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Cryptography and Network Security Module: Transposition Cipher And e-PGPathshala Subject : Computer Science Paper: Cryptography and Network Security Module: Transposition Cipher and Cryptanalysis Module No: CS/CNS/4 Quadrant 1 – e-text Cryptography and Network Security Module 4- Transposition Cipher and Cryptanalysis Learning Objectives ➢ To know the substitution cipher in classical cryptography ➢ To learn about the mono alphabetic substitution cipher ➢ To learn about the poly alphabetic substitution cipher ➢ Cryptanalysis of Substitution cipher 4.1 Introduction Cryptanalysis is the study of analyzing information systems in order to study the hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation. 4.2 Transposition Ciphers ➢ In transposition ciphers, we transpose (scramble) the plaintext letters Transposition (permutation) means rearranging the order of appearance of the elements of the plaintext. In other words cipher text constitutes permutation of plain text. In general transposition depends on the length of the text and it is aperiodic. – The scrambled text is the ciphertext – The transposition is the key ➢ Corresponds to Shannon’s principle of diffusion( property that spreads statistic properties of text all over the text preventing statistic analysis) – This idea is widely used in modern ciphers 4.3 Scytale ➢ One of the oldest cryptography tools was a Spartan scytale , circa 500 BC. ➢ Sender and recipient each had a rod of exactly the same radius. The sender wound a narrow ribbon of parchment around his cylinder. Then he/she wrote on it lengthwise. After the ribbon is unwound, the writing could be read only by a person who had a rod of exactly the same circumference. ➢ It has the advantage of being fast and not prone to mistakes ➢ Wind strip of leather around a rod ➢ Write message across the rod T H E T I M E H A S C O M E T H E W A L R U S S A I D T O T A L K O F M A N Y T H I N G S ➢ When unwrapped, letters are scrambled TSATAHCLONEORTYTMUATIESLHMTS… ➢ Suppose Alice and Bob use Scytale to encrypt a message – What is the key? The diameter of the Scytale can be regarded as the key of the cipher. – How hard is it for Trudy to break without key? It can be easily broken. Since the strip of leather around the rod hints strongly to the crackers. ➢ Suppose many different rod diameters are available to Alice and Bob… – How hard is it for Trudy to break a message? To decrypt, Trudy must wrap the leather strip around the rod and read across. The ciphertext is: " TSATAHCLONEORTYTMUATIESLHMTS…" Every ninth letter will appear on the same line. – Can Trudy attack messages automatically—without manually examining each putative decrypt? Not possible exactly. Putative decrypt over the ciphertext would have to be transferred to something less susceptible which in turn reduces the advantage over it. 4.4 Rail Fence Cipher (Zigzag Cipher) ➢ A Rail Fence Cipher is a transposition cipher. The letters in the message aren’t changed, but their positions are altered. Unless you know the encryption method, these ciphers are very difficult to crack. To decipher these codes, you need to know the number of rails. Sometimes these ciphers include the spaces between words as blank characters in the cipher. ➢ write message letters out diagonally over a number of rows ➢ then read off cipher row by row Example plain text : meet me after the toga party m e m a t r h t g p r y e t e f e t e o a a t giving ciphertext MEMATRHTGPRYETEFETEOAAT The drawback over here is it has no communication security, and it can be easily broken even by hand. 4.5 Columnar Transposition Put plaintext into rows of matrix then read ciphertext out of columns. The simplest transposition cipher is the columnar transposition. This comes in two forms, the complete columnar transposition and the incomplete columnar. In both of these systems, the plain text is written horizontally in a rectangle that is as wide as the length of the key. Example suppose matrix is 3 x 4 Plaintext: SEETHELIGHT Ciphertext: SHGEEHELTTIX Same effect as Scytale.What is the key? Except the transposition of letters based on 3 x 4 matrix no key is used. 4.6 Keyword Columnar Transposition In Columnar transposition plain text can be padded based on key either in regular or irregular method. In regular way the plain text has been padded so that it nearly fits the matrix/rectangle. But in the case of irregular transposition leaves these characters blank, though