8. Cryptography 1

ISA 562Information Security Theory & Practice

Introduction to Cryptography

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Agenda

• Basics & Definitions• Classical Cryptography• Symmetric (Secret Key) Cryptography• DES (Data Encryption Standard)• Multiple Encryptions• Modes of Block Cipher Operations• Math Essential• Asymmetric (Public Key) Cryptography

8. Cryptography 3

Basic Definitions

Cryptography– Crypt = secret– Graph = writing

• science / art of transforming meaningful information into unintelligible text

Relies on mathematics (number theory, algebra)Cryptanalysis • science / art of breaking cryptographic codesCryptology • science / art / study of cryptography and

cryptanalysis

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Applications of Cryptography

• Assuring document integrity• Assuring document confidentiality• Authenticating parties• Document signature• Non-repudiation• Secure transactions• Exchanging keys• Sharing Secrets• Digital cash• Preserving anonymity• Copyright protection …

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Cryptographic Services (I)

Starting from BasicsA B A B

Ca) Source Integrity b) Data Confidentiality Normal Flow Eavesdropping

A B A B C C

c) Data Integrity d) Source Authentication

Modification Fabrication

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Cryptographic Services (II)

A B A B

c

e) Drop f) Replay

A B

C

f) Denial of Service

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Encryption/DecryptionPlaintext ciphertext Plaintext

encryption decryption

key key

• Plaintext: message in original form• Ciphertext: message in the transformed, unrecognized form• Encryption: process that transforms a plaintext into a ciphertext• Decryption: process that transforms a ciphertext back to plaintext• Key: value used to control encryption/decryption.

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Cryptanalytic AttackAttacker only knows Ciphertext– Tries to reveal plaintext and/or key

• Attacker Knows Plaintext, Ciphertext Pairs <plaintext , ciphertext>– Cryptanalysis tries to reveal the key– Relevant when plaintext is known or can be obtained

• Attacker chooses a Plaintext –and receives the Ciphertext– Cryptanalysis tries to reveal the key– Relevant when attacker can “inject” a plaintext message

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Classical Cryptography

Cryptography used by early civilizations (including Egyptians, Greeks, Romans) for Secrecy

Confidentiality now includes Integrity, Authentication & Authenticity, and in sometimes Non-Repudiation.

• Early cryptography mainly encryption by substitution and/or transposition methods– They were simple because of the lack of computing

engines– Could easily be attacked• Same ideas in use today but with stronger properties

and powerful computing engines

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Substitution Ciphers (1)

Caesar Cipher: fixed permutation (move 3 up in the alphabet)

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 zd e f g h i j k l m n o p q r s t u v w x y z a b c

Algorithm is:C = ENC( P ) = P + 3 (mod 26)

For example: GMU →JPX• The secrecy is in the algorithm !• There is one key (fixed permutation)• Easy to break

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Substitution Ciphers (2)Shift Cipher similar to Caesar Cipher, but there is a cyclic shift of the 26

letters of the alphabet by key K, where0 ≤ K < 26.• Algorithm:C = ENCK( P ) = P + K (mod 26)

There are 26 different keys• Easy to break – check which of 26 possible keys returns thea meaningful plaintext• Decipher HAL (the computer from the movie 2001: A SpaceOdyssey) using a shift cipher of one.– So the shift variable n=1.• • HAL ?

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Mono-Alphabetic Ciphers

Generalization: arbitrary mapping of one letter toanother• One of N! permutations on N letters of the alphabet• The key is the index of the permutation• Key is secret (one of N! options)• Example:– N = 26 letters of the English alphabet– N! = 26! ≈ 4 • 1026 ≈ 288 permutations or 309 Septillion– ≈ 309,485,009,821,345,000,000,000,000 permutations• IS IT SECURE?Not with Frequency Analysis

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Cryptanalysis Attacking Mono-Alphabetic Ciphers

Began in later part of the first millennium AD in the Middle East.

• Frequency analysis is the study of the frequency of occurrence of letters. (statistics) • First treatise on it was written by

• Ab‾uY‾us‾uf Ya‘q‾ub ibn Is-h‾aq ibn as-Sabb‾ah• ibn ‘omr‾an ibn Isma‾il al-Kind‾i, the “philosopher• of the Arabs.”

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Letter Frequency

Western Languages are redundant, they have a non-uniform distribution of about 26 letters.

• Each symbol of ciphertext depends on only onesymbol of plaintext and one value of the

permutation key, so guessing part of the key gives part of the plaintext.

• Attack proceeds by guessing parts of key corresponding to most common letters, which makes it possible to decipher an entire message.

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Letter frequency in English

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Attacking Mono-Alphabetic Ciphers in English

Appearance frequency of letters (in long texts) in a language is well known. Appearance frequency of pairs of letters in a language is also well known:

th, ee, oo, tt, qu, is, ae, . . . Not zq, kv, etcAppearance frequency of certain words is also well defined:the ≈ 6.4% a ≈ 2.1% i ≈ 0.9%of ≈ 4.0% in ≈ 1.8% it ≈ 0.9%and ≈ 3.2% that ≈ 1.2% for ≈ 0.8%to ≈ 2.4% is ≈ 1.0% as ≈ 0.8%

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Attacking Mono-Alphabetic Ciphers

Using the appearance frequencies of letters, words,and pairs-of-letters – accelerates the identification ofcertain letter substitutions (part of the key)

• Identification of word patterns, vowels, and consonants helps in finding parts of the text

• The identification of the remaining parts of the key now reduces the search space dramatically (from N!)

