T215B Communication and information technologies (II) Session 3 Block 4 Protecting and prying Arab Open University - Fall

Session Outline Part 5: Encryption Introduction Encryption: basic concepts Breaking a cipher 2 Arab Open University - Fall 2013

1. Introduction [1/4] Data is increasing at an accelerated rate Online services are more abundant and are become more convenient Almost all legal, financial or commercial transactions are digitalized (Banking, get official documents, shopping, etc.). Personal data is the currency of this digital world To access an online service we must “pay” personal data! So: Data is widely abundant It is become much quicker, easier and cheaper to collect, store, analyse and transmit data Opportunities available for prying into the data are increasing at an accelerated rate! It is all too easy to allow this data to ‘leak’ – sometimes with serious consequences 3 Arab Open University - Fall 2013

1. Introduction [2/4] How do we protect data? High-profile security breaches could be prevented by implementing appropriate protection measures. ENCRYPTION is one of these protection measures Encryption is a method of altering data in a systematic way such that it can be restored to its original form by those ‘in the know’. In this part of the block you will learn: What data encryption is. How to use encryption to prevent unauthorised people from having access to private information? i.e. How to use Encryption to Protect from Prying! 4 Arab Open University - Fall 2013

1. Introduction [3/4] Some encryption techniques have been around for hundreds, even thousands, of years  the Caesar cipher Today, computers are available! Computers can do the hard work of trying to break a code and, of course, they can do it much more quickly than a human can! The encryption techniques employed have had to become far more complex and sophisticated. 5 Arab Open University - Fall 2013

1. Introduction [4/4] Encryption is the fundamental building block of all modern security systems. Encryption provides mechanisms for: confidentiality – keeping things secret authentication – ensuring that the identities of people and things are correct integrity – ensuring that data has not been tampered with This part of the block is designed to give an insight into encryption methods. 6 Arab Open University - Fall 2013

Session Outline Part 5: Encryption Introduction Encryption Basic concepts A simple substitution cipher Mathematical Representation: The Caesar Cipher Decrypting the Caesar Cipher A Simple Transposition Cipher Breaking a cipher 7 Arab Open University - Fall 2013

2. Encryption: basic concepts [1/6] Encryption is a process by which information is changed in some systematic way so as to hide its content from everyone except its intended recipient. Cryptology: The branch of science concerned with the concealment of information, a word that has its roots in Greek from kryptos (hidden) and logos (word). Cryptography: the science of creating codes and ciphers. Cryptanalysis: the science of breaking them. In Cryptography ‘codes’ and ‘ciphers’ have different meanings. What is the difference between a code and a cipher? 8 Arab Open University - Fall 2013

2. Encryption: basic concepts [2/6] Codes: A code replaces whole words, phrases or groups of symbols with alternatives (or code words). The purpose of creating a code is not always for secrecy. A code is used simply as an abbreviation A code is used to provide an alternative way of communicating information. A code is the output of an encoding process (the reverse is decoding) and generally relies on sets of look-up tables (codebooks) for the conversion processes 9 Arab Open University - Fall 2013

2. Encryption: basic concepts [3/6] Examples: ASCII: American Standard Code for Information Interchange Used to replace characters (a-z; A-Z; 0-9; some punctuation symbole, etc.) with binary codes (initially 7 bits). 10 ASCII table Morse codes Morse code: A standard for substituting groups of long and short pulses (or groups of dots and dashes) for letters. It has been used extensively in telegraphy because of its resistance to corruption and efficiency. Arab Open University - Fall 2013

2. Encryption: basic concepts [4/6] Ciphers: A cipher is the output of an encryption process that either replaces data symbols with alternative symbols, or rearranges existing symbols. The operation used to create a cipher is systematic (i.e. follows some set rules). A cipher is almost always created for reasons of secrecy. How do we create a cipher? 11 Arab Open University - Fall 2013

