Introduction to Cryptography: Terminology and Basic Encryption Methods

1. EEC 693/793Special Topics in Electrical EngineeringSecure and Dependable Computing Lecture 4 Wenbing Zhao Department of Electrical and Computer Engineering Cleveland State University wenbing@ieee.org

2. Outline • Introduction to cryptography • Terminology • Basic encryption methods • Characteristics of "Good" Ciphers EEC693: Secure & Dependable Computing

3. Cryptography Terminology • Encryption is the process of encoding a message so that its meaning is not obvious • Equivalent terms: encode, encipher • Encryption addresses the need for confidentiality of data • Encryption can also be used to ensure integrity (i.e., unauthorized change can be detected) • Encryption is the basis of protocols that enable us to provide security while accomplishing system or network tasks EEC693: Secure & Dependable Computing

4. Cryptography Terminology • Decryptionis the reverse process, transforming an encrypted message back into its normal, original form • Equivalent terms: decode, decipher • A system for encryption and decryption is called acryptosystem EEC693: Secure & Dependable Computing

5. Cryptography Terminology • The encryption and decryption rules are called encryption and decryptionalgorithms • Encryption/decryptions algorithms often use a device called a key, denoted by K, so that the resulting ciphertext depends on the original plaintext message, the algorithm, and the key value • An encryption scheme that does not require the use of a key is called a keyless cipher EEC693: Secure & Dependable Computing

6. Cryptography Terminology • Plaintext: message to be encrypted • Ciphertext: encrypted message • DK(EK(P)) = P EEC693: Secure & Dependable Computing

7. Symmetric Encryption • The encryption and decryption keys are the same, so P = D(K, E(K,P)) • D and E are closely related. They are mirror-image processes • The symmetric systems provide a two-way channel to their users • The symmetry of this situation is a major advantage of this type of encryption, but it also leads to a problem: key distribution EEC693: Secure & Dependable Computing

8. Asymmetric Encryption • Encryption and decryption keys come in pairs. The decryption key, KD, inverts the encryption of key KE, so that P = D(KD, E(KE,P)) • Asymmetric encryption systems excel at key management EEC693: Secure & Dependable Computing

9. Cryptology • Cryptologyis the research into and study of encryption and decryption; it includes both cryptography and cryptanalysis • Cryptography– art of devising ciphers • Comes from Greek words for“secret writing”. It refers to the practice of using encryption to conceal text • Cryptanalysis–art of breaking ciphers • Study of encryption and encrypted messages, hoping to find the hidden meanings EEC693: Secure & Dependable Computing

10. Cryptanalysis • Attempt to break a single message • Attempt to recognize patterns in encrypted messages, to be able to break subsequent ones • Attempt to deduce the key, in order to break subsequent messages easily • Attempt to find weaknesses in the implementation or environment of use of encryption EEC693: Secure & Dependable Computing

11. Cryptanalysis • Attempt to find general weaknesses in an encryption algorithm • Traffic analysis: attempt to infer some meaning without even breaking the encryption, e.g., • Noticing an unusual frequency of communication • Determining something by whether the communication was short or long EEC693: Secure & Dependable Computing

12. Basic Encryption Methods • Substitutionciphers: one letter is exchanged for another • Transpositionciphers: order of letters is rearranged EEC693: Secure & Dependable Computing

13. Substitution Ciphers • Idea: each letter or group of letters is replaced by another letter or group of letters • Caesar cipher – circularly shift by 3 letters • a -> D, b -> E, … z -> C • More generally, shift by k letters, k is the key • Monoalphabetic cipher – map each letter to some other letter • A b c d e f … w x y z • Q W E R T Y … V B N M <= the key EEC693: Secure & Dependable Computing

14. Cryptanalysis of Substitution Ciphers • Brute force cryptanalysis would have to try 26! permutations of a particular ciphertext message • In practice, it is not difficult to determine the key using frequencies of letters, pairs of letter etc., or by guessing a probable word or phrase • Most frequently occurred • Letters: e, t, o, a, n, … • Digrams: th, in, er, re, an, … • Trigrams: the, ing, and, ion, ent • Words: the, of, and, to, a, in, that, … • When messages are long enough, the frequency distribution analysis quickly betrays many of the letters of the plaintext EEC693: Secure & Dependable Computing

15. Substitution Ciphers - Summary • Substitution cipher – preserves order of plaintext symbols but disguises them • The goal of substitution is confusion • The encryption method is an attempt to make it difficult for a cryptanalyst or intruder to predict what will happen to the ciphertext by changing one character in the plaintext EEC693: Secure & Dependable Computing

16. Transposition Ciphers • Transposition cipher – reorders (rearrange) symbols but does not disguise them. It is also called permutation • With transposition, the cryptography aims for diffusion • Widely spreading the information from the message or the key across the ciphertext • Transpositions try to break established patterns EEC693: Secure & Dependable Computing

17. Columnar Transposition • Plaintext written in rows, number of columns = key length • Key is used to number the columns • Ciphertext read out by columns, starting with column whose key letter is lowest EEC693: Secure & Dependable Computing

