# Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010

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1 CS 494/594 Computer and Network Security Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall

2 Introduction to Cryptography What is cryptography? Types of cryptography Attacks on cryptosystem Early ciphers SKC, PKC, Hash Security notions 2

3 What Is Cryptography? Cryptography is the art of secret writing Traditional use: encryption Cryptographic systems: algorithm+secret Cryptology: cryptography+cryptanalysis 3

4 Types of Cryptography Operations used to transform plaintext to ciphertext: - Substitution: each element in plaintext is mapped into another element - Transposition: elements in plaintext are rearranged Number of keys used: - Single-key: secret-key cryptography - Two-key: public-key cryptography - Zero-key: hash functions The way plaintext is processed: - Block cipher: input & output in blocks - Stream cipher: input & output in bits 4

5 Conventional Cryptography: Symmetric Encryption Plaintext: original message Encryption algorithm: substitutions/transpositions Secret key: independent of plaintext and algorithm Ciphertext: depends on plaintext and key, appears random Decryption algorithm: reverse of encryption 5

6 Attacking Cryptosystems Cryptanalysis: attempts to deduce the plaintext and/or the key being used, with knowledge of the nature of the algorithm + general characteristics of plaintext + some sample plaintext-ciphertext pairs Brute-force attack: attacker tries every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained. On average, half of all possible keys must be tried to achieve success. 6

7 Types of Cryptanalytic Attacks 7

8 Brute-force Attacks Average Time Required for Exhaustive Key Search 8

9 Early Ciphers: Substitution Substitution: letters of plaintext are replaced by other letters or by numbers or symbols, involves replacing plaintext bit patterns with ciphertext bit patterns Caesar cipher Captain Midnight Secret Decoder Rings Monoalphabetic cipher Hill cipher Polyalphabetic cipher (Vigenere) One-time pad 9

10 Caesar Cipher Replacing each letter of the alphabet with the letter three places further down the alphabet, e.g., Captain Midnight Secret Decoder Ring (slightly enhanced): If a numerical value is assigned to each letter, for each plaintext letter p, the ciphertext letter C=E(k, p)=(p+k) mod 26 where k takes on the value in [1,25]: Subject to brute-force attack: simply try all 25 possible k 10

11 Monoalphabetic Cipher The "cipher" line can be any permutation of the 26 alphabetic characters, 26! or around 4x10 26 possible keys: Is it secure enough to resist cryptanalysis? Consider: By exploiting the regularities of the language and counting letter frequencies: The following can be recovered: 11

12 Hill Cipher Takes m successive plaintext letters and substitutes for them m ciphertext letters The substitution is determined by m linear equations in which each character is assigned a numerical value (a = 0, b = 1... z = 25) For example: m = 3 for plaintext paymoremoney and encryption key we have ciphertext: LNSHDLEWMTRW 12

13 Polyalphabetic Cipher Use different monoalphabetic substitutions as one proceeds through the plaintext message Vigenere cipher: best known polyalphabetic cipher. The set of related monoalphabetic substitution rules consists of the 26 Caesar ciphers, with shifts of 0 through 25. For keyword deceptive and plaintext we are discovered save yourself, the encryption works as: Vulnerable to cryptanalysis: the key and plaintext share the same language regularities and frequency distribution of letters. Solutions? 13

14 One-time Pad Use a random key that is as long as the message so that the key need not be repeated The key is used to encrypt and decrypt a single message, and then is discarded Perfectly secure: unbreakable because it produces random output (from the random key) that bears no statistical relationship to the plaintext Drawbacks: large quantities of random keys needed, key distribution and protection (both sender and receiver) 14

15 Early Ciphers: Transposition Different from substituting a ciphertext symbol for a plaintext symbol Transposition cipher: performs some sort of permutation/rearrangement on plaintext letters Cryptanalysis is straightforward: a transposition cipher has the same letter frequency as plaintext Can be made more secure by performing more than one stage of transposition (result is not easily reconstructed) 15

16 Rail Fence Cipher Simplest transposition cipher Plaintext is written down as a sequence of diagonals and then read off as a sequence of rows Plaintext: Ciphertext: Trivial to attack 16

17 Double Transposition A more complex scheme: permute the order of the columns with a key Double transposition: more than one permutation, number the above plaintext letters 1-28 and after the first permutation we have After the 2 nd permutation? 17

18 Secret Key Cryptography (SKC) Aka: conventional cryptography, symmetric cryptography Use a single key Ciphertext about the same length as plaintext Examples: Captain Midnight code, monoalphabetic cipher, DES, AES, RC4 plaintext encryption shared secret key ciphertext ciphertext decryption plaintext 18

19 SKC Applications Transmitting over an insecure channel Secure storage on insecure media Authentication: Integrity check: message authentication code (MAC), aka, message integrity check (MIC) 19

20 Public Key Cryptography (PKC) Aka: asymmetric cryptography, invented in 1970s Use two keys: a public key known to everyone, a private key kept secret to the owner Encryption/decryption: encryption can be done by everyone using the recipient s public key, decryption can be done only by the recipient with his/her private key encryption plaintext ciphertext pub B ( puba, pri A) ( pubb, prib) pri B ciphertext decryption plaintext 20

21 PKC Applications Everything that SKC does can be done by PKC Transmitting over an insecure channel Secure storage over insecure media Authentication Key exchange: establish a shared session key with PKC 21

22 PKC Applications (Cont d) Digital signature: non-repudiation plaintext sign Signed message pri A ( puba, pri A) ( pubb, prib) pub A Signed message verify True or false 22

23 Hash Functions Aka: message digests, one-way transformations Take a message m of arbitrary length (transformed into a string of bits) and computes from it a fixed-length (short) number h(m) Properties: - easy-to-compute: for any message m, it is relatively easy to compute h(m) - non-reversible: given h(m), there is no way to find an m that hashes to h(m) except trying all possibilities of m - computationally infeasible to find m and m such that h(m)=h(m ) and m!=m 23

24 Applications of Hash Functions Password hashing Message integrity: keyed hash File fingerprint Downline load security Digital signature efficiency 24

25 Security Notions Unconditionally secure: ciphertext generated by the scheme does not contain enough information to determine uniquely the corresponding plaintext, no matter how much ciphertext is available. Perfectly secure, unlimited power of adversary Provably secure: under the assumption of well-known hard mathematical problem, e.g., factoring large numbers, discrete logarithm problem Computationally secure: if cost of breaking the cipher exceeds the value of the encrypted information, or time required to break the cipher exceeds the useful lifetime of the information, practical security 25

26 Cryptography vs. Steganography Cryptography conceals the context of message Steganography conceals the existence of message, useful when the fact of secret communication should be concealed - an arrangement of words/letters of the overall message spells out the hidden message - character marking: selected letters overwritten in pencil, not visible unless the paper is held at an angle to bright light - invisible ink: substances used for writing but leave no visible trace until heat or some chemical is applied to the paper - pin punctures: small pin punctures on selected letters are not visible unless the paper is held up in front of a light Drawbacks of steganography: high overhead to hide a relatively few bits of information, becomes worthless once the system is discovered (can make insertion depend on key) 26

27 Reading Assignments [Kaufman] Chapter 2 27

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