International Journal of Technology

P. L. Sharma ¹, Kiran Devi ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla 171 005, IN

Abstract

Normal bases and matrices are widely used in cryptography to enhance the speed of cryptographic algorithms and provide security to the messages which travel through the insecure channels. We propose a public key cryptosystem using normal bases and trace mapping of normal elements over finite fields.

Keywords

Normal Basis, Trace Mapping, Normal Element, Finite Field, Helical Traverse Form.

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P. L. Sharma ¹, S. Kumar ¹

Affiliations
1 Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla - 171005, IN

Abstract

Hadamard matrices have received much attention in the recent past, owing to their well-known and promising applications. Various researchers have used Hadamard matrices to find their applications in image analysis, signal processing, coding theory, cryptology and combinatorial designs. Now, Hadamard rhotrices have been introduced in the literature for the above said applications. Balanced incomplete block design has its wide use in design of experiments in statistics and error-correcting codes. Design of experiments has broad applications across all the natural and social sciences, and engineering. Here, in the present paper, we develop balanced incomplete block design (BIBD) using Hadamard rhotrices.

Keywords

Hadamard Matrix, Hadamard Rhotrix, Incidence Matrix, Balanced Incomplete Block Design.

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P. L. Sharma ¹, S. Sharma ¹

Affiliations
1 Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla - 171005, IN

Abstract

Lester S. Hill in 1929 introduced non-singular matrices to encrypt and decrypt the message in the symmetric key cryptography. Block ciphers designing and cryptographic hash functions have the use of matrices. Here, we introduce permutations, iterations and finite field in the Hill cipher to provide more security and make it free from vulnerable attacks.

Keywords

Encryption, Decryption, Finite Field, Hill Cipher.

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P. L. Sharma ¹, M. Rehan ¹

Affiliations
1 Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla - 171005, IN

Abstract

Cryptography is the science which provides confidentiality, authenticity and integrity to the users over the prevailing insecure communication channels. Encryption is the transformation of data into some unreadable form. The purpose is to ensure privacy by keeping the information hidden from anyone for whom it is not intended, even those who can see the encrypted data. Decryption is the reverse of encryption; it is the transformation of encrypted data back into some intelligible form. Encryption and decryption require the use of some secret information, usually referred to as a key. Hill cipher in cryptography is a symmetric key substitution algorithm, which is vulnerable to known plain text attack. We modify the existing Hill cipher by using Vandermonde matrix and introducing the elements of finite field which provides more security to the said cipher.

Keywords

Plain Text, Symmetric Key, Hill Cipher, Finite Field, Vandermonde Matrix.

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