2. Encryption: basic concepts [5/6] Encryption is the process of transforming data known as plaintext into a cipher known as ciphertext. Decryption reverses the process by transforming ciphertext back into plaintext. There are two basic types of ciphers: Substitution Cipher Transposition Cipher What is the difference between a substitution an transposition cipher? 12 Arab Open University - Fall 2013

2. Encryption: basic concepts [6/6] Substitution cipher: The encryption process systematically manipulate a symbol (or a group of symbols) in the plaintext to produce a different symbol (or group of symbols), which becomes the ciphertext. The substituted symbols in the ciphertext appear in exactly the same order as the original versions in the plaintext. Transposition cipher: The encryption process ‘scrambles’ the order of the symbols of the plaintext in some systematic way. Using this approach, the symbols remain unchanged between plaintext and ciphertext, but the ordering of those symbols changes. 13 Arab Open University - Fall 2013

Session Outline Part 5: Encryption Introduction Encryption Basic concepts A simple substitution cipher Mathematical Representation: The Caesar Cipher Decrypting the Caesar Cipher A Simple Transposition Cipher Breaking a cipher 14 Arab Open University - Fall 2013

2.1 A simple substitution cipher: The Caesar cipher [1/4] Caesar cipher is one of the earliest recorded and best known ciphers was used by Julius Caesar in the 1st century BC. Caesar cipher is one of the simplest of substitution ciphers. How did Caesar preserv the confidentiality of his message? He substituted each letter in his message with the letter three places further forward in the alphabet. Thus the letter ‘a’ would be substituted by the letter ‘d’, the letter ‘b’ by the letter ‘e’, and so on. The process used by Caesar is an example of a systematic manipulation! 15 Arab Open University - Fall 2013

Example: using this method, the word ‘acme’ becomes DFPH. But what if we wanted to encrypt the word ‘zenith’ using the Caesar cipher? How ‘z’ is encrypted? The solution is to jump back to the letter ‘a’ and continue the count as if the letters of the alphabet were arranged in a circle Example: the word ‘zenith’ becomes CHQLWK. Study note: Always represent the plaintext in lower case and ciphertext in UPPER CASE. 16 Arab Open University - Fall A simple substitution cipher: The Caesar cipher [2/4]

The circular nature of the Caesar cipher can be exploited to produce a simple encryption tool known as a cipher wheel. 17 The wheel is made up of two discs The alphabet is written around the circumference of both discs Discs are fitted together at their centers The sender and recipient first agree on the number of shifts One wheel is then rotated using the pre-agreed number of shifts. Each letter of the outer wheel is consiquently aligned with any letter on the inner wheel Arab Open University - Fall A simple substitution cipher: The Caesar cipher [3/4]

18 A key element in Caesar Cipher is “the number of shifts” Changing the “number of shifts” produces different ciphertext from a given plaintext Example: Caesar’s successor, Augustus Caesar, changed the shift from 3 to 2. Any shift of 1 to 25 would work equally and produces different ciphertext from a given plaintext. So here we can say that Julius Caesar used an encryption key of 3 and Augustus Caesar an encryption key of 2. In any encryption process, when altering a “variable” produces different outcome (ciphertext) this “variable” is called a Key Arab Open University - Fall A simple substitution cipher: The Caesar cipher [4/4]

Session Outline Part 5: Encryption Introduction Encryption Basic concepts A simple substitution cipher Mathematical Representation: The Caesar Cipher Decrypting the Caesar Cipher A Simple Transposition Cipher Breaking a cipher 19 Arab Open University - Fall 2013

2.2 Mathematical representation [1/9] Modern communication systems use computers to process messages. Computers do not work with letters but with numbers! How the Caesar cipher can be represented as a numerical algorithm that can be processed by a computer? 20 Arab Open University - Fall 2013

