1. CSE565: Computer Security Lecture 2 Basic Encryption & Decryption
Shambhu Upadhyaya
Computer Science & Eng.
University at Buffalo
Buffalo, New York, 14260
8/31/17
UB Fall 2017

2. Overview Lecture 2 Overview Terminology (10 minutes)
Encryption by Substitutions & Transpositions (60 minutes)
8/31/17
UB Fall 2017

3. Announcements 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
8/31/17
UB Fall 2017

4. 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:
Original
Plaintext
Plaintext
Ciphertext
Encryption
Decryption
P=D(C)
=D(E(P))
P=(p1,p2, …pn)
C=(c1,c2, … cm)
C=E(P)
8/31/17
UB Fall 2017

5. Cryptography & Cryptanalysis
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!
8/31/17
UB Fall 2017

6. Cryptanalysis 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
Brute force attack is the simplest. But may not be practical.
8/31/17
UB Fall 2017

7. Substitutions & Transpositions
Monoalphabetic Ciphers
Polyalphabetic Ciphers
These are called Stream Ciphers
Transpositions
Permutation
These are Block Ciphers
8/31/17
UB Fall 2017

8. 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
8/31/17
UB Fall 2017

9. 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)
Combine distributions that are high with ones that are low.
T is sometimes enciphered as a and sometimes as b, X is sometimes enciphered as a and sometimes as b. The high frequency of T mixes with the low frequency of X. This produces a more moderate distribution for a and b.
8/31/17
UB Fall 2017

10. 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) (
Kasiski method for repeated patterns
Makes use of the regularity of English
Index of coincidence – works on the variation of the frequencies in a distribution – how high is high and how low is low…..it is a probabilistic method
8/31/17
UB Fall 2017

11. 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
8/31/17
UB Fall 2017

12. Unbreakable 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
ciphertext
key
plaintext
ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFPLUYTS
pxlmvmsydofuyrvzwc tnlebnecvgdupahfzzlmnyih
mr mustard with the candlestick in the hall
ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFPLUYT
pftgpmiydgaxgoufhklllmhsqdqogtewbqfgyovuhwt
miss scarlet with the knife in the library
8/31/17
UB Fall 2017

13. 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
8/31/17
UB Fall 2017

14. 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! (
Double transposition algorithm makes breaking more difficult
It uses transposition of a transposed text
Discussion of example
8/31/17
UB Fall 2017

15. 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
8/31/17
UB Fall 2017