computational time. The document implements the original, modified, and CRT-based RSA algorithms in MATLAB and analyzes computation time versus number of prime numbers. It concludes the modified and CRT-based approaches provide more security than the original RSA algorithm with reduced computational time.
This presentation is based on the paper :
"A Method for Obtaining Digital Signatures and Public-Key Cryptosystems" by R.L. Rivest, A. Shamir, and L. Adleman
We will discuss the following: RSA Key generation , RSA Encryption , RSA Decryption , A Real World Example, RSA Security.
https://www.youtube.com/watch?v=x7QWJ13dgGs&list=PLKYmvyjH53q13_6aS4VwgXU0Nb_4sjwuf&index=7
This presentation is based on the paper :
"A Method for Obtaining Digital Signatures and Public-Key Cryptosystems" by R.L. Rivest, A. Shamir, and L. Adleman
We will discuss the following: RSA Key generation , RSA Encryption , RSA Decryption , A Real World Example, RSA Security.
https://www.youtube.com/watch?v=x7QWJ13dgGs&list=PLKYmvyjH53q13_6aS4VwgXU0Nb_4sjwuf&index=7
Cryptography is the practice and study of techniques for conveying information security.
The goal of Cryptography is to allow the intended recipients of the message to receive the message securely.
The most famous algorithm used today is RSA algorithm
traditional private/secret/single key cryptography uses one key
Key is shared by both sender and receiver
if the key is disclosed communications are compromised
also known as symmetric, both parties are equal
hence does not protect sender from receiver forging a message & claiming is sent by sender
This report to document the RSA code and how it works from encrypting certain message to how to decrypt it using general and private keys which will be generated in the given code.
Module 6
Advanced Networking
Security problems with internet architecture, Introduction to Software defined networking, Working of SDN, SDN in data centre, SDN applications, Data centre networking, IoT.
Cryptography is the practice and study of techniques for conveying information security.
The goal of Cryptography is to allow the intended recipients of the message to receive the message securely.
The most famous algorithm used today is RSA algorithm
traditional private/secret/single key cryptography uses one key
Key is shared by both sender and receiver
if the key is disclosed communications are compromised
also known as symmetric, both parties are equal
hence does not protect sender from receiver forging a message & claiming is sent by sender
This report to document the RSA code and how it works from encrypting certain message to how to decrypt it using general and private keys which will be generated in the given code.
Module 6
Advanced Networking
Security problems with internet architecture, Introduction to Software defined networking, Working of SDN, SDN in data centre, SDN applications, Data centre networking, IoT.
De-Noising Corrupted ECG Signals By Empirical Mode Decomposition (EMD) With A...IOSR Journals
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Enhanced RSA Cryptosystem based on Multiplicity of Public and Private Keys IJECEIAES
Security is one of the most important concern to the information and data sharing for companies, banks, organizations and government facilities. RSA is a public cryptographic algorithm that is designed specifically for authentication and data encryption. One of the most powerful reasons makes RSA more secure is that the avoidance of key exchange in the encryption and decryption processes. Standard RSA algorithm depends on the key length only to protect systems. However, RSA key is broken from time to another due to the development of computers hardware such as high speed processors and advanced technology. RSA developers have increased a key length or size of a key periodically to maintain a high security and privacy to systems that are protected by the RSA. In this paper, a method has been designed and implemented to strengthen the RSA algorithm by using multiple public and private keys. Therefore, in this method the security of RSA not only depends on the key size, but also relies on the multiplicity of public and private keys.
Implementation of RSA Algorithm with Chinese Remainder Theorem for Modulus N ...CSCJournals
Cryptography has several important aspects in supporting the security of the data, which
guarantees confidentiality, integrity and the guarantee of validity (authenticity) data. One of the
public-key cryptography is the RSA cryptography. The greater the size of the modulus n, it will be
increasingly difficult to factor the value of n. But the flaws in the RSA algorithm is the time
required in the decryption process is very long. Theorem used in this research is the Chinese
Remainder Theorem (CRT). The goal is to find out how much time it takes RSA-CRT on the size
of modulus n 1024 bits and 4096 bits to perform encryption and decryption process and its
implementation in Java programming. This implementation is intended as a means of proof of
tests performed and generate a cryptographic system with the name "RSA and RSA-CRT Text
Security". The results of the testing algorithm is RSA-CRT 1024 bits has a speed of
approximately 3 times faster in performing the decryption. In testing the algorithm RSA-CRT 4096
bits, the conclusion that the decryption process is also effective undertaken more rapidly.