2.2 Mathematical representation [2/9] Caesar Cipher can be mathematically represented by using “Modular arithmetic” Modular arithmetic operates with a limited set of integers Integer: positive or negative whole number, including zero. Example of a set of integers: S = {0, 1, 2, 3, 4, 5}. In Modular arithmetic: The modulus is the number of integers in the set. In the previous example, the modulus is 6. Whatever mathematical operation we perform on the integers in the set, the result must always be less than the modulus. 21 Arab Open University - Fall 2013

2.2 Mathematical representation [3/9] Example: In a conventional clock, the hour changes in a modular fashion. With a conventional 12-hour clock, what is the modulus? What would be the modulus for a 24-hour clock? With a conventional 12-hour clock The set is: S={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} The modulus is 12 For a 24-hour clock The set is : S={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23} The modulus is 24. What is modular arithmetic? 22 Arab Open University - Fall 2013

2.2 Mathematical representation [4/9] Modular Addition: Let’s assume we want to move forward eight hours from ten o’clock using the 12-hour clock, how can we implement this? Mathematically this can be represented as: modulus 12 is congruent to 6 modulus 12. Firstly, we add the two left-hand integers together in the conventional way: = 18 Secondly, if the result is equal to or greater than the modulus subtract the modulus from the result repeating the subtraction until the result is less than the modulus 18 − 12 = 6 Finally, Now express the answer as a congruence modulus 12: ≡ 6 mod Arab Open University - Fall 2013

2.2 Mathematical representation [5/9] How to apply the same method to implement the Caesar Cipher encryption algorithm? Modular arithmetic deals with integers, so: At first, alphabet is converted to numbers. The following coding table can be used for this purpose: Why we have chosen to set ‘a’ to 0 rather than to 1? Because the result of any calculation in modular arithmetic must always be less than the modulus (i.e. 26). if we had set ‘a’ to 1 and therefore ‘z’ to 26, 26 would be an invalid result. 24 Arab Open University - Fall 2013

2.2 Mathematical representation [6/9] Caesar encryption technique can be mathematically modeled using “Modular addition” The general formula of a Caesar cipher would be expressed as: p + K ≡ c mod n Where: n is the modulus p is used to represent the plaintext c is used to represent the ciphertext K is used to represent the key. For Caesar Cipher: We have 26 different letters so the modulus is n = 26 p, c and K can take any value between 0 and Arab Open University - Fall 2013

2.2 Mathematical representation [7/9] Example: Encrypt the letter ‘z’ with a Caesar cipher using a key of K=3. The numerical form of z is: p=25. The ciphertext is obtained by: c ≡ p + K mod 26 so,c ≡ mod 26 ≡ 28 mod 26 ≡ 2 mod 26 so, the numerical for of the ciphertext is c = 2 The numerical value of 2 represents the letter ‘C’ (the ciphertext) So ‘z’ encrypts to C. 26 Arab Open University - Fall 2013

2.2 Mathematical representation [8/9] Activity 5.5: Write out the following using mathematical notation and evaluate the result. Use the grid in Figure 5.5 to translate between alphabetic symbols and numerical values. (a) The ciphertext resulting from encryption letter ‘f’ using the Caesar cipher with a key of 6. (b) The ciphertext resulting from encryption letter ‘s’ using the Caesar cipher with a key of 12. (c) The ciphertext resulting from encryption letter ‘m’ using the Caesar cipher with a key of Arab Open University - Fall 2013

2.2 Mathematical representation [9/9] 28 Activity 5.1 – Sol. : (a) p f = 5, so when K=6, so c ≡ mod 26 ≡ 11 mod 26 The numerical value of 11 represents the letter L. (b) p s = 18, so when K=12, so c ≡ od 26 ≡ 4 mod 26 The numerical value of 4 represents the letter E. (c) p m = 12, so when K=20, the calculation becomes c ≡ mod 26 ≡ 6 mod 26 The numerical value of 6 represents the letter G. Arab Open University - Fall 2013

