Classical Encryption Techniques

Lecturer:

Prof. Dr. Michael Eichberg

Version:

2023-10-19

Based on:

Cryptography and Network Security - Principles and Practice, 8th Edition, William Stallings

Definitions

Plaintext:

Klartext

An original message.

Ciphertext:

Geheimtext oder Chiffretext oder Krytogramm

The coded (encrypted) message.

Encryption(Enciphering):

The process of converting from plaintext to ciphertext.

Decryption(Deciphering):

Restoring the plaintext from ciphertext.

Definitions

Cryptography:

The area of study of the 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.

Simplified Model of Symmetric Encryption

Symmetric Cipher Model

There are two requirements for secure use of conventional encryption:

1. A strong encryption algorithm

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

Model of Symmetric Cryptosystem

Cryptographic Systems can be Characterized along three independent dimensions.

1. The type of operations used for transforming plaintext to ciphertext.

   • Substitution

   • Transposition

2. The number of keys used.

   Symmetric:

   single-key, secret-key, conventional encryption

   Asymmetric:

   two-key or public-key encryption

3. The way in which the plaintext is processed.

   • Block Cipher

   • Stream Cipher

Cryptanalysis and Brute-Force Attack

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

Classification of Attacks

Type of Attack:

<Known to Cryptanalyst>

Classification of Attacks

Encryption Scheme Security

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

Brute-Force Attack

• 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.

Substitution Technique

• 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.

Caesar Cipher

• 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 Algorithm

Can define transformation as:

Mathematically give each letter a number:

Algorithm can be expressed as:

Caesar Cipher Algorithm

A shift may be of any amount, so that the general Caesar algorithm is:

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

Brute-Force Cryptanalysis of Caesar Cipher

Brute-Force Cryptanalysis (of Caesar Cipher)

Decryption is more complicated when the plaintext is already garble. E.g., as in case of a compressed file as seen below.

Monoalphabetic Cipher

• 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 \(4 \times 10^{26}\) 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.

English Letter Frequency

Monoalphabetic Ciphers

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

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

Playfair Cipher

• 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 x 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 Key Matrix

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. The letters I and J count as one letter.

Using the keyword MONARCHY:

Playfair Encryption

Enryption is done on each pair of letters of the plaintext.

1. If both letters are the same (or only one letter is left), add an "X" after the first letter. Encrypt the new pair and continue. (e.g., ballon would be encryped as ba lx lo on)

2. If the letters appear on the same row, replace them with the letters to their immediate right respectively (wrap around if necessary). (e.g., ar is encrypted as RM)

3. If the letters appear on the same column, replace them with the letters immediately below respectively (wrap around if necessary). (e.g., mu is encrypted as CM)

4. If the letters are not on the same row or column, replace them with the letters on the same row respectively but at the other pair of corners of the rectangle defined by the original pair. (e.g., hs is encrypted as BP and ea as IM)

Hill Cipher

• 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

Polyalphabetic Ciphers

Polyalphabetic substitution ciphers improve on the simple monoalphabetic technique by using different monoalphabetic substitutions as one proceeds through the plaintext message.

Vigenère Cipher

• 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

Vigenère-Tableau

Let's assume the key is D, the plaintext character is b then the ciphertext letter is E.

Example of Vigenère Cipher

• To encrypt a message, a key is needed that is as long as the message.

• Usually, the key is a repeating keyword.

Vigenère Autokey System

• A keyword is concatenated with the plaintext itself to provide a running key.

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.

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

Difficulties when using a One-Time Pad

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

  1. 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

  2. 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

Rail Fence Cipher

• Simplest transposition Vertauschung cipher.

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

Row Transposition 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.

Steganography

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Other Steganography Techniques

Character marking

Selected letters of printed or typewritten text are over-written in pencil. The marks are not visible unless the paper is held at an angle to bright light.

Invisible ink

A number of substances can be used for writing but leave no visible trace until heat or some chemical is applied to the paper.

Pin punctures

Small pin punctures on selected letters are ordinarily not visible unless the paper is held up in front of a light.

...

Steganography vs. Encryption

Steganography has a number of drawbacks when compared to encryption:

• It requires a lot of overhead to hide a relatively few bits of information

• Once the system is discovered, it becomes virtually worthless

The advantage of steganography:

• It can be employed by parties who have something to lose should the fact of their secret communication (not necessarily the content) be discovered.

• Encryption flags traffic as important or secret or may identify the sender or receiver as someone with something to hide.