MODIFICATION IN HILL CIPHER FOR CRYPTOGRAPHIC APPLICATION

In order to keep the information secure from various contenders is an important factor for data security. For any organization, it is an incredibly important feature to timely transmit secured data. Optimized techniques for key management and protected encryption algorithms are always helpful for reducing the overhead of the system and maintain the integrity, authentication and confidentiality of data. Cryptographic applications play an important role in our daily lives through sending emails, exchanging bank account transaction information, through mobile communication and through ATM card transaction. To secure our information from unauthorized users, Hill Cipher is one of the most well-known symmetric cryptosystems. For Hill Cipher, here we are proposed an algorithm for encryption and decryption which is based upon the transposition, substitution and left-right shift


INTRODUCTION
In today's era of information technology, security is highly essential for our sensitive or important data. Our primary concern is to transmit data or information in a secured manner. Cryptography not only protects our information from intruders but also maintains the data integrity, confidentiality and user authenticity. We have proposed a new and secured procedure in the paper (Khan, Shams, Qazi & Agha, 2015) for generating orthogonal matrix which uses as a key matrix in Hill Cipher for enhancing the security, as well as minimize the cost of time in decryption procedure. In another paper (Khan & Qazi, 2018) we have presented a procedure of encryption and decryption to improve the security of Hill Cipher by adopting transposition and substitution technique.
In the current paper, we have to use transposition and substitution technique as defined in (Khan & Qazi, 2018). To reduce the computational complexity orthogonal key matrix is used as described in (Khan, et al., 2015). An advanced procedure for encryption and decryption is proposed for making Hill Cipher more secure and efficient. Hill cipher can be more secure by applying transposition, substitution and bit shifting on original message for encryption because Hill cipher is vulnerable to a known-plaintext attack and it is completely linear but here we combined it with other non-linear operations (transposition, substitution and left-right bit shifting) which provide good diffusion. In this methodology TSLRS techniques have applied on Hill Cipher due to this, efficient outputs are obtained. Saeednia (2000) presents modification on Hill Cipher and proposed a symmetric cipher. Generate a key for encryption of message by applying random permutation on rows and columns. Mohsen and Abolfazl (2011) presented an encryption algorithm to improved the modification of the Affin Hill Cipher and have introduced two more protocols. Through affine transformation, an efficient cryptosystem has created. Kim and Lee (2004) have worked on private and public key crypto processor regarding its design and implementation. The main goal for creating this cryptographic algorithm is to optimize the execution of the microprocessor. Various security applications can apply this crypto processor like: network router security, storage devices and embedded systems. Sukhraliya, Chaudhary and Solanki (2013) presented an algorithm in which numbers are randomly generated and calculate the modulus and remainder of the numbers. Due to this new method for encrypting and decrypting, three or more keys are generated which make the ciphering technique more complicated. Acharya, Rath, Patra and Panigrahy (2007) have proposed a method of generating self-invertible matrix for Hill Cipher. For encrypting the plaintext we need the inverse of the matrix. Decryption cannot be performed on data if the matrix is not invertible. (2012) worked on Hill Cipher. According to the technique, the plaintext is broken into blocks of m size and multiply it by m*m matrix obtaining variable-key length matrix from Maximum Distance Separable (MDS) master key matrix. Sastry and Janaki (2008) developed a block cipher technique by modifying the Hill Cipher. They have mixed binary bits of key matrix and plaintext at a different level of iteration. Krishna and Madhuravani (2012) proposed a randomized approach for Hill Cipher; broken the plaintext into equal block size and encrypt the block one by one. The output is randomized for one plaintext that is able to generate multiple ciphertext. Sastry, et al. (2009) proposed an iterative method of modification in Hill Cipher in three stages. Different functions are used in these stages like inverse, matrix mixing and XOR. Hamamreh and Farajallah (2009) have presented a new model of Hill Cipher by using quadratic residue. Sastry, et al. (2011) proposed the new idea of permuted key and presented as a generalized advanced hill cipher. In the iterations, we find the arithmetic and mix column operation which entailed in the cipher. Binary bits of the key mix with the plaintext in a detailed manner and due to this avalanche effect and cryptanalysis makes the ciphertext more strong. Varanasi, et al. (2011) presented a symmetric block cipher which contains a pair of keys, iteration process, modular arithmetic addition, substitution and mixing. To strengthen the cipher significantly, they have mixed the bits and substitution in each round of iteration. Keliher and Delaney (2013) worked on two variants of the classical hill cipher introduced by Toorani and Falahati. They have designed a system having an ability to overcome the weaknesses of the hill cipher and are resistant to any of the attacks i-e. ciphertext attack, known-plaintext attack, chosen-plaintext attack or chosen-ciphertext attack. Toorani-Falahati hill cipher can easily break through the described chosen-plaintext attack and confirms the effectiveness of the presented attack. Levine and Chandler (1989) proposed an algorithm of cryptographic equations relating ciphertext, plaintext and if the cipher letters are unknown the elements of the key matrix of hill system have a non-linear system of equations. To reduce these equations to the linear system they had introduced a large set of the unknown, if the plaintext is known. Sharma and Rehan (2013) proposed two-fold securities to the existing hill cipher by using logical operations and elements of the finite field.

