A CIPHER BASED ON THE RANDOM SEQUENCE OF DIGITS IN IRRATIONAL NUMBERS
Issues in Information Systems
An encryption method combining a transposition cipher with one-time pad cipher is proposed. The transposition cipher prevents the malleability of the messages and the randomness of one-time pad cipher is based on the normality of "almost" all irrational numbers. Further, authentication and perfect forward secrecy are implemented. This method is quite suitable for communication within groups of people who know one each other in advance, such as mobile chat groups. INTRODUCTION In cryptography, a
... cipher is a procedure for encoding and decoding a message in such a way that only authorized parties can write and read information about the message. Generally speaking, there are two main different cipher methods, transposition, and substitution ciphers, both methods being known from Antiquity. For instance, Caesar cipher consists in substitute each letter of the plaintext some fixed number of positions further down the alphabet. The name of this cipher came from Julius Caesar because he used this method taking a shift of three to communicate to his generals (Suetonius, c. 69-122 AD). In ancient Sparta, the transposition cipher entailed the use of a simple device, the scytale (skytálē) to encrypt and decrypt messages (Plutarch, c. 46-120 AD), which consisted of two equal wood rods and a ribbon rolled up on one of them. When you write down the message along the rod over the ribbon, one letter in each turn of the ribbon, and then you unroll the ribbon, the letters of the message along the ribbon were transposed. The recipient of the message could decipher it rolling up the ribbon over its twin rod. Systems combining substitution and transposition were used first in World War I by the Germans in the so-called ADFGX and ADFGVX ciphers. Invented by Colonel Fritz Nebel, these ciphers combined the substitution method of the Polybius square with a single columnar transposition method. The Germans believed the ADFGVX cipher was unbreakable, but Lieutenant Georges Painvin, a bright member of the Bureau du Chiffre of the French Army, broke this cipher in June 1918 (Childs, 2002) . Nowadays, the combination of substitution and transposition methods is standard for block ciphers. The aim of this paper is to combine also both methods, transposition, and substitution, by using the random sequence of digits in irrational numbers. This method offers a simple way to provide reasonable security in the communication within groups of people. This kind of moderate security would be applicable, for instance, in the nowadays chats through mobile applications. This paper is organized as follows. Section 2 describes a brief history of the substitution method used in this paper, namely the one-time pad cipher, and how it is implemented here. According to the discussion of this method, it will be proposed a simple idea to overcome the main drawback of it, that is, the randomness of the key. Moreover, in order to provide more security, a very simple one-way function is described for updating the key in each message. Despite the fact that one-time pad cipher is absolute safe under certain conditions, the message could be intentionally changed by a third part without knowing the key. In order to avoid this malleability of the message, Section 3 shows how to combine the one-time pad cipher with a simple transposition cipher. Section 4 is devoted to second order encryption methods, that is to say, the ciphering of the keys and the authentication of the message. In Section 5 the operation steps for the proposed cryptosystem are collected. Finally, the conclusions are summarized in Section 6.