Java, How to implement a Shift Cipher (Caesar Cipher)

Java Shift Caesar Cipher by shift spaces.

Restrictions:

1. Only works with a positive number in the shift parameter.
2. Only works with shift less than 26.
3. Does a += which will bog the computer down for bodies of text longer than a few thousand characters.
4. Does a cast number to character, so it will fail with anything but ascii letters.
5. Only tolerates letters a through z. Cannot handle spaces, numbers, symbols or unicode.
6. Code violates the DRY (don’t repeat yourself) principle by repeating the calculation more than it has to.

Pseudocode:

1. Loop through each character in the string.
2. Add shift to the character and if it falls off the end of the alphabet then subtract shift from the number of letters in the alphabet (26)
3. If the shift does not make the character fall off the end of the alphabet, then add the shift to the character.
4. Append the character onto a new string. Return the string.

Function:

String cipher(String msg, int shift){
    String s = "";
    int len = msg.length();
    for(int x = 0; x < len; x++){
        char c = (char)(msg.charAt(x) + shift);
        if (c > 'z')
            s += (char)(msg.charAt(x) - (26-shift));
        else
            s += (char)(msg.charAt(x) + shift);
    }
    return s;
}

How to invoke it:

System.out.println(cipher("abc", 3));  //prints def
System.out.println(cipher("xyz", 3));  //prints abc