9/03/15 UB Fall 2015CSE565: S. Upadhyaya

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CSE565: Computer SecurityLecture 2

Basic Encryption & Decryption

CSE565: Computer SecurityLecture 2

Basic Encryption & Decryption

Shambhu Upadhyaya

Computer Science & Eng.

University at Buffalo

Buffalo, New York, 14260

9/03/15 UB Fall 2015CSE565: S. Upadhyaya

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Overview Lecture 2 Overview

Terminology (10 minutes) Encryption by Substitutions & Transpositions

(60 minutes)

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AnnouncementsAnnouncements

Background Material – 1 Properties of Arithmetic

Inverses Divisors Prime Numbers Greatest Common Divisor

Background Material – 2 Modular arithmetic

Basic properties Operations

Refer to Useful Notes on Handouts page

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Terminology Encryption

A process of encoding a message Decryption

It is the reverse process

Encryption Algorithms A key K is generally used Symmetric encryption: Asymmetric encryption:

)),(,( PKEKDP

)),(,( PKEKDP ED

Plaintext

P=(p1,p2, …pn)

CiphertextOriginalPlaintext

Encryption Decryption

C=(c1,c2, … cm)C=E(P)

P=D(C) =D(E(P))

9/03/15 UB Fall 2015CSE565: S. Upadhyaya

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Cryptography &

Cryptanalysis Cryptography

Hidden writing – encryption to conceal text Cryptanalysis

Break an encryption Attempt to break a single message Attempt to recognize patterns in encrypted

messages Attempt to find general weaknesses

Breakable Encryption Given enough time and data, encryption can

be broken Practicality is an issue Risky to proclaim an algorithm secure!

Cryptanalysis AttacksCryptanalysis Attacks

Type of attack What is known to cryptanalyst

Ciphertext only Algorithm, ciphertext

Known plaintext Algorithm, ciphertext, corresponding plaintext

Chosen plaintext Algorithm, ciphertext, plaintext chosen by analyst with corresponding ciphertext

Chosen ciphertext Algorithm, ciphertext, ciphertext chosen by analyst with corresponding decrypted plaintext

Chosen text Combination of the above two

9/03/15 UB Fall 2015CSE565: S. Upadhyaya

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Substitutions & Transpositions

Substitutions Monoalphabetic Ciphers Polyalphabetic Ciphers These are called Stream Ciphers

Transpositions Permutation These are Block Ciphers

9/03/15 UB Fall 2015CSE565: S. Upadhyaya

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Monoalphabetic

Ciphers Caesar Cipher Formula: Treaty Impossible --> wuhdwb lpsrvvleoh Advantages & Disadvantages

Easy to perform Simple, so easy to predict the pattern Repeat characters give clue to break

Permutation Cipher Use a key ABCDE ……… Keyab………. Since key is short, most plaintext letters are only one

or two positions off Time complexity of these algorithms – linear in n where n

is the no. of characters in plaintext

3)( iii ppEc

9/03/15 UB Fall 2015CSE565: S. Upadhyaya

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Polyalphabetic Substitution

Ciphers Main problem with mono-alphabetic ciphers is the non-flat frequency distribution

A flat distribution gives no information to cryptanalyst

Flattening by combining distributions Two or more separate encryption alphabets for the

same character of the plaintext E.g., one encryption for characters in odd positions

and another for at even positions Reduces the repeat symbols in the ciphertext Makes it hard to break (Discussion of an example)

9/03/15 UB Fall 2015CSE565: S. Upadhyaya

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Vigenere Tableau Need to smooth out peaks and valleys of frequency

distribution Can be done by extending no. of permutations Extreme case – extend to 26 permutations A 26 X 26 table is used (discussion of example) Key word of length 3 is sufficient to smooth out the

distribution Cryptanalysis of Polyalphabetic Substitution

Reading exercise Focus on Kasiski method and Index of

Coincidence method (Look up Ref. Texts) (http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher)

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Perfect Substitution

Cipher Requires an infinite non-repeating sequence of alphabets

This will confound the cryptanalyst One-Time pads Vernam Cipher

Uses an arbitrarily long sequence of numbers Formula:

Random Numbers Middle digits of phone numbers in a residential

directory Pseudo random numbers – linear congruential

random number generator Formula:

nprc iii mod

nbrar i mod)*(1i

Unbreakable CipherUnbreakable Cipher

Use a Vigenere table with 27 characters (includes space)

Use a one-time key as long as the message Two different decryptions using two keys Cryptanalyst cannot figure out which key is

correct – hence the code is unbreakable

9/03/15 UB Fall 2015CSE565: S. Upadhyaya

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ciphertextkeyplaintext

ciphertextkeyplaintext

ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFPLUYTSpxlmvmsydofuyrvzwc tnlebnecvgdupahfzzlmnyihmr mustard with the candlestick in the hall

ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFPLUYTpftgpmiydgaxgoufhklllmhsqdqogtewbqfgyovuhwtmiss scarlet with the knife in the library

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Transpositions It is a method where letters of the message are rearranged

Goal here is diffusion rather than confusion Information is spread widely across the ciphertext

Columnar transposition is an easy one Characters are rearranged into columns (Study of an example)

Encipherment/Decipherment Complexity Algorithm is constant in the amount of work per character Time is proportional to length of message Space required is directly proportional to message length Output characters cannot be produced until all characters are

read in Delay depends on the length of the message

Not appropriate for long messages

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Cryptanalysis Digrams, trigrams & other patterns used to break

encryption Digram – letter pairs such as -re- -th- -en- -ed- etc. Trigram – groups such as ent, and, ing, thi etc.

Cryptanalysis by trial & error & using a moving window for comparison This is a reading exercise! (http://en.wikipedia.org/wiki/Transposition_cipher)

Double transposition algorithm makes breaking more difficult It uses transposition of a transposed text Discussion of example

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Summary Stream Ciphers

Mono and poly-alphabetic encryptions Since they convert one symbol of plaintext immediately

into a symbol of ciphertext Features include: a) speed of transformation, b) low

error propagation Disadvantages are: a) low diffusion, b) susceptible to

malicious insertions Block Ciphers

Columnar transposition algorithm and fractionated Morse

Group of plaintext symbols are encrypted as one block Features include: a) diffusion, b) immunity to insertions Disadvantages are: a) slowness of encryption, b) error

propagation