However, the flaws in the key generation process and the RSA 4096 bits RSA-CRT is that the
time needed is longer to generate the keys.
Over this thesis, we did try to optimize tow major challenges of RSA policy:
1# Computational complexity.
2# Apology of unbreakability.
We use here multidimensional random padding scheme (MRPS) as an outer layer protection. RSA policy itself is inner or core layer but not ever unbreakable if additional layers are imposed. Here in this work, our MRPS scheme would able to ensure fully parametrized randomization process.
ANALYSIS OF RSA ALGORITHM USING GPU PROGRAMMINGIJNSA Journal
Modern-day computer security relies heavily on cryptography as a means to protect the data that we have become increasingly reliant on. The main research in computer security domain is how to enhance the speed of RSA algorithm. The computing capability of Graphic Processing Unit as a co-processor of the CPU can leverage massive-parallelism. This paper presents a novel algorithm for calculating modulo value that can process large power of numbers which otherwise are not supported by built-in data types. First the traditional algorithm is studied. Secondly, the parallelized RSA algorithm is designed using CUDA framework. Thirdly, the designed algorithm is realized for small prime numbers and large prime number . As a result the main fundamental problem of RSA algorithm such as speed and use of poor or small prime numbers that has led to significant security holes, despite the RSA algorithm's mathematical soundness can be alleviated by this algorithm.
Modern-day computer security relies heavily on cryptography as a means to protect the data that we have
become increasingly reliant on. The main research in computer security domain is how to enhance the
speed of RSA algorithm. The computing capability of Graphic Processing Unit as a co-processor of the
CPU can leverage massive-parallelism. This paper presents a novel algorithm for calculating modulo
value that can process large power of numbers which otherwise are not supported by built-in data types.
First the traditional algorithm is studied. Secondly, the parallelized RSA algorithm is designed using
CUDA framework. Thirdly, the designed algorithm is realized for small prime numbers and large prime
number . As a result the main fundamental problem of RSA algorithm such as speed and use of poor or
small prime numbers that has led to significant security holes, despite the RSA algorithm's mathematical
soundness can be alleviated by this algorithm.
Chaotic Rivest-Shamir-Adlerman Algorithm with Data Encryption Standard Schedu...journalBEEI
Cryptography, which involves the use of a cipher, describes a process of encrypting information so that its meaning is hidden and thus, secured from those who do not know how to decrypt the information. Cryptography algorithms come with the various types including the symmetric key algorithms and asymmetric key algorithms. In this paper, the authors applied the most commonly used algorithm, which is the RSA algorithm together with the Chaos system and the basic security device employed in the worldwide organizations which is the Data Encryption Standard (DES) with the objective to make a hybrid data encryption. The advantage of a chaos system which is its unpredictability through the use of multiple keys and the secrecy of the RSA which is based on integer factorization’s difficulty is combined for a more secure and reliable cryptography. The key generation was made more secure by applying the DES schedule to change the keys for encryption. The main strength of the proposed system is the chaotic variable key generator that chages the value of encrypted message whenever a different number of key is used. Using the provided examples the strength of security of the proposed system was tested and demonstrated.
Performance evaluation of modified modular exponentiation for rsa algorithmeSAT Journals
Abstract
Authentication is a very important application of public-key cryptography. Cryptographic algorithms make use of secret keys
known to send and receive information. When the keys are known the encryption / decryption process is an easy task, however
decryption will be impossible without knowing the correct key. The shared public key is managed by the sender, to produce a
message authentication code (MAC) for every transmitted message. There are many algorithms to enable security for message
authentication (secret key). RSA is one such best algorithm for public key based message authentication approaches. But it takes
more time for encryption and/or decryption process, when it has large key length. This research work evaluates the performance
of RSA algorithm with modified modular exponentiation technique for message authentication. As a result modified modular
exponent based RSA algorithm reduces execution time for encryption and decryption process.
