Pfleeger Security in Computing, Chapter 2

Security in Computing Chapter 2 Elementary Cryptography

Pfleeger, Security in Computing, ch. 2

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Chapter Outline • • • • • • • • •

2.1 Terminology and Background 2.2 Substitution Ciphers 2.3 Transpositions (Permutations) 2.4 Making “Good” Encryption Algorithms 2.5 The Data Encryption Standard (DES) 2.6 The AES Encryption Algorithm 2.7 Public Key Encryption 2.8 Uses of Encryption 2.9 Summary


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Elementary Cryptography • important tool • rooted in some heavy-duty math – – – –

number theory group & field theory computational complexity probability

• our goal: – be able to intelligently use crypto – not design/break cryptosystems

• some more detailed analysis in ch. 10 Pfleeger, Security in Computing, ch. 2

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2.1 Terminology and Background 2.2 Substitution Ciphers 2.3 Transpositions (Permutations) 2.4 Making “Good” Encryption Algorithms 2.5 The Data Encryption Standard (DES) 2.6 The AES Encryption Algorithm 2.7 Public Key Encryption 2.8 Uses of Encryption 2.9 Summary


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Text’s Notation • S sender

O might try to:

• R recipient

• block

• T trans. medium • O outsider or intruder


• intercept • modify • fabricate

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Terminology • • • • •

encryption (or encipher) decryption (or decipher) note: encode/decode different meaning plaintext ciphertext


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Graphical View plaintext

encryption


ciphertext

decryption

plaintext

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Notation • denote plaintext P = • denote ciphertext C = • Example: – – – –

plaintext “I like cheesy poofs” P = ciphertext “X QXVC JMCCZB ARREZ” C =

• More formally: – C=E(P) – P=D(E(P))

P=D(C)


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How Codes Are Different • code uses linguistic units • codebook is the key word

code

bored car poultry students .

9685 2307 7902 1092 .

.

.


bored students 9685 1092

• may use phrases as well • e.g., “return to base for supplies” enciphered GIDIZZLEDUNK 9

Cryptographic Keys • most algorithms use keys • encryption: – C = E(K, P) – P = D(K, C) – P = D(K, E(K,P))


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Cryptosystem • Cryptographic algorithm (aka cipher) – mathematical function used for encrypt

• Cryptosystem consists of: – cryptographic algorithm – set of all possible plaintexts – set of all possible ciphertexts


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Symmetric Algorithm • encryption, decryption keys are the same key plaintext

encryption


ciphertext

decryption

plaintext

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Asymmetric Algorithm • encryption, decryption keys different • encryption key: KE • decryption key: KD – C = E(KE, P) – P = D(KD,C) – P = D(KD, E(KE, P))


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Asymmetric Algorithm Diagram KE

plaintext

encryption


KD

ciphertext

decryption

plaintext

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Restricted Algorithms • algorithm itself is secret • security of algorithm depends on its secrecy • bad idea: – can’t be used by large or changing group – if one accidentally reveals algo, everyone must change – how do you know if the algo is strong?

• think of regular (i.e., physical) locks Pfleeger, Security in Computing, ch. 2

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Kerckhoff’s Principle • secrecy must reside entirely with the key • must assume that the enemy has complete details of the cryptographic algorithm • Kerkhoff’s assumption: people will: – reverse engineer your algorithm – disassemble your code – e.g., RC4 in 1994


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Cryptology

Cryptography


Cryptanalysis

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Cryptanalysis • Cryptanalyst tries to break an algorithm • Categories (due to Lars Knudsen) – total break - find the key K such that D(K,C)=P – global deduction - find alternative algorithm, A, equivalent to D(K,C) without knowing K – instance (or local) deduction - find the plaintext of an intercepted ciphertext – information deduction - get some information about the key or plaintext, e.g., first bits of the key, info about the form of the plaintext, …

• Attempt at cryptanalysis called an attack Pfleeger, Security in Computing, ch. 2

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How is Cryptanalysis Done? • Analyst works with whatever is available: – – – – – – –

encrypted messages known algorithms intercepted plaintext known or suspected plaintext properties of the likely plaintext properties of computers properties of network protocols


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Breakable Encryption • • • • •

breakable algorithm breakable but not practical to break more breakable with tricks effects of sloppy procedures Moore’s law


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Character Arithmetic • Usually don't consider case • Can do arithmetic on letters • Example: A+2, Y+5, etc.