Session Outline Part 5: Encryption Introduction Encryption Basic concepts A simple substitution cipher Mathematical Representation: The Caesar Cipher Decrypting the Caesar Cipher A Simple Transposition Cipher Breaking a cipher 29 Arab Open University - Fall 2013

2.3 Decrypting the Caesar cipher [1/3] Using the cipher wheel the decryption process simply involves: Displacing the outer wheel clockwise a number of places corresponding to the agreed key Translating each ciphertext letter shown on the inner wheel to its equivalent plaintext letter on the outer wheel. Using Julius Caesar’s version of the cipher this would require a clockwise displacement of three places. This would be just the same as displacing the outer wheel 23 places in an anticlockwise direction. An anticlockwise displacement of 23 (or 26 − 3) is the equivalent of a clockwise displacement of 3. Thus 3 and 23 form a complementary pair Two numbers X and Y are said to be complementary pair when X+Y = modulus (3+23 = 26 = modulus) 30 Arab Open University - Fall 2013

2.3 Decrypting the Caesar cipher [2/3] 31 Arab Open University - Fall 2013

2.3 Decrypting the Caesar cipher [3/3] You noted that one key is so easy to derive from the other Effectively the encryption and decryption key of a Caesar cipher can be regarded as a single key. if we know the encryption key we also know the decryption key or we can decrypt the ciphertext by reversing the encryption algorithm. Encryption systems like this are known as symmetric key systems In a Symmetric Key system: only a single key is involved in the encryption and decryption processes. 32 Arab Open University - Fall 2013

Session Outline Part 5: Encryption Introduction Encryption Basic concepts A simple substitution cipher Mathematical Representation: The Caesar Cipher Decrypting the Caesar Cipher A Simple Transposition Cipher Breaking a cipher 33 Arab Open University - Fall 2013

2.4 A simple transposition cipher [1/4] A transposition cipher: is an anagram of the plaintext created systematically using a method that can be shared with the intended recipient so that it can be decrypted. One way to create the transposition is to use a matrix of cells and to write the message a letter at a time in sequential cells across the matrix. Encryption is performed by reordering the columns of the matrix in some systematic way and then reading off the result to produce the ciphertext. This kind of cipher is known as a columnar transposition cipher. 34 Arab Open University - Fall 2013

2.4 A simple transposition cipher [2/4] Columnar Transposition Cipher: 1.The sender and receiver agree on a codeword and a way to reorder the letters in the keyword into an anagram. For example: Suppose the code word is Tuesday and the agreed transposition is: to reverse the order of the letters (YADSEUT) then swap pairs of letters, starting at the right-hand end to produce the anagram YDAESTU. The number of letters in the keyword dictates the number of columns in the matrix 2.The plaintext is entered into each of the columns (with the keyword at the top) a letter at a time working across the rows. 3.Any empty places in a row can be padded with redundant letters (the ‘x’ in the chosen example). 4.The columns are then reordered according to the keyword anagram. 5.The ciphertext is given by reading back the letters from the reordered matrix. 35 Arab Open University - Fall 2013

2.4 A simple transposition cipher [3/4] Example: The sender and recipient agreed to use the keyword “tuesday” and its anagram”YDAESTU” to encrypt the following message using columnar transposition cipher: “Mary had a little lamb its fleece was white as snow”. What the ciphertext from this message? 36 The resulting ciphertext is: “DHARYMAETLITALSITMBLAWCEEEFLEITWHASXOWSNAS” Arab Open University - Fall 2013

2.4 A simple transposition cipher [4/4] There are many variations of transposition ciphers: One of the earliest recorded originated in Sparta in the 5th century BC. It used a wooden pole (or staff) known as a “scytale” A strip of parchment or leather was wound around the pole so that it formed a sleeve. The message was written in rows along the length of the sleeve When the sleeve was unwound the letters of the message were transposed into a different order. To reconstruct the original message a pole of the correct diameter was needed. 37 what is the key of this transposition cipher ? Arab Open University - Fall 2013