• Using heuristics and associative word-completions, the rest of the key can be easily revealed

– In English the most common letters: are E, T, A, O, I, N, S, H. more than half of all words end in E, T, D, S. Q is always followed by U.

– most common word is “THE.” and most common doublets are EE, TT, OO, SS, LL, FF.

– most common 2-letter combos: HE, RE, AN, TH, ER,IN.– most common 3-letter combos: ION, AND, ING, THE, ENT.

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Possible solutions

• Do not use redundant letters, like the letter e– Done by French writer Georges Perec in 1969. He

published a 300-page novel La Disparition (The Disappearance)…translated into English by Gilbert Adair and called “A Void”

• Or use different Mono-Alphabetic Ciphers in different parts of the plaintext:“Poly-Alphabetic Ciphers”. Quite strong

• • Or group plaintext into blocks that go through a transformation

8. Cryptography 19

Vig`enere Cipher (I)

Blaise de Vig`enere: (1523) Created the cipher but unused almost 200 years.

• One type of Poly-Alphabetic Cipher The collection of Mono-Alphabetic Ciphers consists of the 26 options for Caesar Cipher (with K = 0, 1, 2, . . ., 25) where each of the 26 is given a letter, which is the ciphertext letter that replaces the letter ‘a’

In practice:• A table of 26 rows by 26 columns is built. Row i in the

table contains the 26 letters of the alphabet circularly shifted by i.

• A keyword is used (over and over again) to select which of the mono-alphabetic ciphers to use. The cipher used is selected by the current letter in the keyword.

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The Cipher 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 ZA 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 ZB 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 AC C D E F G H I J K L M N O P Q R S T U V W X Y Z A BD D E F G H I J K L M N O P Q R S T U V W X Y Z A B CE E F G H I J K L M N O P Q R S T U V W X Y Z A B C DF F G H I J K L M N O P Q R S T U V W X Y Z A B C D EG G H I J K L M N O P Q R S T U V W X Y Z A B C D E FH H I J K L M N O P Q R S T U V W X Y Z A B C D E F GI I J K L M N O P Q R S T U V W X Y Z A B C D E F G HJ J K L M N O P Q R S T U V W X Y Z A B C D E F G H IK K L M N O P Q R S T U V W X Y Z A B C D E F G H I JL L M N O P Q R S T U V W X Y Z A B C D E F G H I J KM M N O P Q R S T U V W X Y Z A B C D E F G H I J K LN N O P Q R S T U V W X Y Z A B C D E F G H I J K L MO O P Q R S T U V W X Y Z A B C D E F G H I J K L M NP P Q R S T U V W X Y Z A B C D E F G H I J K L M N OQ Q R S T U V W X Y Z A B C D E F G H I J K L M N O PR R S T U V W X Y Z A B C D E F G H I J K L M N O P QS S T U V W X Y Z A B C D E F G H I J K L M N O P Q RT T U V W X Y Z A B C D E F G H I J K L M N O P Q R SU U V W X Y Z A B C D E F G H I J K L M N O P Q R S TV V W X Y Z A B C D E F G H I J K L M N O P Q R S T UW W X Y Z A B C D E F G H I J K L M N O P Q R S T U VX X Y Z A B C D E F G H I J K L M N O P Q R S T U V WY Y Z A B C D E F G H I J K L M N O P Q R S T U V W XZ Z 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

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Class Exercise using Vig`enere Cipher

• Keyword: GMU

• • Plaintext: SECURITY

• • Ciphertext:

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Attacking Vig`enere CipherCheck whether the cipher is Mono-Alphabetic– Check whether the appearance frequency of letters in the ciphertext

complies with that of a Mono-Alphabetic cipherDetermine the length of the keyword– If two identical sequences of plaintext letters occur at a distance that

is an integer multiple of the keyword length – than the two corresponding sequences of ciphertext letters will be identical

– Detect identical sequences of ciphertext letters– Conjecture that the keyword length is the GCD (greatest common

divisor) of distances between identical sequences of ciphertext• Neutralize shifts and break each of the suspected Mono-Alphabetic

Ciphers independently

8. Cryptography 23

Running Key Cipher One Time Pads

Running Key Does not use mathematical formula, instead uses everyday item such as a set of books

– Numbers give the book, page number, line number, and word number

One Time Pad

• Cipher only used for a small message and then destroyed

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Transposition Methods

Letters rearranged in particular fashion

Plaintext buffered in size N bufer

Plaintext scrambled to a defiined order in buffer

Key is the transposition mapping

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Spartan Scytale

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Rail-Fence Cipher

Method:• Plaintext written as a sequence of diagonals and

read as a sequence of rows

m e m t d y t

e t e o a a 9

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Row-Column Cipher

Key is 2 4 1 5 3

A T T A C

K F R O M

E A S T A

T D A W N

Ciphertext is TRSAAKETCMANTFADAOTW

8. Cryptography 28

Attacking Transposition Methods

Pure Transposition Cipher easily recognized: it has same letter frequencies as original text

Di-grams and tri-grams also are visible

Arrange text in rectangle and move rows and columns

8. Cryptography 29

Rotor Machines

Combine Substitution and Transposition Methods

• produce ciphers that are very difficult to break

Rotor Machines in World War II: German “Enigma” and Japanese “Purple”

• Breaking by the Allies was a significant factor in the outcome of the war (Turing)

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Example of Rotor Machine