Classical cryptography

The Shift Cipher Encryption example... The Shift Cipher Encryption example... “Security” The process of attempting to compute the key k, given a string of ciphertext y, is called cryptan

• Douglas Stinson, Cryptography: Theory and Practice, 3rd, Chapman & Hall CRC, 2006.

– Chapter 1

Secure communication scheme

The set of integers modulo m:

Lab computing: try operators + and * modulo

m in Python

The Shift Cipher

Caesar cipher (K = 3)

• x = “NGUYENTHANHNHUT”

• y = “QJXBHQWKDQKQKXW”

The Shift Cipher Encryption example

The Shift Cipher Encryption example

The Shift Cipher Decryption example

ow Cryptool it! Cryptool it!

Practical cryptosystems

1 Each encryption function ek and each decryption

function dk should be efficiently computable

2 An opponent, upon seeing a ciphertext string y,

should be unable to determine the key k that was

used, or the plaintext string x

“Security”

The process of attempting to compute the key k, given

a string of ciphertext y, is called cryptanalysis

Security of the Shift cipher

• The Shift Cipher (modulo 26) is not secure.

• It can be cryptanalyzed by the obvious method

of exhaustive key search

– How many possible keys with the A Z alphabet?

“Secure”  the keyspace should be very

large.

The Substitution Cipher

The Substitution Cipher

• The number of possible permutations is 26!,

which is more than 4*1026, a very large number

Compute the Euler phi-function

The multiplicative inverse modulo m

For m = 26:

Exercise

The Affine Cipher

So the three ciphertext characters are 0, 23, and 6, which corresponds to the alphabetic string AXG

Security of the Affine cipher

Take a short break ☺☺

The Vigenère Cipher

• Each key k is an alphabetic string of length m, called

a keyword

• The Vigenere Cipher encrypts m alphabetic characters

at a time

Security of the Vigenere Cipher

• How many possible keywords of length m with the A Z alphabet.

The Hill Cipher

Try Python Matrix modulo n

Try Cryptool it!

1.12

• Think about the security of the Hill Cipher!

Take a short break ☺☺

The Permutation Cipher

1.16

1.17

The Permutation Cipher is a special case of the

Hill Cipher

Short break!

Stream ciphers

• Periodic stream cipher with period d

– zi+d = zi for all i > 0.

– Vigenere is a periodic stream cipher with period m.

• Some basic stream cipher: (self-reading)

– Linear feedback shift register (LFSR)

The Vigenère cipher is a stream cipher

• We define the keystrean as follow:

• This generate the keystream Short break!

• The goal of the adversary/the opponent:

– Determine the key K

• General assumption (Kerckhoff’s principle):

– Oscar knows the cryptosystem being used.

• Four attack models:

Basic tool for cryptanalysis

• Statistical properties of language (English)

– Beker and Piper partition

Digrams and trigrams in English

• The 30 most common digrams

Cryptanalysis of Affine Cipher

• Big problem:

– Statistical properties of Vietnamese language

• Cryptanalyses of: (self-reading)

– Substitution Cipher

– Vigenere Cipher

– Hill Cipher

– LFSR Cipher