Key Words: Cryptography, Message authentication, RSA, Modular Exponentiation.
An Advance Approach of Image Encryption using AES, Genetic Algorithm and RSA ...IJEACS
In current scenario the entire world is moving towards digital communication for fast and better communication. But in this a problem rises with security i.e. when we have to store information (either data or image) at any casual location or transmit information through internet. As internet is an open transmission medium, security of data becomes very important. To defend our information from piracy or from hacking we use a technique and i.e. known as Encryption Technique. In this paper, we use image as information and use an advance approach of well-known encryption techniques like AES, Genetic Algorithm, and RSA algorithm to encrypt it and keep our information safe from hackers or intruders making it highly difficult and time consuming to decipher the image without using the key.
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Connector Corner: Automate dynamic content and events by pushing a button
F010243136
1. IOSR Journal of Electronics and Communication Engineering (IOSR-JECE)
e-ISSN: 2278-2834,p- ISSN: 2278-8735.Volume 10, Issue 2, Ver. IV (Mar - Apr.2015), PP 31-36
www.iosrjournals.org
DOI: 10.9790/2834-10243136 www.iosrjournals.org 31 | Page
Improvised Asymmetric Key Encryption Algorithm Using
MATLAB
K.Sony1
, Desowja Shaik1,
B.Divya Sri2
, G.Anitha3
1
Assistant Professor, K L University, Vaddeswaram, Guntur District, AP
2,3, 4
ECE Department, K L University, Vaddeswaram, Guntur District, AP
Abstract: In this paper, A new technique is deployed to improve Asymmetric Key Encryption Technique with
multiple keys and Chinese remainder theorem(CRT) .The main aim of this Technique is to provide secure
transmission of data between any networks through a channel. The Scope of this paper deals with Multiple
Public and Private keys and its computation time. RSA algorithm is used to utilize asymmetric key encryption
technique .In proposed model RSA will be implemented using MATLAB with original RSA Algorithm
,Proposed RSA Algorithm and RSA using Chinese Remainder Theorem(CRT). The Computational time and its
mere effects are briefly dealt by varying the multiple number of keys .
Keywords: RSA, Multiple key, Chinese Remainder Theorem (CRT), Secure, MATLAB.
I. Introduction
In Communications regardless of the platform such as email, Voice messages or direct messages the
end users ultimate motive is to send or receive the information without any intervention from the intruder. So a
mechanism is to be deployed such that only the users should understand the information and for others it should
be in the unreadable format .The process of encoding the plain text messages into cipher text is referred as
Encryption and the reverse transforming process is decryption. In a Computer to Computer communications, the
sender usually does the encryption and at the receiving end the decryption is done[1] .
Every encryption and decryption process has two primarily goals : Algorithm and the key generation .
Algorithm is made public to all the users an it’s the key which makes the communication secure
between the user domain. If the same key is used at both the ends then it is referred as Symmetric Key
Cryptography and if different keys(Public and private key ) are used at both the ends its Asymmetric key
Cryptography[16]. The above mentioned process is depicted in the figure.
In this paper we deal about the Asymmetric key cryptography[3] since it overcomes the disadvantages
of symmetric key cryptography such as key exchange and also digital signature can be deployed using this
technique .It also deals about doing the encryption and decryption using two keys at both the ends so that the
information can be sent more securely using the Modified RSA Algorithm and with Chinese Remainder
Theorem .
II. RSA Crypto System
The RSA Algorithm was developed by Ron Rivest, Adi Shamir and Leonard in 1978[17]. The original
RSA algorithm follows 4 phases: Key Generation, Encryption, Decryption and Digital signature [9].
