This paper constructs two encryption methods using 2-D chaotic maps, Duffings and Arnold’s cat maps
respectively. Both of the methods are designed using message embedded scheme and are analyzed for
their validity, for plaintext sensitivity, key sensitivity, known plaintext and brute-force attacks. Due to the
less key space generally many chaotic cryptosystem developed are found to be weak against Brute force
attack which is an essential issue to be solved. For this issue, concept of identifiability proved to be a
necessary condition to be fulfilled by the designed chaotic cipher to resist brute force attack, which is a
basic attack. As 2-D chaotic maps provide more key space than 1-D maps thus they are considered to be
more suitable. This work is accompanied with analysis results obtained from these developed cipher.
Moreover, identifiable keys are searched for different input texts at various key values.
Cryptosystem An Implementation of RSA Using Verilogijcncs
This document describes an implementation of the RSA cryptosystem using Verilog for an FPGA. It presents the design of modules for key generation, encryption, and decryption. For key generation, it generates random prime numbers using an LFSR and primality tester, then calculates the public and private keys. Encryption and decryption are performed through modular exponentiation implemented with a right-to-left binary method. The modules are coded in Verilog and synthesized for an FPGA to provide a secure cryptosystem.
Image Encryption Using Advanced Hill Cipher AlgorithmIDES Editor
The Hill cipher algorithm is one of the symmetric
key algorithms that have several advantages in data
encryption. But, the inverse of the key matrix used for
encrypting the plaintext does not always exist. Then if the
key matrix is not invertible, then encrypted text cannot be
decrypted. In the Involutory matrix generation method the
key matrix used for the encryption is itself invertible. So, at
the time of decryption we need not to find the inverse of the
key matrix. The objective of this paper is to encrypt an
image using a technique different from the conventional Hill
Cipher. In this paper a novel advanced Hill (AdvHill)
encryption technique has been proposed which uses an
involutory key matrix. The scheme is a fast encryption
scheme which overcomes problems of encrypting the images
with homogeneous background. A comparative study of the
proposed encryption scheme and the existing scheme is
made. The output encrypted images reveal that the
proposed technique is quite reliable and robust.
Combined Implementation of Robust Cryptosystem for Non-invertible Matrices ba...IDES Editor
In this paper, we have combined the Robust
Cryptosystem for Non-invertible matrices based on Hill Cipher
technique with steganography method in order to securely
transmit text message. The steganography method used is LSB
insertion technique. The encryption and steganography
methods are used subsequently along with two randomization
technique: one of XOR the encrypted text and another of
randomized LSB insertion in any cover image. These two layers
of shuffling of text at different stages of encryption and
steganography provide two extra layers of security and make
the system robust against cryptanalytic attacks.
On the Usage of Chained Codes in CryptographyCSCJournals
This document summarizes a research paper on using randomized chained linear codes for digital signatures. The summary is:
1) Randomized chained linear codes are proposed to address attacks on previous signature schemes that used regular chained codes. Random vectors are concatenated to the generator matrix of a chained code to create randomized chained codes.
2) A digital signature scheme is presented that uses randomized chained codes. The private key consists of the generator matrix and randomization matrices. The public key is the randomized parity check matrix. Signatures are created using the chain code decoding algorithm.
3) Security analysis shows the scheme is secure if the code length is over 1350 bits, preventing an attacker from determining the private key from the public information
WEAKNESS ON CRYPTOGRAPHIC SCHEMES BASED ON REGULAR LDPC CODESIJNSA Journal
We propose a method to recover the structure of a randomly permuted chained code and how to cryptanalyse cryptographic schemes based on these kinds of error coding. As application of these methods is a cryptographic schema using regular Low Density Parity Check (LDPC) Codes. This result prohibits the use of chained code and particularly regular LDPC codes on cryptography
Multiple Encryption using ECC and Its Time Complexity AnalysisIJCERT
Rapid growth of information technology in present era, secure communication, strong data encryption technique and trusted third party are considered to be major topics of study. Robust encryption algorithm development to secure sensitive data is of great significance among researchers at present. The conventional methods of encryption used as of today may not sufficient and therefore new ideas for the purpose are to be design, analyze and need to be fit into the existing system of security to provide protection of our data from unauthorized access. An effective encryption/ decryption algorithm design to enhance data security is a challenging task while computation, complexity, robustness etc. are concerned. The multiple encryption technique is a process of applying encryption over a single encryption process in a number of iteration. Elliptic Curve Cryptography (ECC) is well known and well accepted cryptographic algorithm and used in many application as of today. In this paper, we discuss multiple encryptions and analyze the computation overhead in the process and study the feasibility of practical application. In the process we use ECC as a multiple-ECC algorithm and try to analyze degree of security, encryption/decryption computation time and complexity of the algorithm. Performance measure of the algorithm is evaluated by analyzing encryption time as well as decryption time in single ECC as well as multiple-ECC are compared with the help of various examples.
This document is a worksheet for a cryptography and network security course. It contains definitions of key terms like cryptography, encryption, decryption, and types of attacks. It also outlines classical encryption techniques like the Caesar cipher, Playfair cipher, Hill cipher, Vigenere cipher, and transposition techniques. Finally, it covers number theory topics such as prime numbers, factorization, Fermat's theorem, Euler's theorem, and primitive roots as they relate to cryptography.
New Technique Using Multiple Symmetric keys for Multilevel EncryptionIJERA Editor
In a world of accelerating communications, cryptography has become an essential component of the modern
means of communication systems. The emergence of the webas a reliable medium for commerce and
communication has made cryptography an essential component. Many algorithms or ciphers are in use
nowadays. The quality of the cipher is judged byits ability to prevent an unrelated party fromknowingthe
original content of the encrypted message. The proposed “Multilevel Encryption Model” is a cryptosystem that
adopts the basic principles of cryptography. It uses five symmetric keys (multiple)
in floating point numbers, plaintext, substitution techniques and key combinations with unintelligible
sequence to produce the ciphertext. The decryption process is also designed to reproduce the plaintext
Cryptosystem An Implementation of RSA Using Verilogijcncs
This document describes an implementation of the RSA cryptosystem using Verilog for an FPGA. It presents the design of modules for key generation, encryption, and decryption. For key generation, it generates random prime numbers using an LFSR and primality tester, then calculates the public and private keys. Encryption and decryption are performed through modular exponentiation implemented with a right-to-left binary method. The modules are coded in Verilog and synthesized for an FPGA to provide a secure cryptosystem.