Session Outline Part 5: Encryption Introduction Encryption: basic concepts Breaking a cipher Introduction Brute Force Attack 38 Arab Open University - Fall 2013

3. Breaking a cipher [1/2] Breaking (or cracking) a cipher: is to derive the plaintext from the ciphertext without knowledge of the key (and often without knowledge of the encryption algorithm). The strength of a cipher is measured by how long it takes to break it. Notice that we said ‘how long it takes to break it’ and NOT ‘whether it can be broken’. Potentially all known ciphers except one are thought to be breakable ! The time and effort required to break a cipher is not justified by the value of the information retrieved. The cipher may take so long to break that by the time the information is retrieved it has lost its value. 39 Arab Open University - Fall 2013

3. Breaking a cipher [2/2] Strong Ciphers take a long time to break, but they also tend to be more difficult to use. Weak ciphers are quicker to break but are usually also quite easy to use. The choice of cipher will usually be determined by the value of the information it is designed to protect The use of any cipher induces an overhead in terms of time and processing demands How to break a cipher? 40 Arab Open University - Fall 2013

Session Outline Part 5: Encryption Introduction Encryption: basic concepts Breaking a cipher Introduction Brute Force Attack 41 Arab Open University - Fall 2013

3.1 Brute force attack [1/9] The obvious thing to do is to try every key in the lock in turn. If you are lucky, the first one you try will open the door. If you are unlucky it may be the last one. A similar method to this can be used to break a cipher using a known algorithm! 42 Imagine that you have a bunch of keys and you know that one of them (but not which one) will unlock the door to a room you wish to enter. What would you do to unlock the door? Arab Open University - Fall 2013

3.1 Brute force attack [2/9] Example: if you have a ciphertext message that you know has been encrypted using the simple Caesar cipher described earlier, how many keys would you need to try before you could be certain of finding the right one? The answer is 26, since there are 26 possible keys that could be used with this algorithm. This method of trying all possible combinations in a key space is known as a brute force attack. The number of possible key combinations for a particular algorithm is known as its key space. 43 Arab Open University - Fall 2013

3.1 Brute force attack [3/9] The time taken to break a cipher by this method alone is directly proportional to the key space. For example: The Caesar cipher has a very small key space and so can be broken very quickly. A brute force attack can be applied to transposition ciphers as well as substitution ciphers: Substitution cipher: test every key in the key space. Transposition cipher: test every permutation of the possible transpositions. 44 How long would it take a Brute force attack to break a cipher? Arab Open University - Fall 2013

3.1 Brute force attack [4/9] Activity 5.5: How many different arrangements would be possible using the seven letters of the word ‘article’? Sol: Each letter in the word ‘article’ appears only once. Taking one letter at a time, the first can appear in any of the seven positions; the second in any of the 6 remaining positions; the third in any of the five remaining positions; and so on. This gives a total possible number of combinations of 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = Arab Open University - Fall 2013

3.1 Brute force attack [5/9] 46 Arab Open University - Fall 2013

3.1 Brute force attack [6/9] 47 Arab Open University - Fall 2013

3.1 Brute force attack [7/9] Activity 5.6 – Sol. : 48 Arab Open University - Fall 2013

3.1 Brute force attack [8/9] 49 Arab Open University - Fall 2013

3.1 Brute force attack [9/9] Weakness of a transposition cipher: the number of possible permutations to crack a transposition cipher depends on the content of the message. A transposition cipher is incapable of encrypting a string of identical characters! A transposition cipher weak when there are long blocks of identical characters within the string → Easier to break However, given text with normal language characteristics, a transposition cipher can be strong against a brute force attack. 50 Is there any other technique to break a cipher? Arab Open University - Fall 2013

Yes there is: The linguistic analysis To be discussed Next Week! 51 Arab Open University - Fall 2013