18. Columnar Transposition • A transposition cipher example EEC693: Secure & Dependable Computing

19. Cryptanalysis of Transposition Ciphers by Digram Analysis • Step 1: compute the letter frequencies. If all letters appear with their normal frequencies, we can infer that a transposition has been performed • Step 2: break the ciphertext into columns • Two different strings of letters from a transposition ciphertext can represent pairs of adjacent letters from the plaintext • The problem is to find where in the ciphertext a pair of adjacent columns lies and where the ends of the columns are EEC693: Secure & Dependable Computing

20. Cryptanalysis of Transposition Ciphers by Digram Analysis • In step 2, we must do an exhaustive comparison of strings of ciphertext • The process compares a block of ciphertext characters against characters successively farther away in the ciphertext • To see how this works, imagine a moving window that locates a block of characters for checking EEC693: Secure & Dependable Computing

21. Moving Comparisons A F L L S K S O S E L A W I A T O O S S C T A F L L S K S O S E L A W I A T O O S S C T A F L L S K S O S E L A W I A T O O S S C T A F L L S K S O S E L A W I A T O O S S C T A F L L S K S O S E L A W I A T O O S S C T EEC693: Secure & Dependable Computing

22. One-Time Pads • One-time pad: construct an unbreakable cipher • Choose a random bit string as the key • Convert the plaintext into a bit string • Compute the XOR of these two strings, bit by bit • The resulting ciphertext cannot be broken, because in a sufficiently large sample of ciphertext, each letter will occur equally often, as will every digram, every trigram, and so on => There is simply no information in the message because all possible plaintexts of the given length are equally likely EEC693: Secure & Dependable Computing

23. The Vernam Cipher • The Vernam Cipher is a type of one-time pad devised by Gilbert Vernam for AT&T EEC693: Secure & Dependable Computing

24. The Vernam Cipher • The encryption involves an arbitrarily long nonrepeating sequence of numbers that are combined with the plaintext • Assume that the alphabetic letters correspond to their counterparts in arithmetic notation mod 26 • That is, the letters are represented with numbers 0 through 25 • To use the Vernam cipher, we sum this numerical representation with a stream of random two-digit numbers EEC693: Secure & Dependable Computing

25. The Vernam Cipher - Example EEC693: Secure & Dependable Computing

26. The Vernam Cipher - Observations • The repeated letter t comes from different plaintext letters • Duplicate ciphertext letters are generally unrelated when this encryption algorithm is used => there is no information in the message to be exploited EEC693: Secure & Dependable Computing

27. The Vernam Cipher - Decryption • To decrypt: (Ci – Ki) mod 26 • Note on rules of mod on negative number: “The mod function is defined as the amount by which a number exceeds the largest integer multiple of the divisor that is not greater than that number” (http://mathforum.org/library/drmath/view/52343.html) • Modula op always return non-negative number • E.g., (19-76) mod 26 = (-57) mod 26 = (-78+21) mod 26 = 21 EEC693: Secure & Dependable Computing

28. The Vernam Cipher - Decryption EEC693: Secure & Dependable Computing

29. One-Time Pads • Disadvantages • The key cannot be memorized, both sender and receiver must carry a written copy with them • Total amount of data can be transmitted is limited by the amount of key available • Sensitive to lost or inserted characters EEC693: Secure & Dependable Computing

30. Characteristics of "Good" Ciphers-- Claude Shannon (1949) • The amount of secrecy needed should determine the amount of labor appropriate for the encryption and decryption • The set of keys and the enciphering algorithm should be free from complexity • The implementation of the process should be as simple as possible • Errors in ciphering should not propagate and cause corruption of further information in the message • The size of the enciphered text should be no larger than the text of the original message EEC693: Secure & Dependable Computing

31. Shannon's Characteristics of "Good" Ciphers • The amount of secrecy needed should determine the amount of labor appropriate for the encryption and decryption • Even a simple cipher may be strong enough to deter the casual interceptor or to hold off any interceptor for a short time EEC693: Secure & Dependable Computing

32. Shannon's Characteristics of "Good" Ciphers • The set of keys and the enciphering algorithm should be free from complexity • We should restrict neither the choice of keys nor the types of plaintext on which the algorithm can work • For example, an algorithm that works only on plaintext having an equal number of As and Es is useless EEC693: Secure & Dependable Computing

33. Shannon's Characteristics of "Good" Ciphers • Errors in ciphering should not propagate and cause corruption of further information in the message • One error early in the process should not throw off the entire remaining ciphertext EEC693: Secure & Dependable Computing

34. Shannon's Characteristics of "Good" Ciphers • The size of the enciphered text should be no larger than the text of the original message • A ciphertext that expands dramatically in size cannot possibly carry more information than the plaintext, yet it gives the cryptanalyst more data from which to infer a pattern • A longer ciphertext implies more space for storage and more time to communicate EEC693: Secure & Dependable Computing

35. Properties of "Trustworthy" Encryption Systems • It is based on sound mathematics • It has been analyzed by competent experts and found to be sound • It has stood the "test of time" EEC693: Secure & Dependable Computing