Image Encryption Using Advanced Hill Cipher AlgorithmIDES Editor
The Hill cipher algorithm is one of the symmetric
key algorithms that have several advantages in data
encryption. But, the inverse of the key matrix used for
encrypting the plaintext does not always exist. Then if the
key matrix is not invertible, then encrypted text cannot be
decrypted. In the Involutory matrix generation method the
key matrix used for the encryption is itself invertible. So, at
the time of decryption we need not to find the inverse of the
key matrix. The objective of this paper is to encrypt an
image using a technique different from the conventional Hill
Cipher. In this paper a novel advanced Hill (AdvHill)
encryption technique has been proposed which uses an
involutory key matrix. The scheme is a fast encryption
scheme which overcomes problems of encrypting the images
with homogeneous background. A comparative study of the
proposed encryption scheme and the existing scheme is
made. The output encrypted images reveal that the
proposed technique is quite reliable and robust.
Combined Implementation of Robust Cryptosystem for Non-invertible Matrices ba...IDES Editor
In this paper, we have combined the Robust
Cryptosystem for Non-invertible matrices based on Hill Cipher
technique with steganography method in order to securely
transmit text message. The steganography method used is LSB
insertion technique. The encryption and steganography
methods are used subsequently along with two randomization
technique: one of XOR the encrypted text and another of
randomized LSB insertion in any cover image. These two layers
of shuffling of text at different stages of encryption and
steganography provide two extra layers of security and make
the system robust against cryptanalytic attacks.
On the Usage of Chained Codes in CryptographyCSCJournals
This document summarizes a research paper on using randomized chained linear codes for digital signatures. The summary is:
1) Randomized chained linear codes are proposed to address attacks on previous signature schemes that used regular chained codes. Random vectors are concatenated to the generator matrix of a chained code to create randomized chained codes.
2) A digital signature scheme is presented that uses randomized chained codes. The private key consists of the generator matrix and randomization matrices. The public key is the randomized parity check matrix. Signatures are created using the chain code decoding algorithm.
3) Security analysis shows the scheme is secure if the code length is over 1350 bits, preventing an attacker from determining the private key from the public information
WEAKNESS ON CRYPTOGRAPHIC SCHEMES BASED ON REGULAR LDPC CODESIJNSA Journal
We propose a method to recover the structure of a randomly permuted chained code and how to cryptanalyse cryptographic schemes based on these kinds of error coding. As application of these methods is a cryptographic schema using regular Low Density Parity Check (LDPC) Codes. This result prohibits the use of chained code and particularly regular LDPC codes on cryptography
Multiple Encryption using ECC and Its Time Complexity AnalysisIJCERT
Rapid growth of information technology in present era, secure communication, strong data encryption technique and trusted third party are considered to be major topics of study. Robust encryption algorithm development to secure sensitive data is of great significance among researchers at present. The conventional methods of encryption used as of today may not sufficient and therefore new ideas for the purpose are to be design, analyze and need to be fit into the existing system of security to provide protection of our data from unauthorized access. An effective encryption/ decryption algorithm design to enhance data security is a challenging task while computation, complexity, robustness etc. are concerned. The multiple encryption technique is a process of applying encryption over a single encryption process in a number of iteration. Elliptic Curve Cryptography (ECC) is well known and well accepted cryptographic algorithm and used in many application as of today. In this paper, we discuss multiple encryptions and analyze the computation overhead in the process and study the feasibility of practical application. In the process we use ECC as a multiple-ECC algorithm and try to analyze degree of security, encryption/decryption computation time and complexity of the algorithm. Performance measure of the algorithm is evaluated by analyzing encryption time as well as decryption time in single ECC as well as multiple-ECC are compared with the help of various examples.
This document is a worksheet for a cryptography and network security course. It contains definitions of key terms like cryptography, encryption, decryption, and types of attacks. It also outlines classical encryption techniques like the Caesar cipher, Playfair cipher, Hill cipher, Vigenere cipher, and transposition techniques. Finally, it covers number theory topics such as prime numbers, factorization, Fermat's theorem, Euler's theorem, and primitive roots as they relate to cryptography.
New Technique Using Multiple Symmetric keys for Multilevel EncryptionIJERA Editor
In a world of accelerating communications, cryptography has become an essential component of the modern
means of communication systems. The emergence of the webas a reliable medium for commerce and
communication has made cryptography an essential component. Many algorithms or ciphers are in use
nowadays. The quality of the cipher is judged byits ability to prevent an unrelated party fromknowingthe
original content of the encrypted message. The proposed “Multilevel Encryption Model” is a cryptosystem that
adopts the basic principles of cryptography. It uses five symmetric keys (multiple)
in floating point numbers, plaintext, substitution techniques and key combinations with unintelligible
sequence to produce the ciphertext. The decryption process is also designed to reproduce the plaintext
AN ADAPTIVE PSEUDORANDOM STEGO-CRYPTO TECHNIQUE FOR DATA COMMUNICATIONIJCNCJournal
The document describes a proposed adaptive pseudorandom stego-crypto technique for data communication. The technique combines stream cipher cryptography with a modified pseudorandom LSB substitution technique. This provides an evenly distributed cipher text while also enhancing security through increased brute force search times and reduced time complexity by avoiding collisions during random pixel selection. The proposed method uses three parameters that are optimized through experimental analysis to minimize distortions, increase cipher text scattering, and reduce collisions and time complexity. Results demonstrate the technique maintains good perceptual quality while improving upon previous methods.
This document contains a question bank for the subject Cryptography and Network Security. It includes questions grouped under different units of the subject: Introduction and Number Theory, Block Ciphers and Public Key Cryptography, Hash Functions and Digital Signatures. For each question, it provides the question number, question, marks allotted, knowledge level and number of times the question may appear in the assessment. The document also provides details of the subject code, name, class, staff in-charge and course code.
A FRACTAL BASED IMAGE CIPHER USING KNUTH SHUFFLE METHOD AND DYNAMIC DIFFUSIONIJCNCJournal
This paper proposes a fractal-based image encryption algorithm which follows permutation-substitution structure to maintain confusion and diffusion properties. The scheme consists of three phases: key generation process; pixel permutation using the Knuth shuffle method; and the dynamic diffusion of scrambled image. A burning ship fractal function is employed to generate a secret key sequence which is further scanned using the Hilbert transformation method to increase the randomness. The chaotic behavior of the fractal strengthens the key sensitivity towards its initial condition. In the permutation phase, the Knuth shuffle method is applied to a noisy plain image to change the index value of each pixel. To substitute the pixel values, a dynamic diffusion is suggested in which each scrambled pixel change its value by using the current key pixel and the previously ciphered image pixel. To enhance the security of the cryptosystem, the secret key is also modified at each encryption step by performing algebraic transformations. The visual and numerical analysis demonstrates that the proposed scheme is reliable to secure transmission of gray as well as color images.
1. Digital signatures provide authentication of digital documents by using asymmetric cryptography techniques. A digital signature is generated using a private key and can be verified by anyone using the corresponding public key.