Letter A B C D E F G H I J K L M Code 0 1 2 3 4 5 6 7 8 9 10 11 12 Letter N O P Q R S T U V W X Y Z Code 13 14 15 16 17 18 19 20 21 22 23 24 25 • What if you go past the end, e.g. Y+3? Pfleeger, Security in Computing, ch. 2

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modular arithmetic – quick review a and b are integers, b ≥ 1 divide a by b (using regular long division) result is: q (quotient) r (remainder or residue)

a = qb + r, where 0 ≤ r < b r = a mod b Pfleeger, Security in Computing, ch. 2

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Cryptographic Elements • Primitive operations: – substitutions - exchange one letter for another – transpositions – rearrange the order of the letters


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2.1 Terminology and Background 2.2 Substitution Ciphers 2.3 Transpositions (Permutations) 2.4 Making “Good” Encryption Algorithms 2.5 The Data Encryption Standard (DES) 2.6 The AES Algorithm 2.7 Public Key Encryption 2.8 Uses of Encryption 2.9 Summary


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Keyword Mixed Alphabet • Form ciphertext alphabet by: – pick a keyword – spell it without duplicates – then, fill in the rest of the alphabet in order

• Example, keyword VACATION A ABCDEFGHIJKLMNOPQRSTUVWXYZ C V A C T I O N B DE F G H J K L M P Q R S U W X Y Z

• Encrypt “I should be sailing” as: – DQBK SGTA IQVD GDJN Pfleeger, Security in Computing, ch. 2

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Another Substitution • Shift plaintext chars. three characters A: A B C D E F G H I J K L M C: D E F G H I J K L M N O P A: N O P Q R S T U V W X Y Z C: Q R S T U V W X Y Z A B C

• Example: – P = “Old School cracked me up” – C = ROG VFKRRO FUDFNHG PH XS Pfleeger, Security in Computing, ch. 2

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• Example: – P = “Old School cracked me up” notice wrap – C = ROG VFKRRO FUDFNHG PH XS Pfleeger, Security in Computing, ch. 2

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• Algorithm called Caesar Cipher notice wrap Pfleeger, Security in Computing, ch. 2

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Caesar Example A C

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 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 • What is: VFUXEV LV D IXQQB VKRZ ?


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Caesar Cipher (more formal def) • encryption: – EK(m) = m + 3 mod 26

• decryption: – DK(c) = c – 3 mod 26

• review: – if a and m are positive integers, a mod m is the remainder when a is divided by m

• Caesar cipher special case of shift cipher Pfleeger, Security in Computing, ch. 2

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Shift Cipher • encryption: – EK(m) = m + K mod 26

• decryption: – DK(c) = c – K mod 26

• example: k=5 A: 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 C: 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 E • “summer vacation was too short” encrypts to – XZRR JWAF HFYN TSBF XYTT XMTW Y Pfleeger, Security in Computing, ch. 2

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Breaking Shift Ciphers • How difficult? • How many possibilities? • Example: – AKZC JAQA IZMI TTGN CVVG APWE


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First 13 Possibilities 0 1 2 3 4 5 6 7 8 9 10 11 12

A B C D E F G H I J K L M

K L M N O P Q R S T U V W

Z A B C D E F G H I J K L

C D E F G H I J K L M N O

J K L M N O P Q R S T U V


Q R S T U V W X Y Z A B C



I J K L M N O P Q R S T U


M N O P Q R S T U V W X Y


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 S

N O P Q R S T U V W X Y Z


V W X Y Z A B C D E F G H




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P Q R S T U V W X Y Z A B

W X Y Z A B C D E F G H I

Last 13 Possibilities 13 14 15 16 17 18 19 20 21 22 23 24 25


X Y Z A B C D E F G H I J



W X Y Z A B C D E F G H I


D E F G H I J K L M N O P

















J K L M N O P Q R S T U V

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R S T U V W X Y Z A B C D

So easily crackable • Someone should have explained this to the mafia boss: http://dsc.discovery.com/news/briefs/20060417/mafi aboss_tec.html?source=rss


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Monoalphabetic Ciphers • simple substitutions, e.g., shift, keyword mixed, newspapaer cryptogram ... are monoalphabetic ciphers • how many possible substitution alphabets? • can we try all permutations? • how would you try to break them?


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monoalphabetic – brute force • how many possible substitution alphabets? – 26! ≈ 4 * 1026

• can we try all permutations? – sure. have some time? – at 1 test/μsec, about 12 trillion years.

• how would you try to break them? – use what you know to reduce the possibilities


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breaking substitutions • how do you break the newspaper cryptogram? – look at common letters (E, T, O, A, N, ...) – single-letter words (I, and A) – two-letter words (of, to, in, ...) – three-letter words (the, and, ...) – double letters (ll, ee, oo, tt, ff, rr, nn, ...) – other tricks? Pfleeger, Security in Computing, ch. 2

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breaking substitutions (cont'd) • use language statistics of plaintext – English, java, TCP packet headers, etc.

• example: – frequencies in English char: A B C D E F G H I J K L M pct: 8 1.5 3 4 13 2 1.5 6 6.5 0.5 0.5 3.5 3 char: N O P Q R S T U V W X Y Z pct: 7 8 2 0.25 6.5 6 9 3 1 1.5 0.5 2 0.25 Pfleeger, Security in Computing, ch. 2

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Character Frequencies (English) 14 12 10

percent

8 6 4 2 0

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

characters

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Common English Digrams and Trigrams Digrams EN RE ER NT TH ON IN TF AN OR Pfleeger, Security in Computing, ch. 2

Trigrams ENT ION AND ING IVE TIO FOR OUR THI ONE 41

Pfleeger Security in Computing, Chapter 2

Pfleeger Security in Computing, Chapter 2

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