Secure Message Transmission using Lagrange Polynomial Interpolation and Huffman Coding

In this paper, an algorithm for secure transmission of message is proposed based on Lagrange's interpolation. The message is viewed as a polynomial of degree n where n is kept secret and transmitted to the receiver's side using the concept of a digital envelope. As any nth degree polynomial is uniquely determined by n+1 points, n +1 points are communicated to the other side, where the polynomial and hence the message is reconstructed. Padding of length m is added to the message to overcome the message length issue. Although any coding scheme may be used, in this paper Huffman coding is used for converting the plaintext into binary form. Finally, the proposed algorithm is compared with the performance of RSA algorithm and found to be efficient.

[1]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[2]  Jianfeng Ma,et al.  Publicly Verifiable Secret Sharing Schemes Using Bilinear Pairings , 2012, Int. J. Netw. Secur..

[3]  Rudolf Lide,et al.  Finite fields , 1983 .

[4]  M.Y. Javed,et al.  A Performance Comparison of Data Encryption Algorithms , 2005, 2005 International Conference on Information and Communication Technologies.

[5]  William H. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[6]  T. Sauer,et al.  On multivariate Lagrange interpolation , 1995 .

[7]  David A. Huffman,et al.  A method for the construction of minimum-redundancy codes , 1952, Proceedings of the IRE.

[8]  C. Ezin.  Modeling Data Transmission through a Channel Based on Huffman Coding and Encryption Methods , 2010 .

[9]  K. Conrad,et al.  Finite Fields , 2018, Series and Products in the Development of Mathematics.

[10]  Saurabh Singh,et al.  Use of Chinese Remainder Theorem to generate random numbers for cryptography , 2010 .

[11]  D. Lou,et al.  Computational Complexity Analyses of Modular Arithmetic for RSA Cryptosystem , 2006 .

[12]  Simon L. Peyton Jones,et al.  Haskell 98 Libraries: Random Numbers , 2003, J. Funct. Program..

[13]  Yi-Shiung Yeh,et al.  An efficient decryption method for RSA cryptosystem , 2005, 19th International Conference on Advanced Information Networking and Applications (AINA'05) Volume 1 (AINA papers).