2. There are various types of attacks against digital signature schemes like key-only attacks, generic chosen message attacks, and adaptive chosen message attacks. The security goals are to prevent total key breaks or the ability to forge signatures selectively or existentially.
3. A secure digital signature scheme must produce signatures that depend on the message, use secret information to prevent forgery and denial, be efficient to generate and verify, and make forgery computationally infeasible. Timestamps can be included to require message freshness.
STEGANOGRAPHY BASED ASYMMETRIC KEY CRYPTOSYSTEM USING TRELLIS CODED GENETIC A...ijesajournal
This paper focuses on generating a random bit sequence using Trellis coded Genetic Algorithm (TCGA)
with boolean function as source of input. Randomness of the generated bit sequence is tested using the
methods proposed by National Institute of Standards and Technology (NIST) to be used as random key
for cryptographic applications. Generated random key is transmitted using Blue Pixel Least Significant
bit (BPLSB) steganographic technique. The extracted random key is then used for image encryption and
decryption for asymmetric key cryptosystem.
The document discusses stream ciphers and block ciphers. It explains that stream ciphers encrypt data bit-by-bit or byte-by-byte, requiring a randomly generated keystream, while block ciphers encrypt fixed-length blocks, allowing for broader applications. It then focuses on the Feistel cipher structure for block ciphers, proposed by Feistel to approximate an ideal block cipher for large block sizes. The Feistel structure uses a product cipher approach involving substitutions and permutations to provide diffusion and confusion and resist statistical cryptanalysis.
A Secure Encryption Technique based on Advanced Hill Cipher For a Public Key ...IOSR Journals
This document presents a secure encryption technique based on an advanced Hill cipher for a public key cryptosystem. The technique uses an involutory matrix and permuted key to encrypt plaintext into ciphertext. It further encrypts the ciphertext through two levels of scrambling and adds tamper detection by calculating and transmitting the determinant of the ciphertext matrix. The decryption process reverses these steps to recover the original plaintext. The technique aims to make the cipher highly secure against cryptanalytic attacks by introducing multiple transformations and ensuring the integrity of the ciphertext through determinant verification.
Implementation Secure Authentication Using Elliptic Curve CryptographyAM Publications
Elliptic curve cryptography is the most efficient public key encryption scheme based on the elliptic curve concepts that
can be used to create faster, smaller, and efficient cryptographic keys. As a use of network increase for critical transaction, so
huge damages are caused by intrusion attacks hence there is the need of computer network security. To protect network against
various active and passive attack, various technique have been suggested. Mobile devices have many differences in their
capabilities, computational powers and security requirements. The security of mobile communication has stopped the list of
concerns for mobile phone users. Confidentiality, Authentication, Integrity and Non-repudiation are required security services for mobile communication.
Lightweight Cryptography for Distributed PKI Based MANETSIJCNCJournal
This document proposes a lightweight cryptography solution for secure communication in mobile ad hoc networks (MANETs). It describes creating a distributed public key infrastructure (PKI) using Shamir's secret sharing to decentralize the certificate authority role among MANET nodes. Each node holds a share of the private key. It then proposes using Tiny Encryption Algorithm (TEA), an efficient symmetric-key cipher, along with elliptic curve Diffie-Hellman key exchange to establish secure communication between nodes with limited resources. The system initializes by having founding MANET nodes act as dealers to distribute secret shares. Nodes then use Diffie-Hellman to independently derive a secret key to encrypt communications.
This document summarizes a research paper on a Probabilistic Data Encryption Scheme (PDES). The paper presents a probabilistic encryption scheme that combines the security of Goldwasser and Micali's probabilistic encryption with the efficiency of deterministic schemes. The scheme is based on the assumption that solving the quadratic residuacity problem is computationally infeasible without knowing the factorization of the composite integer. An example is provided to illustrate how the encryption and decryption algorithms work using quadratic residues modulo a composite integer. The paper concludes that the scheme provides semantic security similar to Goldwasser-Micali under the assumption that the quadratic residuacity problem is hard.
A Novel Method for Preventing Selective Jamming Attacks in Wireless NetworksIJMER
The document proposes three novel methods to prevent selective jamming attacks in wireless networks:
1. Strong Hiding Commitment Scheme (SHCS) which uses asymmetric cryptography to commit a sender to a value while keeping it hidden.
2. Cryptographic Puzzle Hiding Scheme which generates puzzles that force attackers to spend time solving before obtaining secret keys.
3. Hiding based on All-Or-Nothing Transformation which partitions messages into blocks that are meaningless individually, preventing selective jamming until all blocks are received.
Somewhat Homomorphic Encryption TechniqueNaishil Shah
This document summarizes the implementation of a somewhat homomorphic encryption technique. It describes modifying an existing somewhat homomorphic encryption scheme to enable addition, subtraction, and multiplication of integers. The key changes include replacing the modulo 2 operation in decryption with modulo X, where X is the maximum value for supported computations. AES encryption is used to securely transmit the homomorphically encrypted data between a client and server, which perform operations on the encrypted integers and return the encrypted result to the client for decryption. Several challenges arose during implementation related to the data types and block sizes supported by AES encryption.
Design and Implementation of a Secure Communication Protocol IJECEIAES
The main object of this paper is to present a mutual authentication protocol that guarantees security, integrity and authenticity of messages, transferred over a network system. In this paper a symmetric key cryptosystem, that satisfies all the above requirements, is developed using theorems of J.R. Chen, I.M. Vinogradov and Fermat and the decimal expansion of an irrational number.
A new RSA public key encryption scheme with chaotic maps IJECEIAES
Public key cryptography has received great attention in the field of information exchange through insecure channels. In this paper, we combine the Dependent-RSA (DRSA) and chaotic maps (CM) to get a new secure cryptosystem, which depends on both integer factorization and chaotic maps discrete logarithm (CMDL). Using this new system, the scammer has to go through two levels of reverse engineering, concurrently, so as to perform the recovery of original text from the cipher-text has been received. Thus, this new system is supposed to be more sophisticated and more secure than other systems. We prove that our new cryptosystem does not increase the overhead in performing the encryption process or the decryption process considering that it requires minimum operations in both. We show that this new cryptosystem is more efficient in terms of performance compared with other encryption systems, which makes it more suitable for nodes with limited computational ability.
RSA ALGORITHM WITH A NEW APPROACH ENCRYPTION AND DECRYPTION MESSAGE TEXT BY A...ijcisjournal
In many research works, there has been an orientation to studying and developing many of the applications of public-key cryptography to secure the data while transmitting in the systems, In this paper we present an approach to encrypt and decrypt the message text according to the ASCII(American Standard Code for Information Interchange) and RSA algorithm by converting the message text into binary representation and dividing this representation to bytes(8s of 0s and 1s) and applying a bijective function between the group of those bytes and the group of characters of ASCII and then using this mechanism to be compatible with using RSA algorithm, finally, Java application was built to apply this approach directly.
