cryptography

· Cryptography

· The area of study of the many schemes used for

encryption

· Cryptographic system/cipher

· A scheme

· Cryptanalysis

· Techniques used for deciphering a message without any knowledge of the enciphering details

· Cryptology

· The areas of cryptography and cryptanalysis

Symmetric Encryption

Figure 3.1 Simplified Model of

· There are two requirements for secure use of conventional

encryption:

· A strong encryption algorithm

· Sender and receiver must have obtained copies of the secret key in a secure fashion and must keep the key secure

Symmetric Cipher Model

Figure 3.2 Model of Symmetric Cryptosystem

· Characterized along three independent dimensions:

· The type of operations used for transforming plaintext to

ciphertext

· Substitution

· Transposition

· The number of keys used

· Symmetric, single-key, secret-key, conventional

encryption

· Asymmetric, two-key, or public-key encryption

· The way in which the plaintext is processed

· Block cipher

· Stream cipher

Cryptographic Systems

· Cryptanalysis

· Attack relies on the nature of the algorithm plus some knowledge of the general characteristics of the plaintext

· Attack exploits the characteristics of the algorithm to attempt to deduce a specific plaintext or to deduce the key being used

· Brute-force attack

· Attacker tries every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained

· On average, half of all possible keys must be tried to

achieve success

Cryptanalysis and Brute-Force Attack

Encrypted Messages

Table 3.1 Types of Attacks on

· Unconditionally secure

· No matter how much time an opponent has, it is impossible for him or her to decrypt the ciphertext simply because the required information is not there

· Computationally secure

· The cost of breaking the cipher exceeds the value of the encrypted information

· The time required to break the cipher exceeds the useful lifetime of the information

Encryption Scheme Security

· Involves trying every possible key until an intelligible

translation of the ciphertext into plaintext is obtained

· On average, half of all possible keys must be tried to

achieve success

· To supplement the brute-force approach, some degree of knowledge about the expected plaintext is needed, and some means of automatically distinguishing plaintext from garble is also needed

Brute-Force Attack

· The term strong encryption refers to encryption schemes that make it impractically difficult for unauthorized persons or systems to gain access to plaintext that has been encrypted

· Properties that make an encryption algorithm strong are:

· Appropriate choice of cryptographic algorithm

· Use of sufficiently long key lengths

· Appropriate choice of protocols

· A well-engineered implementation

· Absence of deliberately introduced hidden flaws

Strong Encryption

· Is one in which the letters of plaintext are replaced by other letters or by numbers or symbols

· If the plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext bit patterns with ciphertext bit patterns

Substitution Technique

· Simplest and earliest known use of a substitution cipher

· Used by Julius Caesar

· Involves replacing each letter of the alphabet with the

letter standing three places further down the alphabet

· Alphabet is wrapped around so that the letter following Z

is A

plain: meet me after the toga party cipher: PHHW PH DIWHU WKH WRJD SDUWB

Caesar Cipher

· Can define transformation as:

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

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 C

· Mathematically give each letter a number

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

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

· Algorithm can be expressed as:

c = E(3, p) = (p + 3) mod (26)

· A shift may be of any amount, so that the general Caesar algorithm is: C = E(k , p ) = (p + k ) mod 26

· Where k takes on a value in the range 1 to 25; the decryption algorithm is

simply:

p = D(k , C ) = (C − k ) mod 26

Caesar Cipher Algorithm

of Caesar Cipher

Figure 3.3 Brute-Force Cryptanalysis

Figure 3.4 Sample of Compressed Text

Sample of Compressed Text

· Permutation

· Of a finite set of elements S is an ordered sequence of all the elements of S , with each element appearing exactly once

· If the “cipher” line can be any permutation of the 26 alphabetic characters, then there are 26! or greater than 4 x 1026 possible keys

· This is 10 orders of magnitude greater than the key space for DES

· Approach is referred to as a monoalphabetic substitution cipher because a single cipher alphabet is used per message

Monoalphabetic Cipher

Letters in English Text

Figure 3.5 Relative Frequency of

· Easy to break because they reflect the frequency data of the original alphabet

· Countermeasure is to provide multiple substitutes (homophones) for a single letter