PROPOSED METHODOLOGY
In this procedure, we combine previously proposed traditional hill cipher procedures with additional transposition, substitution and left-right shifting functions.
In this method, transposition and substitution of plaintext are performed on n*n matrix respectively. After this second procedure of right and left shifting is applied on the encryption process, all encryption functions are applied in reverse order to perform the decryption process.
Previously we have described the complete procedure of key generation (Khan, et al., 2015). The generated orthogonal key is, We have some negative values in the generated key so, by taking additive inverse in mod 26 make all the values positive and for further simplification, we will take mod 26, due to this secured key will be generated, after that k will turn into : (1)

PROPOSED METHOD FOR ENCRYPTION
Previously we have introduced a new method for securing the hill cipher algorithm. To make hill cipher algorithm more secure and more powerful we can combine both methods consider any plaintext : The first step is to apply transposition on plaintext in reverse order so, plaintext becomes: In this way generate a new key by using the Caesar cipher substitution on , which is obtained by picking the values, convert the above plaintext into binary form then perform right shifting so, will be similar to: Convert into decimal number so, is newly produces plaintext: Now, applying the general method of hill cipher for encryption so will be similar to: (2) Where c is the newly generated ciphertext.

PROPOSED METHOD FOR DECRYPTION
As we discuss in the beginning we are using orthogonal key, therefore, the inverse of the orthogonal key will be the transpose of : 3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143 248 Later than, apply the general method of decryption for hill cipher so, will be produced (3) Now, convert into binary form and perform left shifting on it Apply back substitution of poly alphabetic technique on so, it will similar to: Apply transposition in reverse order and get the original text 4. ALGORITHM i.
Step 1: Take any plain text. ii.
Step 2: Apply the simple transposition on the plane text as defined in section. iii.
Step 3: Apply the Caesar cipher substitution as defined in section iv.
Step 4: Apply the right shift procedure after step 3. v.
Step 5: Apply the procedure of encryption defined by section 3.1. vi.
Step 6: Perform the procedure of decryption explained in section 3.2.

EXAMPLE
In this procedure, the plaintext "SECURITY" is divided into a block size of four letters with the key size of 4*4. For encryption process, we can apply simple transposition, Caesar cipher substitution and one-bit right shift operation on the plaintext. After this apply the regular procedure of Hill cipher and obtain the ciphertext. For decryption process, multiply the inverse of the key with the ciphertext then apply one bit left shift operation, reverse substitution and reverse transposition so, we get the original plaintext "SECU".
Consider an orthogonal key which we have generated through the previous defined procedure.
After taking additive inverse and mod 26, k will become k': In the way, the plain text will be recover.

EXPERIMENTAL RESULTS
To quantify the experimental results different parameters are used to obtain the execution of this algorithm and their comparison with the existing method. Through simulation, experimental results are obtained by using MATLAB. Table  1 shows the overall performance evaluation and encryption time, decryption time and the orthogonal key evaluation time.

Calculation of Encryption & Decryption Throughput:
Decryption

CONCLUSION
From the above experimental results, it has examined that the proposed algorithm provides optimized results in comparison with the inverse process as well as the encryption and decryption algorithms. This algorithm provides better throughput for file sizes of any type when compared with the actual algorithm.