HOW TO AVOID THE N-1 ATTACK WITHOUT COSTLY IMPLEMENTATIONSIJNSA Journal
Simple Power Analysis (SPA) attacks are widely used against several cryptosystems, principally against cryptosystems based on modular exponentiation. Many types of SPA have been reported in the literature, Yen et al. introduced the N-1 attack, which uses chosen input messages to obtain relevant information from the attacked cryptosystem. Their attack was implemented on the square-and-multiply always and on
the BRIP algorithm, both algorithms in left-to-right form. There are possible countermeasures against this attack, but all of them are costly and time consuming. In this paper, a computationally efficient and effective method to avoid the N-1 attack is investigated.
Random Keying Technique for Security in Wireless Sensor Networks Based on Mem...ijcsta
The document proposes a random keying technique combined with memetics concepts to provide security in wireless sensor networks. It involves randomly selecting keys from ranges distributed from the base station to cluster heads and nodes. When a node communicates, it selects keys that undergo crossover and mutation to generate header and trailer keys. The receiving node verifies packets by applying the same operations to the header keys and comparing the results to the trailer keys. Simulations showed this technique effectively combats spoofing attacks while being energy efficient compared to cryptographic methods.
The Quality of the New Generator Sequence Improvent to Spread the Color Syste...TELKOMNIKA JOURNAL
This paper shows a new technic applicable for the digital devices that are the result of the finite’s
effect precision in the chaotic dynamics used in the coupled technic and the chaotic map’s perturbation
technics used for the generation of a Pseudo-Random Number Generator (PRNGs).The use of the
pseudo- chaotic sequences coupled to the orbit perturbation method in the chaotic logistic map and the
NewPiece-Wise Linear Chaotic Map (NPWLCM). The pseudo random number generator’s originality
proposed from the perturbation of the chaotic recurrence. Furthermore the outputs of the binary sequences
with NPWLCM are reconstructed conventionally with the Bernoulli’s sequences shifts map to change the
shapes with the bitwise permetation then the results in simulation are shown in progress.After being
perturbed, the chaotic system can generate the chaotic binary sequences in uniform distribution and the
statistical properties invulnerable analysis. This generator also has many advantages in the possible useful
applications of spread spectrum digitalimages, such as sensitive secret keys, random uniform distribution
of pixels in Crypto system in secure and synchronize communication.
This document proposes a medical image encryption technique that uses multiple chaotic maps. It utilizes the logistic map, Arnold cat map, and Baker's map within a triple data encryption standard (3DES) scheme. The technique encrypts and decrypts medical images efficiently and securely, making it suitable for transmission over insecure networks. It was tested using the transmission control protocol (TCP)/internet protocol (IP) to transfer encrypted images between a server and client. Experimental results found the method resistant to attacks while maintaining encryption performance.
Image encryption using chaotic sequence and its cryptanalysisIOSR Journals
1) The document analyzes an image encryption algorithm that uses chaotic sequences. It finds that the algorithm can be broken with only a small number of known or chosen plaintexts using two attacks.
2) A chosen plaintext attack is described that requires only one known plaintext and two chosen plaintexts to reveal the secret chaotic sequences and encryption keys.
3) A known plaintext attack is also introduced that requires two known plaintext-ciphertext pairs to determine the secret parameters and completely break the encryption scheme.
A NOVEL SECURE COSINE SIMILARITY COMPUTATION SCHEME WITH MALICIOUS ADVERSARIESIJNSA Journal
Similarity coefficients play an important role in many aspects. Recently, several schemes were proposed, but these schemes aimed to compute the similarity coefficients of binary data. In this paper, a novel scheme
which can compute the coefficients of integer is proposed. To the best knowledge of us, this is the first scheme which canesist malicious adversaries attack.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
AN ADAPTIVE PSEUDORANDOM STEGO-CRYPTO TECHNIQUE FOR DATA COMMUNICATIONIJCNCJournal
The document describes a proposed adaptive pseudorandom stego-crypto technique for data communication. The technique combines stream cipher cryptography with a modified pseudorandom LSB substitution technique. This provides an evenly distributed cipher text while also enhancing security through increased brute force search times and reduced time complexity by avoiding collisions during random pixel selection. The proposed method uses three parameters that are optimized through experimental analysis to minimize distortions, increase cipher text scattering, and reduce collisions and time complexity. Results demonstrate the technique maintains good perceptual quality while improving upon previous methods.
This document contains a question bank for the subject Cryptography and Network Security. It includes questions grouped under different units of the subject: Introduction and Number Theory, Block Ciphers and Public Key Cryptography, Hash Functions and Digital Signatures. For each question, it provides the question number, question, marks allotted, knowledge level and number of times the question may appear in the assessment. The document also provides details of the subject code, name, class, staff in-charge and course code.
A FRACTAL BASED IMAGE CIPHER USING KNUTH SHUFFLE METHOD AND DYNAMIC DIFFUSIONIJCNCJournal
This paper proposes a fractal-based image encryption algorithm which follows permutation-substitution structure to maintain confusion and diffusion properties. The scheme consists of three phases: key generation process; pixel permutation using the Knuth shuffle method; and the dynamic diffusion of scrambled image. A burning ship fractal function is employed to generate a secret key sequence which is further scanned using the Hilbert transformation method to increase the randomness. The chaotic behavior of the fractal strengthens the key sensitivity towards its initial condition. In the permutation phase, the Knuth shuffle method is applied to a noisy plain image to change the index value of each pixel. To substitute the pixel values, a dynamic diffusion is suggested in which each scrambled pixel change its value by using the current key pixel and the previously ciphered image pixel. To enhance the security of the cryptosystem, the secret key is also modified at each encryption step by performing algebraic transformations. The visual and numerical analysis demonstrates that the proposed scheme is reliable to secure transmission of gray as well as color images.
1. Digital signatures provide authentication of digital documents by using asymmetric cryptography techniques. A digital signature is generated using a private key and can be verified by anyone using the corresponding public key.
2. There are various types of attacks against digital signature schemes like key-only attacks, generic chosen message attacks, and adaptive chosen message attacks. The security goals are to prevent total key breaks or the ability to forge signatures selectively or existentially.
3. A secure digital signature scheme must produce signatures that depend on the message, use secret information to prevent forgery and denial, be efficient to generate and verify, and make forgery computationally infeasible. Timestamps can be included to require message freshness.
