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 G with edge set E and face set F as (a, d)-face antimagic if there exist positive integers a and d and a bijection g: E → {1, 2, 3, …, |E|} such that the induced mapping Ψg: F → {a, a + d, …, a + (|F (G)| − 1)d}, where for a face f, Ψg (f) is the sum of all g(e) for all edges e surrounding f 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 P1P2 is then replaced by a numeric ciphertext block C1C2, where C1 and C2 are different linear combinations of P1 and P2 modulo 26: C1 ≡ aP1 + bP2 (mod 26) and C2 ≡ cP1 + dP2 (mod 26)” with condition as gcd(ad − bc, 26) 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.