Encryption - Securing Data PDF

Securing data - Encryption What is encryption, how does it work? (at a really, really basic level!) Encryption – Basic Principles  Encryption – what and why? Read the message...

Securing data - Encryption What is encryption, how does it work? (at a really, really basic level!) Encryption – Basic Principles  Encryption – what and why? Read the message Alter the ‘Attacker’ message Send a false response back to the sender Fool the sender into thinking the message was Sender received when it Plaintext Plaintext Receiver wasn’t message (pt) Falsify the Sender’s identity System is insecure  Encryption – what and why? Encryption function translates plaintext to ciphertext c Decryption function translates ciphertext back to plaintext ‘Attacker’ p E and D must be easy to perform by sender and receiver. System is secure if: The decryption process, D, is Sender Encryptio Decryptio Plaintext n (E) Cipertext n Receiver not known by the ‘attacker’ (D) message (pt) It is impossible to directly calculate pt from ct without knowing D. Analysis of the ciphertext (and encryption algorithm) cannot be used to ‘guess’ the plaintext without knowing D –  Encryption keys Usually, the encryption/decryption processes take a key as an input parameter ‘Attacker’ Encryption function translates plaintext to ciphertext Encryption Key, Decryption Key, KE c KD Decryption function Sender Encryptio Decryptio translates ciphertext back Plaintext n (E) Ciphertext n Receiver (D) to plaintext p message (pt) Symmetric Encryption: * *Note that encryption will be still categorised as symmetric even if but can be Asymmetric Encryption: computed easily from. I.e. and or  Making the system secure The decryption process, D, is not known by the ‘attacker’. The decryption process, D, is an algorithm: it converts the ciphertext into the plaintext. Usually does this piece-by-piece – letter at a time, or block of data at a time. for( i = 0; i < length(ciphertext); i++ ) { plaintext[i] = D( KD, ciphertext[i] ); } The exact relationship between each piece of the ciphertext and plaintext depends on the decryption function/algorithm, D, and the decryption key, KD. At least one of D and KD must be secret. Convention is that the algorithm (both D and E) is made public and open to scrutiny Only needs to be one, secure algorithm Different keys allow it to be reused by multiple users The decryption key, KD, is kept secret and is different each time the algorithm is used  Making the system secure It is impossible to directly calculate pt from ct without knowing D and KD. This statement is never really true in practice. There is always a finite number of possible KD, so just try them all – a brute-force attack There must be enough possible keys so that someone is extremely unlikely to be able to guess the correct key in a reasonable amount of time. It is then impractical to directly calculate pt from ct without knowing KD 9.2 days The key is usually just a number of a particular size, size usually quoted in bits. (1998) For DES algorithm (developed in 70’s, previously used for https://): 56-bit key, number of possible keys = 256 = 72x1015 26 hours (now) Can now be cracked in 26 hours by trying 768,000,000,000 keys/second! Cracking DES by brute-force Source and more info: https://crack.sh  Making the system secure It is impossible to directly calculate pt from ct without knowing D and KD. AES (developed 2001, currently used for https://) 128, 192 or 256 bit key, up to 2256 = ~116x1075 possible keys Assuming same hardware/search rate it would take ~1.5x10 60 days to check all keys 9.2 days Clearly not practical to brute-force modern encryption algorithms using available hardware, hence cryptanalysis (1998) Obviously evolving hardware could make encryption methods that are currently secure, insecure 26 hours See progress on previous slide (now) Quantum computing? Cracking DES by brute-force Source and more info: https://crack.sh  Making the system secure Analysis of the ciphertext (and encryption algorithm) cannot be used to ‘guess’ the plaintext contents or KD Cryptanalysis analyses patterns in ct, and/or weaknesses in the algorithm, to reduce the number of keys that must be tried. For a secure algorithm, there will be no quicker method than brute-force Secure encryption algorithms applied incorrectly