STEGANOGRAPHY BASED ASYMMETRIC KEY CRYPTOSYSTEM USING TRELLIS CODED GENETIC A...ijesajournal
This paper focuses on generating a random bit sequence using Trellis coded Genetic Algorithm (TCGA)
with boolean function as source of input. Randomness of the generated bit sequence is tested using the
methods proposed by National Institute of Standards and Technology (NIST) to be used as random key
for cryptographic applications. Generated random key is transmitted using Blue Pixel Least Significant
bit (BPLSB) steganographic technique. The extracted random key is then used for image encryption and
decryption for asymmetric key cryptosystem.
The document discusses stream ciphers and block ciphers. It explains that stream ciphers encrypt data bit-by-bit or byte-by-byte, requiring a randomly generated keystream, while block ciphers encrypt fixed-length blocks, allowing for broader applications. It then focuses on the Feistel cipher structure for block ciphers, proposed by Feistel to approximate an ideal block cipher for large block sizes. The Feistel structure uses a product cipher approach involving substitutions and permutations to provide diffusion and confusion and resist statistical cryptanalysis.
A Secure Encryption Technique based on Advanced Hill Cipher For a Public Key ...IOSR Journals
This document presents a secure encryption technique based on an advanced Hill cipher for a public key cryptosystem. The technique uses an involutory matrix and permuted key to encrypt plaintext into ciphertext. It further encrypts the ciphertext through two levels of scrambling and adds tamper detection by calculating and transmitting the determinant of the ciphertext matrix. The decryption process reverses these steps to recover the original plaintext. The technique aims to make the cipher highly secure against cryptanalytic attacks by introducing multiple transformations and ensuring the integrity of the ciphertext through determinant verification.
Implementation Secure Authentication Using Elliptic Curve CryptographyAM Publications
Elliptic curve cryptography is the most efficient public key encryption scheme based on the elliptic curve concepts that
can be used to create faster, smaller, and efficient cryptographic keys. As a use of network increase for critical transaction, so
huge damages are caused by intrusion attacks hence there is the need of computer network security. To protect network against
various active and passive attack, various technique have been suggested. Mobile devices have many differences in their
capabilities, computational powers and security requirements. The security of mobile communication has stopped the list of
concerns for mobile phone users. Confidentiality, Authentication, Integrity and Non-repudiation are required security services for mobile communication.
Lightweight Cryptography for Distributed PKI Based MANETSIJCNCJournal
This document proposes a lightweight cryptography solution for secure communication in mobile ad hoc networks (MANETs). It describes creating a distributed public key infrastructure (PKI) using Shamir's secret sharing to decentralize the certificate authority role among MANET nodes. Each node holds a share of the private key. It then proposes using Tiny Encryption Algorithm (TEA), an efficient symmetric-key cipher, along with elliptic curve Diffie-Hellman key exchange to establish secure communication between nodes with limited resources. The system initializes by having founding MANET nodes act as dealers to distribute secret shares. Nodes then use Diffie-Hellman to independently derive a secret key to encrypt communications.
This document summarizes a research paper on a Probabilistic Data Encryption Scheme (PDES). The paper presents a probabilistic encryption scheme that combines the security of Goldwasser and Micali's probabilistic encryption with the efficiency of deterministic schemes. The scheme is based on the assumption that solving the quadratic residuacity problem is computationally infeasible without knowing the factorization of the composite integer. An example is provided to illustrate how the encryption and decryption algorithms work using quadratic residues modulo a composite integer. The paper concludes that the scheme provides semantic security similar to Goldwasser-Micali under the assumption that the quadratic residuacity problem is hard.
A Novel Method for Preventing Selective Jamming Attacks in Wireless NetworksIJMER
The document proposes three novel methods to prevent selective jamming attacks in wireless networks:
1. Strong Hiding Commitment Scheme (SHCS) which uses asymmetric cryptography to commit a sender to a value while keeping it hidden.
2. Cryptographic Puzzle Hiding Scheme which generates puzzles that force attackers to spend time solving before obtaining secret keys.
3. Hiding based on All-Or-Nothing Transformation which partitions messages into blocks that are meaningless individually, preventing selective jamming until all blocks are received.
Somewhat Homomorphic Encryption TechniqueNaishil Shah
This document summarizes the implementation of a somewhat homomorphic encryption technique. It describes modifying an existing somewhat homomorphic encryption scheme to enable addition, subtraction, and multiplication of integers. The key changes include replacing the modulo 2 operation in decryption with modulo X, where X is the maximum value for supported computations. AES encryption is used to securely transmit the homomorphically encrypted data between a client and server, which perform operations on the encrypted integers and return the encrypted result to the client for decryption. Several challenges arose during implementation related to the data types and block sizes supported by AES encryption.
Design and Implementation of a Secure Communication Protocol IJECEIAES
The main object of this paper is to present a mutual authentication protocol that guarantees security, integrity and authenticity of messages, transferred over a network system. In this paper a symmetric key cryptosystem, that satisfies all the above requirements, is developed using theorems of J.R. Chen, I.M. Vinogradov and Fermat and the decimal expansion of an irrational number.
A new RSA public key encryption scheme with chaotic maps IJECEIAES
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In many research works, there has been an orientation to studying and developing many of the applications of public-key cryptography to secure the data while transmitting in the systems, In this paper we present an approach to encrypt and decrypt the message text according to the ASCII(American Standard Code for Information Interchange) and RSA algorithm by converting the message text into binary representation and dividing this representation to bytes(8s of 0s and 1s) and applying a bijective function between the group of those bytes and the group of characters of ASCII and then using this mechanism to be compatible with using RSA algorithm, finally, Java application was built to apply this approach directly.
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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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The document discusses a hybrid approach to steganography and visual cryptography for improved data security. It proposes combining principles of steganography, which hides data in a cover media, and visual cryptography, which encrypts images in a way that can be decrypted by human vision without algorithms. Specifically, it describes generating two random grids from a secret image that reveal the image when overlaid but hide it individually. The random grids are created by inverting or substituting pixels based on the secret image. This hybrid approach aims to provide stronger security than either technique alone by incorporating advantages of both.
UNIT - 2
SYMMETRIC CIPHERS: Symmetric Cipher Model, Substitution Techniques,
Transposition Techniques, Simplified DES, Data encryption standard (DES), The strength of
DES, Differential and Linear Cryptanalysis, Block Cipher Design Principles and Modes of
Operation, Evaluation Criteria for Advanced Encryption Standard, The AES Cipher.