2. Improvised Asymmetric Key Encryption Algorithm Using MATLAB
DOI: 10.9790/2834-10243136 www.iosrjournals.org 32 | Page
Keygeneration
In key generation we typically need keys that are public and private keys. We will generate public and
private key using below steps [2]. Public key is visible to both sender and receiver, where as private key is kept
secret and is generated and made invisible to the end user. Public key is used during encryption process where
as private key is used during decryption process. The steps to find out public and private key in key generation
is given below.
1). Select two random prime numbers: r, s and find n=r*s.
2). Compute the value of ϕ(n)=(r-1)*(s-1)
3). Select a random integer e[12], such that 1<e<n and gcd(e, ϕ(n))=1.
4). Compute value of d, such that d*e ≡1 mod(n).
5). Public Key {e, n}, Private key {d, n}
Encryption
We generated public and private keys using Key generation. Now, we have to encrypt the message
using Public key. The process is dealt as given below
1). Take the message which represents Plain text. The Plain text should be encrypted using public key e. If a
sender wants to transmit the information to receiver, the receiver should send the public key to the sender ,and
then the sender will encrypt the message(M) with a Public key(e).
2). Now calculate the cipher text (C) by using given formula.
C=M ^ e mod(n)
Decryption
In decryption we will find out decrypted message(M) by using cipher text(C) and Private key(d).Then Compare
if the original message is equal to decrypted message[5]. If it is equal then algorithm is proven .
M=C ^ d mod(n)
Digital Signature
In order to find whether the process we followed in designing the algorithm is accurate or not we use
the concept of digital signature[6]. Here we will find signature(s) using private key(d) and H(m). And we will
find verification m‟ using signature(s) and public key(e) where H is the hash function. If m‟=H(m) then our
signature is correct[7]. The following formula are given below:
s = (H(m)^d)mod n
m‟=(s^ e) mod n.
.
2.1 Modified RSA Algorithm Using Multiple Keys
Here in Modified RSA algorithm we will generate multiple public and private keys. In modified RSA
algorithm the computational time is more due to multiple keys but security is more compared to original RSA
algorithm[10]. In modified RSA algorithm we are using two public and private keys it is less subjected to brute
force attack. Here in this we are having 3 phases are: key generation, encryption, decryption[14].
Key Generation In Modified RSA Algorithm
In key generation process we will generate multiple public and private keys using below steps. Here in
order to increase security we are generating multiple keys. Here public keys are visible to both sender and
receiver. And private keys are kept secret and. The following steps for key generation process in given below:
1). Select two set random numbers say p, q and r, s.
2). Find the value of n, z i.e., n=p*q, z=r*s
3). Compute the value of ϕ(n)=(p-1)*(q-1), k(z)=(p-1)*(q-1).
4). Select a random integer e, g such that 1<e<n, 1<g<z and gcd(e, ϕ (n))=1gcd(e, k(z))=1
5). Compute value of d, T such that d*e ≡1 mod(n) and t*g ≡1 mod(z)
6). Public Key {e, g, n, z}, Private key {d, t, n, z}
Encryption
We have generated multiple public and private key in above key generation. Now we will encrypt
using public keys. Since we will do two times encryption such a way reliability will be more compared to that
3. Improvised Asymmetric Key Encryption Algorithm Using MATLAB
DOI: 10.9790/2834-10243136 www.iosrjournals.org 33 | Page
of original RSA algorithm. We take message(M) and first public key(e) during encryption and find out C1=M^
e mod(n). By using c1 and second public key(g) we will find cipher text in encryption process.
C=C1^ g mod(z)
Decryption
In decryption we decrypt original message using private keys d, g. Here first we will decrypt using first
private key (d) which is m1=C ^ d mod(n).
And we will find out decrypted message using second private key (t).