can still result in insecure ct (see later lecture) Security of the RC4 stream cipher relies on generating a stream of random numbers to be used during encryption. There were non- Image encrypted using 128-bit AES. Despite AES random patterns in this stream and as a result the ciphertext could being a secure algorithm, the encrypted image is be analysed to reveal information about they key. RC4 was used for similar to the original. the WEP secure wi-fi protocol:  Cryptanalysis Methods Ciphertext only Patterns in the ciphertext indicate the contents of the plaintext or key. Frequency analysis is an example of a ciphertext only attack (see later). Known-plaintext An attacker knows some of the plaintext, and the corresponding ciphertext, and by analysing the relationship between them finds the unknown key. This can occur if part of the plaintext is predictable (e.g. it always starts with the same greeting / header). Linear cryptanalysis is an example of a known plaintext attack, see later. Chosen-plaintext An attacker has the ability to generate any plaintext, get it encrypted and analyse the resulting ciphertext. This analysis would then be used to determine an unknown key. This is possible in asymmetric/public key encryption but efforts are made to secure symmetric encryption against these attacks too. Differential cryptanalysis is an example of a chosen-plaintext attack. Chosen-ciphertext An attacker can generate some ciphertext and submit it for decryption. By analysis of the resulting plaintext, the unknown decryption key can be determined. Classical Symmetric Methods Basic substitution ciphers Introduction to modular arithmetic The obvious example – Caesar’s Cipher The most famous (and most simple) example of encryption. p A B C D E F G H I J K L M N O P Q R S T U V WX Y Z t ct A B C D E F G H I J K L M N O P Q R S T U V WX Y Z Each letter of the alphabet is shifted forward by a fixed amount The shift “wraps around” p A B C D E F G H I J K L MN O P Q R S T U V WX Y Z t ct F G H I J K L M N O P Q R S T U V WX Y Z A B C D E  pt: the cat sat on the Caesar’s Cipher mat ct: ymj hfy xfy ts ymj rfy Each letter is encoded as a number in the range [0-25] A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 The encryption function is: The decryption function is: The keys are: ( = 5 in this example) There are 26 possible keys [], ≈5 bit encryption The encryption method is symmetric: if you know the algorithm and encryption key, you can also easily decrypt the ciphertext. The encryption method is mono-alphabetic: there is unique and static 1:1 mapping between each possible unit/character of plaintext and ciphertext  Modular Arithmetic Mathematically: 52 53 The means that the expression should be evaluated modulo 26, where 26 is called the modulus. 51 26 27 50 25 0 1 28 49 24 2 29 Mathematical way saying the result “wraps-around” when you reach 26, 26 is equivalent to 0 48 23 3 Effectively a circular number system 22 4 30 47 21 5 31 Eg, to evaluate the expression: 46 20 6 32 , where pt = 5, K = 23 E 45 19 11 7 33 44 18 8 34 Divide the answer by the modulus (=26) 43 17 9 35 16 10 42 15 11 36 12 The answer is the remainder 41 14 13 38 37 40 39 Modular arithmetic is trivial here but it forms the basis of public key encryption Modular Arithmetic Some further examples And so on. The answer to any expression followed by (mod n) is just the remainder when the answer is divided by n.  Modular Arithmetic - Examples 1. Evaluate the expression: 2. Using modular arithmetic, encrypt the character ‘e’ with Caesar’s cipher using n = 26 for both K E = 5 and KE = 31 3. Find KD as a positive integer given that: KE = 20 and n = 52 Final note: Modular Arithmetic only deals with integers – you can never have answers that are not whole integers!  Affine Cryptosystems a and b are positive integers and together form the encryption key, KE. In theory 26*26 key combinations Restrictions on the key (b): b is again limited in practice to: []. You could use , but this doesn’t increase the number of unique keys. Restrictions on the key (a): a and 26 must be relatively prime or co-prime This means they must have no common factors other than 1. We’ll look at what this means and why on the following slides. Note: As with modular arithmetic, prime numbers and the concept of co-primality are important in public-key encryption. Again, that’s why we are looking at these examples.  