Caesar cipher (shift cipher) is a simple substitution cipher based on a replacement of every single character of the open text with a character, which is fixed number of positions further down the alphabet.
In the times of Julius Caesar was used only the shift of 3 characters, but nowadays the term Caesar cipher refers to all variants (shifts) of this cryptosystem.
The encryption can be described with the following formula:
Ti - i-th character of the open text
k - shift
m - length of the alphabet
The process of decryption uses reverted procedure:
Example
Encryption
Open text: "attackatdawn", shift: 3
a + 3 = 0 + 3 = 3 = d t + 3 = 19 + 3 = 22 = w t + 3 = 19 + 3 = 22 = w a + 3 = 0 + 3 = 3 = d c + 3 = 2 + 3 = 5 = f k + 3 = 10 + 3 = 13 = n a + 3 = 0 + 3 = 3 = d t + 3 = 19 + 3 = 22 = w d + 3 = 3 + 3 = 6 = g a + 3 = 0 + 3 = 3 = d w + 3 = 22 + 3 = 25 = z n + 3 = 13 + 3 = 16 = q
Closed text: "dwwdfndwgdzq"
Decryption
Closed text: "dwwdfndwgdzq", shift: 3
d - 3 = 3 - 3 = 0 = a w - 3 = 22 - 3 = 19 = t w - 3 = 22 - 3 = 19 = t d - 3 = 3 - 3 = 0 = a f - 3 = 5 - 3 = 2 = c n - 3 = 13 - 3 = 10 = k d - 3 = 3 - 3 = 0 = a w - 3 = 22 - 3 = 19 = t g - 3 = 6 - 3 = 3 = d d - 3 = 3 - 3 = 0 = a z - 3 = 25 - 3 = 22 = w q - 3 = 16 - 3 = 13 = n
Open text: "attackatdawn"
Breaking the cipher
All variants
Because the number of variants of the cipher is very limited (number of characters in the alphabet), it is possible to try all of them and choose the one, where the deciphered text makes sense.
Frequency analysis
If we know in which language was the open text written, we also know, how often (percentually) are used different characters in this language. So if we calculate the frequency of characters of the encrypted text, it should be shifted in comparison to the language frequency by fixed number of characters. With the knowledge of the shift, we can decipher the closed text.
Code
/**
* Caesar cipher
* @author Pavel Micka
*/
public class CaesarCipher {
/**
* Shift (the original variant had 3)
*/
public static final int SHIFT = 3;
/**
* Encrypt using Caesar cipher
* @param s string containing only uppercase characters
* @return ecrypted string (closed text)
*/
public static String encipher(String s){
StringBuilder builder = new StringBuilder();
for(int i = 0; i < s.length(); i ++){
if(s.charAt(i) < 65 || s.charAt(i) > 90){ //znak v ASCII
throw new IllegalArgumentException("" +
"The string does not contain only uppercase characters");
}
//modularly add the shift
char enciphered = s.charAt(i) + SHIFT > 90 ? (char)((s.charAt(i) + SHIFT) - 26) : (char)(s.charAt(i) + SHIFT);
builder.append(enciphered);
}
return builder.toString();
}
/**
* Decrypt using Caesar cipher
* @param s string containing only uppercase characters
* @return decrypted string (open text)
*/
public static String decipher(String s){
StringBuilder builder = new StringBuilder();
for(int i = 0; i < s.length(); i ++){
if(s.charAt(i) < 65 || s.charAt(i) > 90){ //znak v ASCII
throw new IllegalArgumentException("" +
"The string does not contain only uppercase characters");
}
//modularly subtract the shift
char deciphered = s.charAt(i) - SHIFT < 65 ? (char)((s.charAt(i) - SHIFT) + 26) : (char)(s.charAt(i) - SHIFT);
builder.append(deciphered);
}
return builder.toString();
}
}