M=m1 ^ t mod(z)
2.3 RSA Algorithm Using Chinese Remainder Theorem
By using Chinese remainder theorem(CRT)[4] we will increase processing time and security of
algorithm. By using CRT an efficient implementation of RSA algorithm can be implemented. Chinese
remainder theorem(CRT) states that, if input M, raise it to the eth
(or dth
) power modulo P and modulo Q the
intermediate results are then combined through multiplication and addition with some pre defined constant to
compute final result. By using CRT in RSA algorithm it requires four times less processing time compared and
smaller amount of memory for final decoded result. By Using Multi Prime Concept[19] we implement RSA
using CRT. They are 3 operations present in RSA using CRT are:
Key Generation Operation
The steps included in the key generation operation of multi-prime RSA-CRT are illustrated as:
i. Select three large prime r, s and w at random, each of which is n/3-bit in length.
ii. Set N = r x s x w and φ (N) = (r−1) x (s−1) x (w−1).
iii. Randomly pick an odd integer e such that gcd (e, φ (N)) = 1.
iv. After that compute d = e−1 mod (N).
v. Finally, calculate dr = d mod (r − 1), ds = d mod (s − 1) and dw = d mod (w − 1).
vi. The public key would be (e, N) and the private key would be (dr, ds, dw, r, s, w)[20].
Encryption Operation
For a given plain text m which belongs to Zn the encryption algorithm is the same as that of the original RSA:
c = m^ e mod N
Decryption Operation
In order to decrypt a cipher-text c:
i. The decipher first computes m1 =cr^ dr mod r, m2 = cs^ dq mod s, and m3 = cw^ dw mod w where cr = c
mod r, cs = c mod s and cw = c mod w
ii. Next, using CRT m can be obtained as m = c^ d mod N, in order to increase its efficiency.
III. Implementation And Results
3.1Original RSA Algorithm Implemented Using Alphabetic Message and Numerical Message
4. Improvised Asymmetric Key Encryption Algorithm Using MATLAB
DOI: 10.9790/2834-10243136 www.iosrjournals.org 34 | Page
3.2Modified RSA Algorithm Using Multiple Public and Private Keys
5. Improvised Asymmetric Key Encryption Algorithm Using MATLAB
DOI: 10.9790/2834-10243136 www.iosrjournals.org 35 | Page
3.3 RSA Algorithm Using Chinese Remainder Theorem(CRT)
IV. Graphs
Computation Time V/s Prime numbers
V. Conclusion
The observed results from our work clearly mention that by using a single (public and private key)the
computational time required is less but problem is less secure. To have more secured transmission of
information we can use Chinese remainder theorem so that there will be reduction of time of evaluation. So to
have both secure transmission and time bound application we can use two key methods.
Acknowledgements
Authors like to express their deep gratitude to K Sony, Assistant Professor Department of ECE K L
University for her great support and encouragement during the implementation of this work and also we would
also like to thank our communications research members and also our friends for their help in completion of this
paper.
References
[1]. William Stallings, “Cryptography and Network Security”, ISBN 81-7758-011-6, Pearson Education, Third Edition
[2]. R.L.Rivest,A. Shamir, and L.Adleman, ”A method for obtaining digital signature and public key cryptosystem”,
[3]. comm..ACM feb1978, 21(2):120-126
[4]. W.Diffie and M.E.Hellman, ”New directions in cryptography”, IEEE Trans. Inform. Theory, Nov.1976,22: 644-654.
6. Improvised Asymmetric Key Encryption Algorithm Using MATLAB
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Authors Profile
K.SONY is Assistant Professor in KL University. She Completed M.Tech Electronics and Communication
Engineering from ANNA University. He is getting his specialization in Signal processing
applications.. He is member of IETE. Her interest in research areas includes Optical
Communication and Image processing applications
DESOWJA SHAIK was born in India, A.P, in 1994.He is pursuing her B.Tech in Electronics and
Communication Engineering from K L University. He is getting his specialization in
communication. He presented 3 papers in International technical fests at reputed engineering
colleges. He is member of IETE. His interest in research areas includes Networking and
Cryptography and Communication.
B.DIVYA SRI was born in India, A.P, in 1994. She is pursuing her B.Tech in Electronics and Communication
Engineering from K L University. She is getting her specialization in communication. She is
member of IETE. Her interest in research includes VLSI and Image processing.
G.ANITHA was born in India, A.P, in 1994. She is pursuing her B.Tech in Electronics and Communication
Engineering from K L University. She is getting her specialization in communication. She is
member of IETE. Her interest in research includes Antennas and Networking.