Affine Cryptosystems - Decryption Rearrange for pt… Encryption: 1 𝑝𝑡 = ( 𝑐𝑡 − 𝑏 ) Decryption: 𝑎 Where: NOTE: ! (unless must be solved to find x where x is the modular multiplicative inverse (MMI) of a. The (or “congruent with”) sign is just like a equals sign in a regular equation. The solution to this equation is where the both sides of the give the same remainder when divided by 26. Obviously 1/26 is always going to give a remainder of 1, so also need to find a value of x where xa/26 also gives a remainder of 1 There is no guarantee that a solution exists for any given a and n If a MMI does not exist, a valid decryption key does not exist.  Finding MMI Take the expression: x, a and n are all positive integers a and n are known x is unknown – we must find a value that satisfies the equation This means that there must be a value of x such that: or or or or … (i.e. xa gives a remainder of 1 when divided by n) So there must be an integer value for x that satisfies the equation: here 0 ≤ m < ∞) If you can find a combination of x and m that satisfy this equation, then you’ve found the MMI – MMI Example - find x for all possible values of a. ,… Need an integer x to satisfy: a X Impossible to satisfy 0 - (1/26 = 0r1) 1 1 Impossible to satisfy 2 - (27/26 = 1r1) 3 9 4 - Impossible to satisfy 5 21 (105/26 = 4r1) 6 - Impossible to satisfy 7 15 8 - (105/26 = 4r1) Impossible to satisfy  MMI Example a x a x a x - find x for all possible values of a. 0 - 9 3 18 - 1 1 10 - 19 11 ,… Need an integer x to satisfy: 2 - 11 19 20 - 3 9 12 - 21 5 4 - 13 - 22 - 5 21 14 - 23 17 6 - 15 7 24 - 7 15 16 - 25 25 If you want to check calculations try the calculator at: 8 - 17 23 26 - https://planetcalc.com/3311/ Modular Multiplicative Inverse – Does it exist? Does it exist? A pattern can be observed in the examples on the previous slide A MMI (x) exists only if a and n are co-prime Another way of saying a and n are co-prime is that their greatest common factor is 1 ( gcf(a,n) = 1 ) They have no common factors other than 1 The gcf is the largest number that you can divide both a and n by and still get an integer result. The gcf(a,n) can be calculated using the Euclidean Algorithm for larger numbers  Affine Cryptosystems - Decryption a x Anyway, back to where this discussion started… 0 - 1 1 Encryption: 2 - 3 9 4 - Decryption: 5 21 6 - 7 15 Where: 8 - And now you are able solve for x in the decryption key if you know the value of a chosen in the encryption key Num unique ct characters b a pt: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 26 What does the 2 1 1 3 5 7 9 11 13 15 17 19 21 23 25 1 3 5 7 9 11 13 15 17 19 21 23 25 13 3 1 1 4 7 10 13 16 19 22 25 2 5 8 11 14 17 20 23 0 3 6 9 12 15 18 21 24 26 ciphertext look like for 4 1 1 5 9 13 17 21 25 3 7 11 15 19 23 1 5 9 13 17 21 25 3 7 11 15 19 23 13 different values of a? (b 5 1 1 6 11 16 21 0 5 10 15 20 25 4 9 14 19 24 3 8 13 18 23 2 7 12 17 22 26 6 1 1 7 13 19 25 5 11 17 23 3 9 15 21 1 7 13 19 25 5 11 17 23 3 9 15 21 13 is fixed at 1): 7 1 1 8 15 22 3 10 17 24 5 12 19 0 7 14 21 2 9 16 23 4 11 18 25 6 13 20 26 8 1 1 9 17 25 7 15 23 5 13 21 3 11 19 1 9 17 25 7 15 23 5 13 21 3 11 19 13 9 1 1 10 19 2 11 20 3 12 21 4 13 22 5 14 23 6 15 24 7 16 25 8 17 0 9 18 26 10 1 1 11 21 5 15 25 9 19 3 13 23 7 17 1 11 21 5 15 25 9 19 3 13 23 7 17 13 11 1 1 12 23 8 19 4 15 0 11 22 7 18 3 14 25 10 21 6 17 2 13 24 9 20 5 16 26 12 1 1 13 25 11 23 9 21 7 19 5 17 3 15 1 13 25 11 23 9 21 7 19 5 17 3 15 13 Affine Cryptosystems - Decryption a x Anyway, back to where this discussion started… 0 - 1 1 Encryption: 2 - 3 9 4 - Decryption: 5 21 6 - Where: 7 15 8 - If x does not exist, the encryption results in fewer than 26 unique characters in ct, the duplicated characters show why Num unique ct decryption is impossible characters b a pt: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 26 2 1 1 3 5 7 9 11 13 15 17 19 21 23 25 1 3 5 7 9 11 13 15 17 19 21 23 25 13 3 1 1 4 7 10 13 16 19 22 25 2 5 8 11 14 17 20 23 0 3 6 9 12 15 18 21 24 26 4 1 1 5 9 13 17 21 25 3 7 11 15 19 23 1 5 9 13 17 21 25 3 7 11 15 19 23 13 5 1 1 6 11 16 21 0 5 10 15 20 25 4 9 14 19 24 3 8 13 18 23 2 7 12 17 22 26 6 1 1 7 13 19 25 5 11 17 23 3 9 15 21 1 7 13 19 25 5 11 17 23 3 9 15 21 13 7 1 1 8 15 22 3 10 17 24 5 12 19 0 7 14 