cryptography

Caesar cipher

Introduction#

It is the simple shift monoalphabetic classical cipher where each letter is replaced by a letter 3 position (actual Caesar cipher) ahead using the circular alphabetic ordering i.e. letter after Z is A. So when we encode HELLO WORLD, the cipher text becomes KHOORZRUOG.

Introduction

The Caesar cipher is a classic encryption method. It works by shifting the characters by a certain amount. For example, if we choose a shift of 3, A will become D and E will become H.

The following text has been encrypted using a 23 shift.

THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG
QEB NRFZH YOLTK CLU GRJMP LSBO QEB IXWV ALD

Python implementation

The ASCII way

This shifts the characters but doesn’t care if the new character is not a letter. This is good if you want to use punctuation or special characters, but it won’t necessarily give you letters only as an output. For example, “z” 3-shifts to ”}“.

def ceasar(text, shift):
    output = ""
    for c in text:
        output += chr(ord(c) + shift)
    return output

ROT13

ROT13 is a special case of Caesar cipher, with a 13 shift. Only letters are changed, and white-space and special characters are left as they are.

What is interesting is that ROT13 is a reciprocal cipher : applying ROT13 twice will give you the initial input. Indeed, 2 * 13 = 26, the number of letters in the alphabet.

As ROT13 doesn’t have a key as input parameter it is often seen more as a encoding algorithm or, more specifically, an obfuscation algorithm rather than a cipher.

ROT13 just makes it hard to read messages directly and is therefore often used for offensive messages or puns of jokes. It doesn’t provide any computational security.

A Java implementation for Caesar Cipher

Implementation of the Caesar cipher.

  • This implementation performs the shift operation only on upper and lower case alphabets and retains the other characters (such as space as-is).
  • The Caesar cipher is not secure as per current standards.
  • Below example is for illustrative purposes only !
  • Reference: https://en.wikipedia.org/wiki/Caesar_cipher
package com.example.so.cipher;

/**
 * Implementation of the Caesar cipher.
 * <p>
 * <ul>
 * <li>This implementation performs the shift operation only on upper and lower
 * case alphabets and retains the other characters (such as space as-is).</li>
 * <li>The Caesar cipher is not secure as per current standards.</li>
 * <li>Below example is for illustrative purposes only !</li>
 * <li>Reference: https://en.wikipedia.org/wiki/Caesar_cipher</li>
 * </ul>
 * </p>
 * 
 * @author Ravindra HV
 * @author Maarten Bodewes (beautification only)
 * @since 2016-11-21
 * @version 0.3
 *
 */
public class CaesarCipher {

    public static final char START_LOWER_CASE_ALPHABET = 'a'; // ASCII-97
    public static final char END_LOWER_CASE_ALPHABET = 'z';   // ASCII-122

    public static final char START_UPPER_CASE_ALPHABET = 'A'; // ASCII-65
    public static final char END_UPPER_CASE_ALPHABET = 'Z';   // ASCII-90
    
    public static final int ALPHABET_SIZE = 'Z' - 'A' + 1;    // 26 of course

    /**
     * Performs a single encrypt followed by a single decrypt of the Caesar
     * cipher, prints out the intermediate values and finally validates
     * that the decrypted plaintext is identical to the original plaintext.
     * 
     * <p>
     * This method outputs the following:
     * 
     * <pre>
     * Plaintext  : The quick brown fox jumps over the lazy dog
     * Ciphertext : Qeb nrfzh yoltk clu grjmp lsbo qeb ixwv ald
     * Decrypted  : The quick brown fox jumps over the lazy dog
     * Successful decryption: true
     * </pre>
     * </p>
     * 
     * @param args (ignored)
     */
    public static void main(String[] args) {

        int shift = 23;
        String plainText = "The quick brown fox jumps over the lazy dog";
        
        System.out.println("Plaintext  : " + plainText);
 
        String ciphertext = caesarCipherEncrypt(plainText, shift);
        System.out.println("Ciphertext : " + ciphertext);
        
