lecture 3 - Cryptography I.ppt

Computer Security I

Computer Security I

Unit 2: Authorization & Authentication

Objectives

Objectives

Introduce the basic concepts of cryptography

Cryptographic algorithms

Basic Concepts

Basic Concepts

Cryptography: is the study of

secret (crypto-) writing (-graphy)

_{It is the practice of using}

encryption to conceal a message from all except the sender and

 _{Encryption: is the process of}

encoding a message so that its meaning is not obvious.

 _{Decryption: is the reverse}

process, transforming an

 _{Cipher: an algorithm for}

transforming an intelligible message into one that is

unintelligible by transposition and/or substitution methods

 _{Key: some critical information}

 _{Plaintext (P): The original form}

of a message. We denote a plaintext message P as a

sequence of individual characters

P = {p1,p2,…pn}

 _{Ciphertext (C): The encrypted}

form of a message. We denote a ciphertext message C as a

sequence of individual characters

 _{The transformation between}

plaintext and ciphertext are denoted :

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

C: Ciphertext

E: Encryption Algorithm

P: Plaintext

 _{Therefore we want a}

cryptosystem for which P = D(E(P))

Encryptio n

Decryptio n

Encryption Algorithms

Encryption Algorithms

 _{Some encryption algorithms use}

a key K, so the cipher text

message depends on the original plaintext message and the key

value, denoted

 _{C = E(K,P) where E is a set of}

encryption algorithms and the key K selects one specific

Symmetric and Asymmetric

Symmetric and Asymmetric

Encryption

Encryption

 _{Symmetric Encryption:}

Encryption key and decryption key are the same, so that

P=D(K,E(K,P)) where D and E are mirror image processes. Parties that communicate share a secret key. Mainly used to encipher/

Symmetric and Asymmetric

Symmetric and Asymmetric

Encryption

Asymmetric Encryption:

Each party has a pair of keys (K_pu, K_pr) where K_pu is the public key and K_pr is the private key.

The Public and Private key pair

comprise of two uniquely related cryptographic keys (basically long random numbers). Below is an

example of a Public Key:

The Public Key is what its name suggests - Public. It is made available to everyone via a publicly accessible repository or

directory. On the other hand, the Private Key must remain confidential to its

respective owner.

Because the key pair is mathematically related, whatever is encrypted with a

Public Key may only be decrypted by its corresponding Private Key and vice

For example, if Cindy wants to send

sensitive data to Lisa, and wants to be sure that only Lisa may be able to read it, she will encrypt the data with Lisa's Public Key. Only Lisa has access to her corresponding Private Key and as a

result is the only person with the

capability of decrypting the encrypted data back into its original form.

Public Key Cryptography can therefore achieve Confidentiality.

Classes of Encryption

Classes of Encryption

 _{Substitution: Exchanging each}

character of a message with another character or symbol

 _{Transposition: The order of the}

Substitution

Substitution

(Monoalphabetic Ciphers)

(Monoalphabetic Ciphers)

◦ Caesar Cipher: Used a shift of 3, so that plaintext P was

enciphered as ciphertext letter C by

 _{An alternative is to use a key, a}

word that controls the enciphering.

 _Eg.

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

 _{Another possibility is to count by}

3s , (or 5s, 7s or 9s) using every third letter

 _{Eg. Using (3*µ) mod 26}

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

Disadvantages

Disadvantages

 _{Monoalphabetic ciphers: -}

Frequency distribution reflects

Substitution

Substitution

(Polyalphabetic Ciphers)

(Polyalphabetic Ciphers)

 _{Flattens distribution by combining}

two distributions, using two

separate encryption alphabets.

 ₁st: For all characters in odd

positions of plaintext

 ₂nd: For all characters in even

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

a d g j m p s v y b e h k

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

n s x c h m r w b g l q v

Table 1 (Odd Position): (3*µ) mod 26

Table 2 (Even Position): ((5*µ)+13) mod 26

C O M P U T E R

g f k k i e m u

Vigenere Tableaux

Vigenere Tableaux

• _{Uses a keyword and lets the}

Vigenere Tableaux

Vigenere Tableaux

 _Eg

P A S S C O D E P A S S C O D E P A S S C O D E

One Time Pads

One Time Pads

 _{Large non-repeating set of keys}

are written on sheets of paper, put together into a pad.

 _{Sender would write the}

non-repeating keys one at a time

 _{The receiver needs an identical}

pad as the sender. Upon

receiving the message, the

receiver takes the appropriate number of keys and deciphers the message.

 _{Explore also Long Random}

Problems with one time

Problems with one time

pads

pads

 _{Need absolute synchronization}

between sender and receiver

 _{Need unlimited number of keys}

(Generating large number of keys is no problem, however, the

Transpositions

Transpositions

(Permutations)

(Permutations)

 _{An encryption process in which}

the letters of the message are rearranged.

 _{Goal: To spread the information}

Columnar Transposition

Columnar Transposition

 _{The plaintext is separated into}

blocks in the form

 _Eg

p1 p2 P3 p4 p5

p6 P7 p8 p9 p10 p11 P12 p13 p14 p15

T H I S I

 _{The resulting ciphertext would}

then be: tsu ham icn soa ilr

 _{Explore also Double Transposition}

Cryptanalytic Attacks

Cryptanalytic Attacks

 _{Ciphertext only: The cryptanalyst}

knows only the ciphertext.

Sometimes the language of the

plaintext and cipher are also known. Goal: Find the plaintext and the key

 _{Known-plaintext attack: The}

cryptanalyst knows several pairs of ciphertext and corresponding

plaintext. Goal: Find the key used to encrypt messages or a way to

 _{Chosen-plaintext: The}

cryptanalyst knows a number of encrypted messages and he can also encrypt any message he

chooses. Goal: To deduce the key used in the other encrypted

messages or decrypt any new message using that key.

 _{Chosen ciphertext: Similar to the}

chosen-plaintext but the

cryptanalyst can choose the

Summary