21 2 9 16 23 4 11 18 25 6 13 20 26 8 1 1 9 17 25 7 15 23 5 13 21 3 11 19 1 9 17 25 7 15 23 5 13 21 3 11 19 13 9 1 1 10 19 2 11 20 3 12 21 4 13 22 5 14 23 6 15 24 7 16 25 8 17 0 9 18 26 10 1 1 11 21 5 15 25 9 19 3 13 23 7 17 1 11 21 5 15 25 9 19 3 13 23 7 17 13 11 1 1 12 23 8 19 4 15 0 11 22 7 18 3 14 25 10 21 6 17 2 13 24 9 20 5 16 26 12 1 1 13 25 11 23 9 21 7 19 5 17 3 15 1 13 25 11 23 9 21 7 19 5 17 3 15 13  Modular Multiplicative Inverse – Final examples: Does a solution exist to each of the following equations? If so, find it. Encryption - Weaknesses Why might encryption not achieve the intended outcome? Why can encryption methods be “weak”. (Again, at a very simple level) Cryptanalysis How do you make encryption methods less susceptible to cryptanalysis Weaknesses & Cryptanalysis The weakness of Mono-Alphabetic Cryptosystems Mono-alphabetic cryptosystems are substitution ciphers Static 1:1 mapping Both examples so far (Caesar and Affine) fall into this category They encrypt the characters/data, but don’t encrypt patterns in the data. pt: the cat sat on the mat ct1: xhq wcx acx mp xhq scx ct2: sub xts dts vg sub rts There are patterns in this sentence that will not be hidden by mono- alphabetic encryption: Because of the static 1:1 mapping, all ‘t’ characters in pt map to the same character in ct, etc Some letters, e.g. ‘t’ appear more frequently than others, this can be used to guess the mapping for these letters The words cat, sat and mat are very similar in both pt and ct, could be used to guess mappings  Patterns in the English Language Letter Frequency: gafsf bdz qx hrf rsfdj hq gaf msffwfs qxs yhy % % gafp aduf jxqfp gx tx gx gaf zgxsf E 12.21 P 2.27 Ciphertext and its statistics T 9.51 F 2.26 Letter Frequency First Letter Frequency First Letter Pair 1 g 5 29.41 Frequency A 7.98 M 2.23 Statistics of English Language f 20.31 ga 3 17.64 O 7.87 W 2.03 3 h 2 11.76 N 7.13 Y 1.67 g 7 10.93 q 2 11.76 gx 2 11.76 I 7.12 B 1.61 x 7 10.93 qx 2 11.76 S 6.54 G 1.60 s 6 9.37 R 5.98 V 0.92 a 5 7.81 H 5.10 K 0.52 q 4 6.25 Not a particularly long ct so statistical analysis L 4.00 Q 0.20 d 3 4.68 isn’t overly reliable, but some patterns still D 3.82 X 0.20 h 3 4.68 emerge: C 3.17 J 0.10 p 3 4.68 U 3.07 Z 0.09 j 2 3.12 Most frequently occurring first letter: g, most r 2 3.12 frequent first letter paring: ga. So likely that g First letter of a y 2 3.12 = T, a = H z 2 3.12 word: T A O S H I W Most frequently occurring letter: f, so is First pair of letters of a word: possible that f = E T H A IN E R E H E N R E S Source of frequency data: H.F. Gaines, Cryptanalysis, Dover Publications, New York, 1939. – PDF can be Letter frequency and most common found online if interested letters in English Language pt generated using random sentence generator: https://randomwordgenerator.com/sentence.php Linear Cryptanalysis We now know some patterns in pt and corresponding patterns in ct – how can you use this to decrypt the entire message DK? Linear cryptanalysis represents the decryption process as a linear mathematical function: The available data is then used to work out the coefficients α, β that give the best fit. For an affine cryptosystem, which is a linear process, this approach can reveal the exact DK. For more complex cryptosystems which are not linear, a similar process can approximate (part of) the decryption process. This is an ongoing area of research and has been used to break modern cryptosystems such as AES under certain, limited conditions. Example: Linear Cryptanalysis Inserting the guessed mappings determined earlier: (mod 26) If a-z have been encoded as 0-25: A B C D E F G H I J K L M N O P Q R S T U V WX Y Z 0 1 2 3 4 5 6 7 8 9 101112131415161718 1 202122232425 9  α α*6 Example: 1 0 6 Linear Cryptanalysis 0 2 12 3 18 4 24 5 30 This happens to be easy to solve as it is obvious that = m 7. m*26+12 6 36 0 12 7 42 1 38 8 48 2 64 9 or54 for m = 0, 1, 2, … 3 90 10 60 4 116 You are not required to be able to solve th 11 There 66 is a solution to this when α = 15 and m = 3 because: simultaneous equations on this slide, just understand the principle of linear 12 72 cryptanalysis 13 78 so:14 84 15 90 at first glance it appears that there is also a solution where α = 2 but this value of α does not have a MMI modulo 26 (because gcf(2,26) ≠ 1) which means the computed decryption function