this makes decryption slightly more difficult. The columns are now reordered such that the letters in the key word are ordered alphabetically. Example Plaintext: CRYPTOISFUN Matrix 3 x 4 and keyword MATH Ciphertext: ROUPSXCTFYIN How can Trudy cryptanalyze this cipher? • Consider the ciphertext VOESA IVENE MRTNL EANGE WTNIM HTMLL ADLTR NISHO • Matrix is n x m for some n and m • Since 45 letters, nm = 45 • The ciphertext is VOESA IVENE MRTNL EANGE WTNIM HTMLL ADLTR NISHO DWOEH • If encryption matrix was 9 x 5, then… 4.6.1 Cryptanalysis ➢ Exhaustive key search o Always an option for Intruders. o With the advent of computers and computer cipher systems, cryptanalysts have had to fall back on brute-force guessing to extract the key from a large set of cryptograms. ➢ If keyspace is too large, such an attack will not succeed in a reasonable time o Or it will have a low probability of success ➢ A large keyspace is necessary for security ➢ But, large keyspace is not sufficient 4.7 Double Transposition One of the most secure hand ciphers used for military field-grade inSecond World War. To perform a Double Columnar Transposition we write out the key as column header. The key is numbered in alphabetical order. If two letters of the key are the same, the first in the key gets the lowest number. Example Plain text : THIS IS A SECRET MESSAGE 1st Columnar Key: LEONARDO 2nd Columnar Key: DAVINCI Note that, in reality, two keywords with a length up to 20 letters each were used to encipher a message. The plain text is written out in successive rows beneath the headers: L E O N A R D O 4 3 6 5 1 8 2 7 --------------- T H I S I S A S E C R E T M E S S A G E First cipher text: ITAEHCATESSEEIRGSSSM Next, we write it down again, in successive rows, and perform the second transposition. D A V I N C I 3 1 7 4 6 2 5 ------------- I T A E H C A T E S S E E I R G S S S M Again, we read off the ciphertext by the column and write down the text in groups of five: The final cipher text: TEGCE MITRE SSAIH ESASS 4.7.1 Cryptanalysis ➢ Divide and conquer o Trudy attacks part of the keyspace o A great shortcut attack strategy ➢ Requires careful analysis of algorithm ➢ We will see this again and again in the attacks discussed later ➢ Of course, cryptographers try to prevent divide and conquer attacks ➢ Its main weakness was that if the attacker intercepts two or more messages of same length using the same key then they could be compared by a tedious process known as “multiple anagramming”. 4.8 One-Time Pad(Vernam Cipher/Perfect Cipher) ➢ A provably secure cipher ➢ The One Time Pad encryption method is nothing new. In 1882, Frank Miller was the first to describe the One Time Pad system for securing telegraphy. In 1917, Gilbert Vernam invented a cipher solution for a teletype machine. U.S. Army Captain Joseph Mauborgne realized that the character on the key tape could be completely random. Together, they introduced the first One Time Pad encryption system. ➢ No other cipher we discuss is provably secure ➢ Why not use one-time pad for everything? o Impractical for most applications o But it does have its uses 4.8.1 One-Time Pad Encryption ➢ The One Time Pad encryption method is a binary additive stream cipher, where a stream of truly random keys is generated and then combined with the plain text for encryption or with the cipher text for decryption by an ‘exclusive OR’ (XOR) addition. It is possible to prove that a stream cipher encryption scheme is unbreakable if the following preconditions are met 1. The key must be as long as the plain text. 2. The key must be truly random. 3. The key must only be used once ➢ One Time Pad keys are used in pairs. The keys are distributed securely prior to encryption. One copy of the key is kept by the sender and one by the recipient. ➢ Both sender’s and recipient’s keys are automatically destroyed after use, so that erroneous re-application of the same key is impossible Figure 4.1 One-Time pad Encryption 4.8.2 ONE-TIME PAD DECRYPTION Figure 4.2 One-Time pad Decryption 4.8.3 One-Time Pad Summary ➢ Provably secure, when used correctly – Ciphertext provides no info about plaintext – All plaintexts are equally likely – Pad must be random, used only once – Pad is known only by sender and receiver – Pad is same size as message – No assurance of message integrity ➢ Why not distribute message the same way as the pad? Because the messages are vulnerable to attacks by the intruders.
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