        String decrypted = caesarCipherDecrypt(ciphertext, shift);
        System.out.println("Decrypted  : " + decrypted);
        System.out.println("Successful decryption: "
                + decrypted.equals(plainText));
    }

    public static String caesarCipherEncrypt(String plaintext, int shift) {
        return caesarCipher(plaintext, shift, true);
    }

    public static String caesarCipherDecrypt(String ciphertext, int shift) {
        return caesarCipher(ciphertext, shift, false);
    }

    private static String caesarCipher(
            String input, int shift, boolean encrypt) {

        // create an output buffer of the same size as the input
        StringBuilder output = new StringBuilder(input.length());

        for (int i = 0; i < input.length(); i++) {
            
            // get the next character
            char inputChar = input.charAt(i);
            
            // calculate the shift depending on whether to encrypt or decrypt
            int calculatedShift = (encrypt) ? shift : (ALPHABET_SIZE - shift);

            char startOfAlphabet;
            if ((inputChar >= START_LOWER_CASE_ALPHABET)
                    && (inputChar <= END_LOWER_CASE_ALPHABET)) {
                
                // process lower case
                startOfAlphabet = START_LOWER_CASE_ALPHABET;
            } else if ((inputChar >= START_UPPER_CASE_ALPHABET)
                    && (inputChar <= END_UPPER_CASE_ALPHABET)) {
                
                // process upper case
                startOfAlphabet = START_UPPER_CASE_ALPHABET;
            } else {
                
                // retain all other characters
                output.append(inputChar);
                
                // and continue with the next character
                continue;
            }                
                
            // index the input character in the alphabet with 0 as base
            int inputCharIndex =
                    inputChar - startOfAlphabet;

            // cipher / decipher operation (rotation uses remainder operation)
            int outputCharIndex =
                    (inputCharIndex + calculatedShift) % ALPHABET_SIZE;

            // convert the new index in the alphabet to an output character
            char outputChar =
                    (char) (outputCharIndex + startOfAlphabet);

            // add character to temporary-storage
            output.append(outputChar);
        }

        return output.toString();
    }
}

Program Output:

Plaintext  : The quick brown fox jumps over the lazy dog
Ciphertext : Qeb nrfzh yoltk clu grjmp lsbo qeb ixwv ald
Decrypted  : The quick brown fox jumps over the lazy dog
Successful decryption: true

Python implementation

The following code example implements the Caesar cipher and shows the properties of the cipher.

It handles both uppercase and lowercase alpha-numerical characters, leaving all other characters as they were.

The following properties of the Caesar cipher are shown:

  • weak keys;
  • low key space;
  • the fact that each key has a reciprocal (inverse) key;
  • the relation with ROT13;

it also shows the following - more generic - cryptographic notions:

  • weak keys;
  • the difference between obfuscation (without a key) and encryption;
  • brute forcing a key;
  • the missing integrity of the ciphertext.
def caesarEncrypt(plaintext, shift):
    return caesarCipher(True, plaintext, shift)

def caesarDecrypt(ciphertext, shift):
    return caesarCipher(False, ciphertext, shift)

def caesarCipher(encrypt, text, shift):
    if not shift in range(0, 25):
        raise Exception('Key value out of range')

    output = ""
    for c in text:
        # only encrypt alphanumerical characters
        if c.isalpha():
            # we want to shift both upper- and lowercase characters
            ci = ord('A') if c.isupper() else ord('a')
            
            # if not encrypting, we're decrypting
            if encrypt:
                output += caesarEncryptCharacter(c, ci, shift)
            else:
                output += caesarDecryptCharacter(c, ci, shift)
        else:
            # leave other characters such as digits and spaces
            output += c
    return output

def caesarEncryptCharacter(plaintextCharacter, positionOfAlphabet, shift):
    # convert character to the (zero-based) index in the alphabet
    n = ord(plaintextCharacter) - positionOfAlphabet
    # perform the >positive< modular shift operation on the index
    # this always returns a value within the range [0, 25]
    # (note that 26 is the size of the western alphabet)
    x = (n + shift) % 26 # <- the magic happens here
    # convert the index back into a character
    ctc = chr(x + positionOfAlphabet)
    # return the result
    return ctc