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In world of computer network, fears come in many different forms. Some of the most common fears today are software attacks. If we want to secure any type of data then we can use encryption method. All traditional encryption methods use substitution and switch. Substitution methods map plain text into ciphertext in which characters, numbers and special symbols are substituted with other characters, numbers and special symbols. In this paper, we are using a creative cryptographic replacement method is to generate a stronger cipher than the existing replacement algorithms. This method focuses on the replacement of characters, numbers and special symbols with color blocks. This algorithm of substitution is based on Play Color Cipher. Yashvanth. L | Dr. N. Shanmugapriya "Color Cryptography using Substitution Method" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-1 , December 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29360.pdfPaper URL: https://www.ijtsrd.com/engineering/computer-engineering/29360/color-cryptography-using-substitution-method/yashvanth-l
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Chaos Image Encryption using Pixel shuffling cscpconf
This document proposes a chaos-based image encryption algorithm using pixel shuffling. It uses elements from a chaotic map like the Henon map or Lorentz map to shuffle the pixel positions of an image. The chaotic elements are divided into blocks corresponding to the RGB channels. Pixel positions are reordered according to the sorted indices of each block. Encryption scrambles the pixel positions, while decryption restores the original positions using the same chaotic map. Experimental results on brain and Lena images show the encrypted images have very low correlation with the originals. Slight key changes also result in completely different decryptions, demonstrating key sensitivity of the algorithm.
COLOR IMAGE ENCRYPTION BASED ON MULTIPLE CHAOTIC SYSTEMSIJNSA Journal
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known-plaintext attack. In the diffusion stage, four pseudo-random gray value sequences are generated by
another generalized Arnold map. The gray value sequences are applied to perform the diffusion process by bitxoring operation with the permuted image row-by-row or column-by-column to improve the encryption rate. The security and performance analysis have been performed, including key space analysis, histogram analysis, correlation analysis, information entropy analysis, key sensitivity analysis, differential analysis
etc. The experimental results show that the proposed image encryption scheme is highly secure thanks to its
large key space and efficient permutation-substitution operation, and therefore it is suitable for practical image and video encryption.
COLOR IMAGE ENCRYPTION BASED ON MULTIPLE CHAOTIC SYSTEMSIJNSA Journal
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COLOR IMAGE ENCRYPTION BASED ON MULTIPLE CHAOTIC SYSTEMSIJNSA Journal
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operation is applied to achieve the diffusion effect. In permutation stage, the 3D color plain-image matrix
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cipher keys but also depend on plain-image and therefore can resist chosen-plaintext attack as well as
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A New Security Level for Elliptic Curve Cryptosystem Using Cellular Automata ...Editor IJCATR
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Message Embedded Cipher Using 2-D Chaotic Map
1. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
13
MESSAGE EMBEDDED CIPHER
USING 2-D CHAOTIC MAP
Mina Mishra1
and Dr. V.H. Mankar2
1
Ph. D. Scholar, Department of Electronics & Telecommunication, Nagpur University,
Nagpur, Maharashtra, India
minamishraetc@gmail.com
2
Senior Faculty, Department of Electronics Engineering, Government Polytechnic,
Nagpur, Maharashtra, India
vhmankar@gmail.com
ABSTRACT
This paper constructs two encryption methods using 2-D chaotic maps, Duffings and Arnold’s cat maps
respectively. Both of the methods are designed using message embedded scheme and are analyzed for
their validity, for plaintext sensitivity, key sensitivity, known plaintext and brute-force attacks. Due to the
less key space generally many chaotic cryptosystem developed are found to be weak against Brute force
attack which is an essential issue to be solved. For this issue, concept of identifiability proved to be a
necessary condition to be fulfilled by the designed chaotic cipher to resist brute force attack, which is a
basic attack. As 2-D chaotic maps provide more key space than 1-D maps thus they are considered to be
more suitable. This work is accompanied with analysis results obtained from these developed cipher.
Moreover, identifiable keys are searched for different input texts at various key values.
The methods are found to have good key sensitivity and possess identifiable keys thus concluding that
they can resist linear attacks and brute-force attacks.
KEYWORDS
Message embedded scheme, Arnolds Cat map, Duffings map, Identifiability.
1. INTRODUCTION
For last several years many efforts have been made to use chaotic systems for enhancing some
features of communications systems. Chaotic signals are highly unpredictable and random-like
nature, which is the most attractive feature of deterministic chaotic systems that may lead to
novel (engineering) applications. Some of the common features between chaos and
cryptography [1] [2] are being sensitivity to variables and parameters changes. An important
difference between chaos and cryptography lies on the fact that systems used in chaos are
defined only on real numbers, while cryptography deals with systems defined on finite number
of integers. Nevertheless, we believe that the two disciplines can benefit from each other. Thus,
for example, as it is shown in this paper, new encryption algorithms can be derived from chaotic
systems. On the other hand, chaos theory may also benefit from cryptography: new quantities
and techniques for chaos analysis may be developed from cryptography.
During the past two decades, there has been tremendous interest worldwide in the possibility of
using chaos in communication systems [3][4]. Many different chaos-based decryption
algorithms have been proposed up to date.
The aim of this paper is to construct and crypt analyze two of the stream symmetric chaotic
ciphers[5] constructed using one of the latest chaotic scheme known as message-embedded
2. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
14
scheme [6] [7]. Both of the developed methods use 2-D chaotic maps, Duffings and Arnolds Cat
map. Parameters of the respective chaotic maps act as secret key in the ciphers due to which
complexity and key space is increased compared to 1-D chaotic map. Both of the ciphers are
analyzed for key space, avalanche effect and strength against Brute-force and Known-plaintext
attack.
A cryptanalytic method based on the identifiability concept, solves the problem of less key
space in chaotic ciphers. It is possible to test about the cipher strength against Brute-force attack
using it. Both of the mentioned ciphers are concluded to provide security against the Brute-force
attack[8]. Identifiability concept fulfils the necessary condition but not sufficient as the
developed cryptosystems must be tested for sensitivity and other statistical tests to result in a
robust cipher. Thus both the ciphers are tested for sensitivity and it is concluded that some of the
keys selected from domain of key space[9] of the ciphers seem to have good key sensitivity and
resist known plaintext attack for the available first two characters of plaintext [10] [11].
This paper is organized into five sections as follows. Section II, presents the background and in
section III algorithm for encryption used in developing ciphers is provided. Then in section IV,
analysis result in tabulated form and discussions are presented. Section V, discusses about the
conclusions derived.
2. BACKGROUND
Message-Embedded Scheme: According to this scheme at the transmitter side, the plain text is
encrypted by an encryption rule which uses non-linear function and the state generated by the
chaotic system in the transmitter. The scrambled output signal is used further to drive the
chaotic system such that the chaotic dynamics is changed continuously in a very complex way.
Then another state variable of the chaotic system in the transmitter is transmitted through the
channel.
At the receiver side, the reconstruction of the plaintext is done by decrypting the input by using
the reverse of encryption method.
This method can be illustrated along with diagram as shown in fig 1.