· Digram

· Two-letter combination

· Most common is th

· Trigram

· Three-letter combination

· Most frequent is the

Monoalphabetic Ciphers

· Best-known multiple-letter encryption cipher

· Treats digrams in the plaintext as single units and

translates these units into ciphertext digrams

· Based on the use of a 5 × 5 matrix of letters constructed using a keyword

· Invented by British scientist Sir Charles Wheatstone in 1854

· Used as the standard field system by the British Army in World War I and the U.S. Army and other Allied forces during World War II

Playfair Cipher

· Fill in letters of keyword (minus duplicates) from left to right and from top to bottom, then fill in the remainder of the matrix with the remaining letters in alphabetic order

· Using the keyword MONARCHY:

Playfair Key Matrix

Occurrence of Letters

Figure 3.6 Relative Frequency of

· Developed by the mathematician Lester Hill in 1929

· Strength is that it completely hides single-letter frequencies

· The use of a larger matrix hides more frequency

information

· A 3 x 3 Hill cipher hides not only single-letter but also

two-letter frequency information

· Strong against a ciphertext-only attack but easily broken

with a known plaintext attack

Hill Cipher

· Polyalphabetic substitution cipher

· Improves on the simple monoalphabetic technique by using different monoalphabetic substitutions as one proceeds through the plaintext message

· All these techniques have the following features in

common:

· A set of related monoalphabetic substitution rules is

used

· A key determines which particular rule is chosen for a

given transformation

Polyalphabetic Ciphers

· Best known and one of the simplest polyalphabetic

substitution ciphers

· In this scheme the set of related monoalphabetic substitution rules consists of the 26 Caesar ciphers with shifts of 0 through 25

· Each cipher is denoted by a key letter which is the

ciphertext letter that substitutes for the plaintext letter a

Vigenère Cipher

· To encrypt a message, a key is needed that is as long as

the message

· Usually, the key is a repeating keyword

· For example, if the keyword is deceptive, the message “we are discovered save yourself” is encrypted as:

key: deceptivedeceptivedeceptive

plaintext: wearediscoveredsaveyourself

ciphertext: ZICVTWQNGRZGVTWAVZHCQYGLMGJ

Example of Vigenère Cipher

· A keyword is concatenated with the plaintext itself to

provide a running key

· Example:

key: deceptivewearediscoveredsav plaintext: wearediscoveredsaveyourself ciphertext: ZICVTWQNGKZEIIGASXSTSLVVWLA

· Even this scheme is vulnerable to cryptanalysis

· Because the key and the plaintext share the same frequency distribution of letters, a statistical technique can be applied

Vigenère Autokey System

Figure 3.7 Vernam Cipher

Vernam Cipher

One-Time Pad

· Improvement to Vernam cipher proposed by an Army Signal Corp officer, Joseph Mauborgne

· Use a random key that is as long as the message so that the key need not be repeated

· Key is used to encrypt and decrypt a single message and then is discarded

· Each new message requires a new key of the same length as the new message

· Scheme is unbreakable

· Produces random output that bears no statistical relationship to the plaintext

· Because the ciphertext contains no information whatsoever about the plaintext, there is simply no way to break the code

· The one-time pad offers complete security but, in practice, has two fundamental difficulties:

· There is the practical problem of making large quantities of random keys

· Any heavily used system might require millions of random characters on a regular basis

· Mammoth key distribution problem

· For every message to be sent, a key of equal length is needed by both sender and receiver

· Because of these difficulties, the one-time pad is of limited utility

· Useful primarily for low-bandwidth channels requiring very high security

· The one-time pad is the only cryptosystem that exhibits perfect secrecy (see Appendix F)

Difficulties

· Simplest transposition cipher

· Plaintext is written down as a sequence of diagonals and then read off as a sequence of rows

· To encipher the message “meet me after the toga party” with a rail fence of depth 2, we would write:

m e m a t r h t g p r y

e t e f e t e o a a t Encrypted message is:

MEMATRHTGPRYETEFETEOAAT

Rail Fence Cipher

· Is a more complex transposition

· Write the message in a rectangle, row by row, and read the message off, column by column, but permute the order of the columns

· The order of the columns then becomes the key to the

algorithm

Key: 4 3 1 2 5 6 7

Plaintext: a t t a c k p o s t p o n e d u n t i l t w o a mx y z

Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ

Row Transposition Cipher

· Present an overview of the main concepts of symmetric

cryptography

· Explain the difference between cryptanalysis and brute- force attack

· Understand the operation of a monoalphabetic substitution cipher

· Understand the operation of a polyalphabetic cipher

· Present an overview of the Hill cipher

Summary