def caesarDecryptCharacter(plaintextCharacter, positionOfAlphabet, shift):
    # convert character to the (zero-based) index in the alphabet 
    n = ord(plaintextCharacter) - positionOfAlphabet
    # perform the >negative< modular shift operation on the index
    x = (n - shift) % 26
    # convert the index back into a character
    ctc = chr(x + positionOfAlphabet)
    # return the result
    return ctc

def encryptDecrypt(): 
    print '--- Run normal encryption / decryption'
    plaintext = 'Hello world!'
    key = 3 # the original value for the Caesar cipher
    ciphertext = caesarEncrypt(plaintext, key)
    print ciphertext
    decryptedPlaintext = caesarDecrypt(ciphertext, key)
    print decryptedPlaintext
encryptDecrypt()

print '=== Now lets show some cryptographic properties of the Caesar cipher'

def withWeakKey():
    print '--- Encrypting plaintext with a weak key is not a good idea'
    plaintext = 'Hello world!'
    # This is the weakest key of all, it does nothing
    weakKey = 0
    ciphertext = caesarEncrypt(plaintext, weakKey)
    print ciphertext # just prints out the plaintext
withWeakKey();
    
def withoutDecrypt():
    print '--- Do we actually need caesarDecrypt at all?'
    plaintext = 'Hello world!'
    key = 3 # the original value for the Caesar cipher
    ciphertext = caesarEncrypt(plaintext, key)
    print ciphertext
    decryptionKey = 26 - key; # reciprocal value
    decryptedPlaintext = caesarEncrypt(ciphertext, decryptionKey)
    print decryptedPlaintext # performed decryption
withoutDecrypt()
    

def punnify():
    print '--- ROT 13 is the Caesar cipher with a given, reciprocal, weak key: 13'
    # The key is weak because double encryption will return the plaintext
    def rot13(pun):
        return caesarEncrypt(pun, 13)

    print 'Q: How many marketing people does it take to change a light bulb?' 
    obfuscated = 'N: V jvyy unir gb trg onpx gb lbh ba gung.'
    print obfuscated
    deobfuscated = rot13(obfuscated)
    print deobfuscated
    # We should not leak the pun, right? Lets obfuscate afterwards!
    obfuscatedAgain = rot13(deobfuscated)
    print obfuscatedAgain
punnify()

def bruteForceAndLength():
    print '--- Brute forcing is very easy as there are only 25 keys in the range [1..25]'
    # Note that AES-128 has 340,282,366,920,938,463,463,374,607,431,768,211,456 keys
    # and is therefore impossible to bruteforce (if the key is correctly generated)
    key = 10;
    plaintextToFind = 'Hello Maarten!'
    ciphertextToBruteForce = caesarEncrypt(plaintextToFind, key)
    for candidateKey in range(1, 25):
        bruteForcedPlaintext = caesarDecrypt(ciphertextToBruteForce, candidateKey)
        # lets assume the adversary knows 'Hello', but not the name
        if bruteForcedPlaintext.startswith('Hello'):
            print 'key value: ' + str(candidateKey) + ' gives : ' + bruteForcedPlaintext

    print '--- Length of plaintext usually not hidden'
    # Side channel attacks on ciphertext lengths are commonplace! Beware!
    if len(ciphertextToBruteForce) != len('Hello Stefan!'):
        print 'The name is not Stefan (but could be Stephan)'
bruteForceAndLength()

def manInTheMiddle():
    print '--- Ciphers are vulnerable to man-in-the-middle attacks'
    # Hint: do not directly use a cipher for transport security
    moneyTransfer = 'Give Maarten one euro'
    key = 1
    print moneyTransfer
    encryptedMoneyTransfer = caesarEncrypt(moneyTransfer, key)
    print encryptedMoneyTransfer
    # Man in the middle replaces third word with educated guess
    # (or tries different ciphertexts until success)
    encryptedMoneyTransferWords  = encryptedMoneyTransfer.split(' ');
    encryptedMoneyTransferWords[2] = 'ufo' # unidentified financial object
    modifiedEncryptedMoneyTransfer = ' '.join(encryptedMoneyTransferWords)
    print modifiedEncryptedMoneyTransfer
    decryptedMoneyTransfer = caesarDecrypt(modifiedEncryptedMoneyTransfer, key)
    print decryptedMoneyTransfer
manInTheMiddle()
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