Chaotic
function
Non-linear
function
Non-linear
function
Chaotic
function
P
Y
C
C
X X Y
P
(a)Transmitter end (encrypt or) (b) Receiver end (decrypt or)
Figure 1. Message-embedded chaotic cryptosystem
P: plaintext; C: cipher text; X: state of chaotic function;
Z &Y: Intermediate encrypted plaintext;
In the present work modified form of maps has been used that is generated and its randomness
can be clearly seen in fig 2(a) and (b) and fig 3(a) and (b) respectively.
3. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
15
Arnold’s Cat Map: Arnolds Cat map is a 2-D discrete-time dynamical system, which takes a
point(x, y) in the plane and maps it to a new point using equations:
[ ];
),
(
)
(
2
mod
)
1
(
)
1
( N
k
y
k
x
a
k
x +
−
=
+
[ ];
),
(
)
1
(
)
(
mod
)
1
( N
k
y
b
k
x
k
y −
+
=
+
a, b and N are parameters on which the map depends. At a=0.3, b=0.345, map exhibits chaotic
nature.
Figure 2. (a) Plot of Arnolds Cat Map at x(0) = 0.5, y(0) = 0.06, a = - 3.5, b = 0.9, n=1000.
Figure 2. (b) Plot of Arnolds Cat Map at x(0) = 0.5, y(0) = 0.06, a = - 3.5, b = 0.9, n=5000.
4. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
16
Duffings map: Duffings map is a 2-D discrete-time dynamical system, which takes a point
(x, y) in the plane and maps it to a new point using equations:
);
(
)
1
( k
y
k
x =
+
3
)
(
)
(
)
(
)
1
( k
y
k
ay
k
bx
k
y −
+
−
=
+
a and b are parameters on which the map depends. At a = 2.75, b = 0.2, map exhibits chaotic
nature.
Figure 3. (a) Plot of Duffings Map at x(0) = - 0.04, y(0) = 0.2, a= 2.75, b=0.1, n=1000.
Figure 3. (b) Plot of Duffings Map at x(0) = - 0.04, y(0) = 0.2, a= 2.75, b=0.1, n=5000.
5. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
17
Non-Linear Function: Modular function is used as non-linear function in the construction of
ciphers.
The Mod numeric function returns the remainder when the dividend is divided by the divisor.
The result is negative only if the dividend is negative. Both the numbers must be integers. The
function returns an integer. If any number is NULL, the result is NULL. For example:
Mod (5, 3) returns 2.
Mod (-5, 3) returns -2.
Cryptanalysis: Cryptanalysis is the study of attacks against cryptographic schemes to disclose
its possible weakness. During crypt analyzing [12] a ciphering algorithm, the general
assumption made is that the cryptanalyst knows exactly the design and working of the
cryptosystem under study, i.e., he/she knows everything about the cryptosystem except the
secret key. It is possible to differentiate between different levels of attacks on cryptosystems.
They are briefly explained as follows:
1. Cipher text-only attack: The attacker possesses a string of cipher text.
2. Known plain text: The attacker possesses some portion of plain text and the corresponding
cipher text.
3. Chosen plain text: The attacker has obtained temporary access to the encryption machinery.
Hence he/she can choose a plain text string, p, and construct the corresponding cipher text
string.
4. Chosen cipher text: The attacker has obtained temporary access to the decryption
machinery. Hence he/she can choose a cipher text string, c, and construct the corresponding
plain text string.
5. Brute Force Attack: A brute force attack is the method of breaking a cipher by trying every
possible key. The brute force attack is the most expensive one, owing to the exhaustive search.
In addition to the five general attacks described above, there are some other specialized attacks,
like, differential and linear attacks.
Differential cryptanalysis is a kind of chosen-plaintext attack aimed at finding the secret key in
a cipher. It analyzes the effect of particular differences in chosen plaintext pairs on the
differences of the resultant cipher text pairs. These differences can be used to assign
probabilities to the possible keys and to locate the most probable key.
Linear cryptanalysis is a type of known-plaintext attack, whose purpose is to construct a linear
approximate expression of the cipher under study. It is a method of finding a linear
approximation expression or linear path between plaintext and cipher text bits and then extends
it to the entire algorithm and finally reaches a linear approximate expression without
intermediate value.
Security Analysis: Various cryptanalytic procedures are developed to test the validity of newly
constructed ciphers and they are as follows:
(a) Key Space Analysis: Key space belongs to the chaotic region of the system in case of
chaotic ciphers. The total key space is a product of all the parameters involved. Once the key
6. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
18
has been defined and key space has been properly characterized, the good key is chosen
randomly from the large key domain.
(b) Identifiability Test method: From the crypto graphical point of view, the size of the key
space should not be smaller than 2100 to provide a high level security so that it can resist all
kind of Brute force attack. A fundamental issue of all kinds of cryptosystem is the key. No
matter how strong and how well designed the encryption algorithm might be, if the key is
poorly chosen or the key space is too small, the cryptosystem will be easily broken.
Unfortunately, chaotic cryptosystem has a small key space region and it is non-linear because
all the keys are not equally strong. The keys should be chosen from the chaotic region. To solve
the problem of small key space and weakness against brute force attack, identifiability concept
is quite advantageous.
A cryptanalytic procedure, known as output equality based on the identifiability concept, is
carried out on the developed ciphers. It is found that in chaotic ciphers, there exists a unique
solution for a particular input for certain domain of values of parameters. The response of any
system to a particular input is the solution of that particular system and it contains all the
information about the parameters of system. In the discussed ciphers, system parameters are
acting as a secret key. This type of analysis is also known as parametric analysis.
The output equality method is explained as follows:
“For the same inputs and initial condition, transmitter system is parameterized at different
values of parameter taken from the existing domain of parameter space, if the output response of
the system obtained after some value of iteration, parameterized at a particular value coincides
with the output response of the same system parameterized at some other value of parameter
within the domain for the same number of iteration, then both the parameters are said to be
equal and identifiable. The system is said to possess unique solution at that particular value of
parameter and the system is said to be structurally identifiable.”
If parameter of the transmitter is identifiable, it is more difficult for the eavesdropper to find it
by a brute force attack. Consequently, this parameter can play the role of the secret key against
brute force attack. If parameter is not identifiable, the eavesdropper has a higher favorable
chance to find it by a brute force attack and thus, the parameter vector cannot play the role of
the secret key against brute force attack.
(c) Plaintext sensitivity Test Method: The percentage of change in bits of cipher text obtained
after encryption of plaintext, which is derived by changing single bit from the original plaintext
from the bits of cipher text obtained after encryption of original plaintext. With the change in
single bit of plaintext, there, must be ideally 50% change in bits of cipher text to resist
differential cryptanalysis (chosen-plaintext attack) and statistical analysis.
