encryption - Got stuck with Caesar.c -

i trying run program assignment caesar.c edx introduction programming. requires program able encrypt string caesar encryption: therefore, user has enter key (command-line); example key of 2 'a' character needs encrypted in 'c' character; problem starts when have enter key greater 26, number of alphabetical letters. key of 27 , 'a' character example, program must return 'b' key of 1.

i have tried transform ascii values of characters alphabetical values 0 26 in order use modulus operator when key equal or greater 26. returns me segmentation fault. can me suggestions of causes of error?

here's program:

#include <stdio.h> #include <cs50.h> #include <stdlib.h> #include <string.h> #include <ctype.h>  int key;  // function alphabetic value non capital letters  int alpha_low( char c ) {     int alpha_value;     alpha_value = (int) c - 97;     return alpha_value + ( key % 26 ); }  // function return ascii valuee non capital letters  char ascii_low( char c ) {     return (char) alpha_low( c ) + 97; }  // function alphabetic value capital letters  int alpha_up( char c ) {     int alpha_value;     alpha_value = (int) c - 65;     return alpha_value + ( key % 26 ); }  // function return ascii value capital letters  char ascii_up( char c ) {     return (char) alpha_up( c ) + 65; }   int main(int argc, string argv[]) {         int result;         string p;         key = atoi( argv[1] );      if( argc != 2 || key < 0 )     {        printf("usage: ./caesar key(positive integer)\n");        return 1;     }      printf("please, write plaintext: ");     p = getstring();      for( int = 0, n = strlen(p); < n; i++)     {        if ( isalpha(p[i]) )        {           if ( islower(p[i]) )           {              result = alpha_low( p[i] );              printf("%c", ascii_low( p[i] ));           }           else if( islower( p[i]) )           {               result = alpha_up( p[i] );               printf("%c", ascii_up( p[i]) );           }         }       }            return 0; }  

a function caesar alphabetic char should (decomposed in elementary steps):

int caesar_lower(int c,int key) {     int v = c-'a'; // translate 'a'--'z' 0--25     v = v+key;     // translate 0--25 key--key+25     v = v%26;      // translate key--key+25 key--25,0--key-1     v = v+'a';     // translate 0--25 'a'--'z'     return v; }