Cryptography Unit 3b - Comprehensive Study Notes

Cipher is a method for encrypting messages.
Encryption algorithms are standardized & published.
The key, which is an input to the algorithm, is secret.
- Key is a string of numbers or characters.
If the same key is used for encryption & decryption, the algorithm is called symmetric.
If different keys are used for encryption & decryption, the algorithm is called asymmetric.
Encryption flow (as summarized from the transcript):
- Plain Text --(Encryption Algorithm, Key A)--> Cipher Text
- Decryption uses an algorithm with Key B to recover the Plain Text.
Diagrammatic idea (from the transcript): Encryption - Cipher - Plain Text - Encryption Algorithm - Key A - Key B - Cipher Text - Decryption - Plain Text - Algorithm.

Algorithms where the key for encryption and decryption are the same are called symmetric.
Types of symmetric ciphers:
- 1. Stream Ciphers – Encrypt data one bit or one byte at a time.
- Used if data is a constant stream of information.
- Example: Caesar Cipher.
- 2. Block Ciphers – Encrypt data one block at a time (typically 64 bits, or 128 bits).
- Used for a single message.
- Examples: Advanced Encryption Standard (AES), Data Encryption Standard (DES).
Note: The Caesar Cipher is listed as an example of a stream cipher in the transcript.

Strength of an algorithm is determined by the size of the key; the longer the key, the more difficult it is to crack.
Key length is expressed in bits.
Typical key sizes vary between 48 bits and 448 bits.
The set of possible keys for a cipher is called the key space.
Examples:
- For a 40-bit key there are $2^{40}$ possible keys.
- For a 128-bit key there are $2^{128}$ possible keys.
Each additional bit added to the key length doubles the security.
To crack the key, a hacker can use brute-force (try all possible keys until one works).
Transcript claim: a Super Computer can crack a 56-bit key in 24 hours.
Transcript claim (note): it will take 272 times longer to crack a 128-bit key (Longer than the age of the universe!!!). The "272" appears to be a typographical error in the transcript and is commonly interpreted as a much larger factor such as $2^{72}$ .

Caesar Cipher, also known as the "Caesar Box," is one of the earliest known cryptographic systems.
It was developed around 100 BC and used by Julius Caesar to send encrypted messages to his generals during military campaigns.
Mechanism: shifts all letters of the plaintext by a fixed number of letters; this fixed number is the private key.
It is a symmetric algorithm because encryption and decryption use the same key (the shift).
Alphabet rotation example (rotation by 3):
- 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
- (Rotated by three letters as shown)

Encryption example (Shift by 3):
- Plain Text: Attack at Dawn
- Cipher Text: Dwwdfn Dw Gdyq
- Key: 3
Decryption example (Shift by 3):
- Cipher Text: Dwwdfn Dw Gdyq
- Plain Text: Attack at Dawn
- Key: 3
These examples illustrate the symmetric nature and the fixed shift mechanism.

Q1: Encrypt the following message by right-shifting 5 letters: "ATTACK AT DAWN".
- (Student task: submit the encrypted message to Blackboard in Unit 3 folder.)
Q2: Encrypt the message, "THIS IS A MESSAGE," with En(x), n = 3.
- (Submit to Blackboard.)
Q3: Decrypt the message, "WKLV LV D PHVVDJH," with En(x), n = 3.
- (Submit to Blackboard.)

Encryption function: if we encode a letter x as an index 0-25, then the encrypted index is:
- $E(x) = (x + n) \bmod 26$
- where n is the key (the shift), and mod 26 keeps the result within the alphabet.
Decryption function: to decrypt, shift back by n:
- $D(x) = (x - n) \bmod 26$
Notes:
- The right shift corresponds to adding n; the left shift corresponds to subtracting n.
- We have to consider all characters in the plaintext/ciphertext.
- The size of the English alphabet is 26, hence the mod 26 operation.
- The modulo ensures the result stays within the valid index range [0, 25].

This guarantees valid indexes and valid letters after encryption.
It enforces wrap-around when a shift moves past 'Z' back to the start of the alphabet.

The size of the key space is not infinite; it is proportional to the number of possible shifts (i.e., the number of letters in the alphabet).
Transcript answer: It is proportional to the number of letters in the alphabet.

Statement: If we make multiple Caesar encryptions after each other, we can make the cryptosystem more secure.
Transcript answer: False.
Explanation: Multiple sequential Caesar encryptions with fixed shifts effectively combine into a single net shift (the sum of shifts modulo 26). Hence security does not necessarily increase.

Code snippet defines a string of letters:
- letters = ' ABCDEFGHIGKLMNOPQRSTUVWXYZ'
- Note: This string contains a leading space and a likely typo (missing J), which affects indexing and behavior.
KEY = 3
caesarencrypt(plaintext):
- Converts plain_text to uppercase.
- For each character l in plain_text, finds its index in letters via letters.find(l).
- Computes new index: index = (index + KEY) % len(letters).
- Builds cipher_text by appending letters[index].
caesardecrypt(ciphertext):
- For each character l in cipher_text, finds its index in letters.
- Computes index: (index - KEY) % len(letters).
- Builds plain_text by appending letters[index].
Main block example:
- message = 'Welcome to my Cryptography class'
- encryptedmessage = caesarencrypt(message)
- print(encrypted_message)
- print(caesardecrypt(encryptedmessage))
Teaching point: The code uses a fixed alphabet and uppercases input; only characters found in the alphabet are transformed.

The next page explains modifying the code to allow any characters in the plain text and cipher text.
Hint: Use ASCII index to represent a character with ord().
Idea: Instead of a fixed alphabet, map characters to their ASCII codes, apply the shift modulo a chosen range, and map back with chr().
Goal: Create a version that can encrypt/decrypt any text, not just letters from A-Z.
Submission: Submit your solution (Python code) to Lab 2 in Unit 3 on Blackboard.

Practical relevance: Understanding core encryption concepts, key management, and simple ciphers builds intuition for more complex modern cryptography.
Ethical considerations: Use cryptographic techniques responsibly to protect privacy and data; avoid illegal or unethical use (e.g., unauthorized decryption).
Real-world relevance: Recognition that key length and algorithm choice impact security; awareness of brute-force limits and the importance of using sufficiently large keys in practice.