(d) Key sensitivity Test Method: The percentage of change in bits of cipher text obtained after
encryption of plaintext using key, which is flipped by single bit from the original key, from bits
of cipher text obtained after encryption of plaintext using original key, which requires ideally
50% change in cipher text bits to resist Linear and statistical attacks.
(e) Known plaintext attack Method: For observing this attack on developed cryptosystem it is
assumed that the opponent knows everything about the algorithm, he/she has the corresponding
cipher text of plaintext and some portion of plaintext. With this much information, the opponent
tries to find out the secret key.
7. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
19
3. ALGORITHM FOR THE DEVELOPED CIPHERS
Encryption Algorithm:
Step-1: Read plaintext and key vector.
Step-2: Convert plaintext into its ASCII values.
Step-3: Each value of ASCII values are transformed using following steps:
(a) The chaotic map is iterated for a number of times to output a random state.
(b) ASCII value is mixed with non-Linear function and the output state of chaotic system
obtained after a fixed value of iteration.
(c) Again chaotic system is iterated for a fixed number of times and an output state is obtained.
(d) The response obtained in (b) is mixed with the output state obtained in (d) and output values
are obtained as cipher text.
Step-4: Convert cipher text into characters.
Step-5: Read the cipher text.
Decryption algorithm is reverse of encryption process and the original information is retained
using the same secret key using which encryption is being done and it is kept secret between
authenticated sender and receiver only.
4. RESULTS AND ANALYSIS
The simulated result data produced after analyzing both the ciphers using above discussed
(section II) cryptanalytic procedures is summarized with the help of table 1 and 2. Twenty
different values of keys are chosen from key space of respective ciphers and are analyzed for its
security. From both the observation tables, it can be seen that plaintext sensitivity of Arnold’s
cat cipher ranges from 0.5 to 2.5 % and Duffings cipher ranges from 0.5 to 2 %, which is not
sufficient. Key sensitivity for each of the cipher ranges from 0 to 36 % and from 0 to 51 %,
respectively. Thus key sensitivity property of some keys from both the ciphers shows
satisfactory values. Both ciphers are robust against known plaintext attack for the available first
two characters of plaintext. Key space of ciphers shows lesser range than compared to the
required limit i.e. 2100 to resist Brute-force attack but identifiable keys conclude that the
developed ciphers can resist Brute-force attack.
a. Arnold’s Cat cipher: Key space is from [-5 0.4] to [-0.9 1.5] = 5 x 1016
10. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
22
12. Meet me
after 5p.m.
[1.82 -
0.57]
!Nffu!nf!bgufs!6q/n/ 1.4286 48.7500 [1.82 -
0.57] to
[1.83 -
0.57]
NI R NO
13. I have a
gift for
you.
[1.85 -
0.47]
J!ibwf!b!hjgu!gps!zpv/ 0.6494 50 [ 1.85 -
0.47] to
[1.85 -
0.46]
NI NR NO
14. We will go
for walk.
[ 1.89 -
0.3]
"Yg"yknn"iq"hqt"ycn
m0
0.6803 0 [ 1.89 -
0.3] to
[1.9 -0.3]
NI NR NO
15. Study
different
papers.
[1.9 0.2] !Tuvez!ejggfsfou!qbqf
st/
1.1905 0 [1.9 0.2]
to [1.7
0.2]
NI R NO
16. How to do
analysis?
[2.01
0.11]
!Ipx!up!ep!bobmztjt@ 1.4286 0 [2.01 0.11]
to [2.02
0.11]
NI R NO
17. Hai!
Where are
you going?
[ 2.05
0.14]
!Ibj"!Xifsf!bsf!zpv!hpj
oh@
1.0989 0 [2.03 0.14
] to [ 2.05
0.14]
NI NR NO
18. Dolly, are
you
coming
with me?
[ 2.3
0.15]
"Fqnn{."ctg"{qw"eqok
pi"ykvj"ogA
0.4608 0 [ 2. 2 0.15]
to [ 2.3
0.15]
NI NR NO
19. Children
are playing
in park.
[2.5
0.18]
!Dijmesfo!bsf!qmbzjo
h!jo!qbsl/!
0.9217 0 [2.5 0.18]
to [ 2.6
0.18]
I NR YES
20. I shall go
to cinema.
[2.6
0.19]
J!tibmm!hp!up!djofnb/ 1.2987 0 [2.5 0.19]
to [2.6
0.19]
I NR YES
It is seen from the observation table that each of the key possesses individual virtues to resist the
respective attacks.
5. CONCLUSIONS
This paper presents two encryption methods using Duffings and Arnold’s cat maps designed
using message embedded scheme and are analyzed for their validity, for plaintext sensitivity,
key sensitivity, known plaintext and brute-force attacks. As 2-D chaotic maps provide more key
space than 1-D maps thus they are considered to be more suitable. Less key space of the
developed ciphers concludes that they cannot resist brute force attack which is an essential issue
to be solved. For this issue, concept of identifiability proved to be a necessary condition to be
fulfilled by the designed chaotic cipher to resist brute force attack.
The methods are found to have good key sensitivity and possess identifiable keys thus
concluding that they can resist linear attacks and brute-force attacks. A comparison table no.3
shows that both ciphers are found to resist Brute-force attack as they consist of identifiable keys.
Key sensitivity property is also good for some of the keys selected from domain of key space.
Ciphers are determined to resist known plaintext attack for available first two characters of
plaintext. If available characters are not the starting characters of plaintext then ciphers shows
robustness against the attack for available any number of plaintext characters.
Table 3: Comparison between the two ciphers
Name of
Cipher
key Space
Range of plaintext
sensitivity
Range of key
sensitivity
Identifiable
key
Robust
against
known
plaintext
attack
Whether key
space > 2100
Duffing’s 9 x 1014
0.5 to 2 % 0 to 51 % Yes Yes No
Arnold’s
Cat map
5 x 1016
0.5 to 2.5 % 0 to 36 % Yes Yes No
11. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.1, No.1, September 2012
23
ACKNOWLEDGEMENTS
The authors would like to thank the anonymous reviewers for their valuable suggestions and the
proposed references.
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Authors
Mina Mishra, is pursuing Ph.D. (Engg) from Nagpur University, Maharashtra, India.
She received M.E. degree specialization in communication in the year 2010. Her
research area covers chaotic systems, chaotic cryptology, network security and secure
communication.
Vijay H. Mankar received M. Tech. degree in Electronics Engineering from VNIT,
Nagpur University, India in 1995 and Ph.D. (Engg) from Jadavpur University,
Kolkata, India in 2009 respectively. He has more than 16 years of teaching
experience and presently working as a Lecturer (Selection Grade) in Government
Polytechnic, Nagpur (MS), India. He has published more than 30 research papers in
international conference and journals. His field of interest includes digital image
processing, data hiding and watermarking.