Data Encryption Using Face Antimagic Labeling and Hill Cipher

Abstract

An approach to encrypt and decrypt messages is obtained by relating the concepts of graph labeling and cryptography. Among the various types of labelings given in [3], our interest is on face antimagic labeling introduced by Mirka Miller in 2003 [1]. Baca [2] defines a connected plane graph <img src=image/13426646_01.gif> with edge set <img src=image/13426646_02.gif> and face set <img src=image/13426646_03.gif> as <img src=image/13426646_04.gif> face antimagic if there exist positive integers <img src=image/13426646_05.gif> and <img src=image/13426646_06.gif> and a bijection <img src=image/13426646_07.gif> such that the induced mapping <img src=image/13426646_08.gif>, where for a face <img src=image/13426646_09.gif>, <img src=image/13426646_10.gif> is the sum of all <img src=image/13426646_11.gif> for all edges <img src=image/13426646_12.gif> surrounding <img src=image/13426646_09.gif> is also a bijection. In cryptography there are many cryptosystems such as affine cipher, Hill cipher, RSA, knapsack and so on. Amongst these, Hill cipher is chosen for our encryption and decryption. In Hill cipher [8], plaintext letters are grouped into two-letter blocks, with a dummy letter X inserted at the end if needed to make all blocks of the same length, and then replace each letter with its respective ordinal number. Each plaintext block <img src=image/13426646_13.gif> is then replaced by a numeric ciphertext block <img src=image/13426646_14.gif>, where <img src=image/13426646_15.gif> and <img src=image/13426646_16.gif> are different linear combinations of <img src=image/13426646_17.gif> and <img src=image/13426646_18.gif> modulo 26: <img src=image/13426646_19.gif> (mod 26) and <img src=image/13426646_20.gif> (mod 26) with condition as <img src=image/13426646_21.gif> is one. Each number is translated into a cipher text letter which results in cipher text. In this paper, face antimagic labeling on double duplication of graphs along with Hill cipher is used to encrypt and decrypt the message.