wouldn’t give a unique pt ct mapping  Example: Linear Cryptanalysis Results in the translation table: A B C D E F GH I J K L MNO P Q R S T U VWX Y Z h w l a p e t i xmb q f u j y n c r g v k p o d s The final prediction resulting from the frequency analysis also appears to be correct. Decrypted message: gafsf bdz qx hrf rsfdj hq gaf msffwfs qxs yhy gafp aduf jxqfp gx tx gx gaf zgxsf there was no ice cream in the freezer nor did they have money to go to the store (it was generated randomly!) Linear cryptanalysis (on its own) is an example of a known-plaintext attack You know some pt and the corresponding ct and from these work out DK  Summary Mono-alphabetic / Affine Ciphers Example of substitution based encryption process Linear or similar mathematical relationship between ct and pt, with the key giving the coefficients in this relationship Patterns in plaintext result in patterns in ciphertext – major weakness Susceptible to frequency/pattern analysis of ct Also susceptible to linear cryptanalysis Linear Cryptanalysis By comparing pt and ct a linear transformation can be developed that approximates the decryption process, DK. For affine cryptosystems (not secure), this transformation can be an exact replica of the actual decryption process For more advanced cryptosystems it will only be an approximation to (all or part of) the decryption process – see block ciphers later. Making encryption more secure Longer keys, blocks and randomness Polyalphabetic ciphers  Reminder – the problem There is a 1:1 mapping between pt and ct Each ‘a’ in pt always maps to that same character in ct Each ‘b’ in pt always maps to that same character in ct Each ‘c’ in pt always maps to that same character in ct … pt: the cat sat on the This mapping never changes mat ct: xli gex wex sr xli qex This means that patterns in pt appear in ct These patterns can reveal characteristics of pt These characteristics can be used to guess what pt is  Increased key length means the message is effectively encrypted in blocks (of 3 in A simple solution this case) Increased key length also means more difficult to guess key (more combinations) Increase the key length – a polyalphabetic cipher Caesar’s Cipher with KE = This particular variant is also sometimes called a Vigenere Cipher 4 or ‘e’ pt: the cat sat on the Use Caesar’s Cipher as example mat key: eee eee eee ee eee eee Easier to represent the key(shift) as a letter: ct: xli gex wex sr xli qex E.g. KE = 0 → a, KE = 1 → b, KE = 2 → c, … Previously the key was just single value, e.g KE = 4 or ‘e’ Caesar’s Cipher with KE = 10,4,24 or ‘key’ What if KE = ‘key’ or 10,4,24? pt: the cat sat on the mat key: key key key ke yke yke The increased key length eliminates some patterns but not all: ct: dlc mer cer yr rri kkx Because the key still repeats, just at lower frequency Still a chance that the repeating key aligns with patterns in pt The longer the key, the less repetition, the less chance of this happening.  Pseudorandom key sequence ciphers Could you use a random key the same length as the message? Yes, but sender and receiver would both need a copy of the key. To be effective a new key is needed for each message (otherwise you are using the same key repetitively, leading to same problems as before) If you were going to use the encryption system frequently, sender and receiver would need a huge amount of (identical) key data. Old “one-time pad” encryption systems used large code books of random data. Both sender and receiver would hold identical copies of this data. Solution: Pseudorandom key sequence generators A “long key generating machine” The machine must first be initialised to set its internal state Generates a sequence of apparently random key characters – the key sequence or keystream The sequence looks like it is random, but if you have an identical machine which is initialised in the same way you can generate an identical keystream. Ke Key Keystream: y asnvhiepcnancpiancdbegiyak;dfsakps Generator … A short key is used to set the initial machine state Both sender and receiver must use identical initial settings (keys) for their keystream generators  Pseudorandom key sequency ciphers Ke Key Key Ke y y Generator Generator Keystream: Keystream: asnvhiepcnancpiancdbegiya asnvhiepcnancpiancdbegiya kdfsa… kdfsa… pt Encryption ct Decryption pt If the Key Generator generates a perfect pseudorandom keystream: Even if you knew all of the previous values in the keystream, and you knew how the machine was constructed, but didn’t know the machine’s precise internal state or starting key, you wouldn’t be able to predict the next value in the keystream any more accurately than is possible with a complete guess.  