A public key cryptosystem using normal bases over finite fields

P. L. Sharma*, Kiran Devi

Department of Mathematics and Statistics, Himachal Pradesh University, Shimla 171 005, India

*Corresponding Author Email: plsharma1964@gmail.com

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.

Mathematics Subject Classification (2010): 11T71, 94A60, 14G50, 68P25.

INTRODUCTION:

The security of information, integrity of data and confidentiality of messages through insecure channels has become the major issue today. Cryptography is the technique which is used to protect the data which travel through the internet and intranet. The different branches of mathematics like matrix analysis, number theory, rhotrices theory, finite fields , logical operators are used to built the cryptosystems for encryption and decryption processes, see [4, 5, 10, 11-19, 26-27, 32 ]. Various cryptosystems [2, 9, 20-23, 31] provide security in emails, ATM machines, cellular phones, e-commerce, digital signatures and online transactions in banking sectors.

Different types of cryptosystems are studied by several mathematicians which are based on matrices, see [24, 28]. Massey and Omura [6, 7] invented a multiplier which obtains the product of two elements in finite field using the normal bases. Normal bases are used in squaring and multiplication of an element in finite field which can be easily done by a cyclic bit shift of binary digits, see [3, 25, 29, 30]. Due to fast exponentiation and cyclic bit shift operations normal bases are used at large scale. This can be easily seen in word level normal bases multiplier and reordered normal bases multipliers.

Matrix based asymmetric bulk encryption and public key cryptography with matrices is given in [8]. Security can be easily enhanced in cloud computing and cryptographic mechanism using public key and matrices, see [1]. We proposed a public key cryptosystem which contains mainly generation of data matrix, key generation, encryption, decryption process by using normal bases over finite fields and XOR operator.

which is the original data matrix of the text message. The first row of this matrix is the first elementof the normal basis set, which is the alphabet Similarly, other rows give the other elements of the normal basis set which corresponds to the different characters of the text message. Hence, the receiver will get the original message Maths back.

ACKNOWLEDGMENT:

Authors acknowledge the support of UGC - SAP.

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Received on 23.08.2016 Accepted on 08.09.2016

Int. J. Tech. 2016; 6(2): 143-149.

DOI: 10.5958/2231-3915.2016.00023.7