Pseudorandom key sequency ciphers Ke Key Key Ke y y Generator Generator Keystream: Keystream: asnvhiepcnancpiancdbegiya asnvhiepcnancpiancdbegiya kdfsa… kdfsa… pt Encryption ct Decryption pt Actual encryption can be very simple (e.g. character substitution), but… Security depends on the ‘randomness’ of keystream: If you knew something about the plaintext e.g. every message starts with “hello” You may be able to use this knowledge to reveal the first 5 keystream characters (linear cryptanalysis) If the key sequence is random enough, this won’t tell you anything about the rest of the keystream But if these keystream characters reveal anything about the original key, the machine’s internal state, or allow you to predict other characters in the keystream, the cryptosystem will be insecure.  Example: Enigma WW2 era German Enigma machine A substitution cipher where the substitution is determined by the precise position of a number of components in a machine – the machine’s state. Electrical connection between a-z keys and a-z lights set by moving rotors and wires on plugboard The machine is initialised in the same way by By TedColes sender and receiver https://upload.wikimedia.org/wikipedia/co Rotor position, plugboard wires mmons/d/d8/Enigma_rotors_and_spindle_ showing_contacts_rachet_and_notch.jpg These initialisation settings are effectively the key After each substitution the machine state changes according to some predefined sequence. Rotors move to change internal wiring This changes the pt:ct mapping for the next character By Karsten Sperling, http://spiff.de/photo, https://commons.wikimedia.org/wiki/File:EnigmaMachi neLabeled.jpg  Example: Enigma The machine is generating a pseudorandom key-sequence The receiving machine is able to compute the next value in the key sequence as it knows the sending machine’s internal state. To everyone else, the key sequence would appear to be random. The encryption itself is just a basic letter substitution the same as Caesar. At each step each input (pt) a-z character maps to a single output (ct) a-z character This is the similar to a Caesar/affine cipher but with a constantly changing key The substitution step itself is not secure, security is a result of the pseudorandom key-sequence. Modern stream ciphers work in this way. Enigma was beaten with cryptanalysis to reduce the number of possible initial machine states (keys), and a known-plaintext, brute force attack to find the exact  Summary – Polyalphabetic ciphers Mono-alphabetic ciphers use the same key to repetitively encrypt units (character / byte/ bytes) of plaintext which results in patterns appearing in the plaintext, also appearing in the ciphertext. This makes cryptanalysis easy (simple analysis of ct results in key) Polyalphabetic ciphers use a key that changes with each unit of plaintext to avoid this. The problem is that when you reach the end of the key, you have to repeat using the same key sequence. Polyalphabetic ciphers reduce the frequency with which patterns appear in ct but don’t eliminate them (as the key still repeats, just at a lower frequency). Longer keys improve the performance – a random key the same length as the message (known as a one-time pad system) should mean that all patterns in pt are prevented from appearing in ct, but this is impractical in practice. A variation on polyalphabetic ciphers is to use a pseudorandom key sequence– an infinitely long and apparently (but not actually) random key The key sequence is generated by two key generating machines – one at either end of the communication channel The machines must be initialised exactly the same so that they both generate the same sequence The key sequence must appear random to an observer who doesn’t know the machine configuration If not, the encryption is weak – if an attacker knows the plaintext for part of the message and can use this to obtain the corresponding part of the key, they can use the non-randomness to reveal all of the key