The why that you have it coded, it will only store a new value other than zero is if the encrypted string has a 'H' and only way to get a 'H' is to have a 'A' in the encrypting string. Now if 'A' is the first char in the string the deque will store the value 0 which looks no different than the other 0 values created by the deque<int>a_deque(ilength); statement.
I got this using the input string "This is A test" notice that 'A' is not at the beginning and 8 shows up in the output at the first position as coded using the a_deque.push_front(i);
$ ./a.out
Write a word to encrypt: This is A test
Test: Bhis is H test
0
1
2
3
4
5
6
7
Pushing(8)
8
9
10
11
12
13
Place: 0 Number: 8 <--- Place is 0 in the deque and 8 is the position in the input string.
Place: 1 Number: 0
Place: 2 Number: 0
Place: 3 Number: 0
Place: 4 Number: 0
Place: 5 Number: 0
Place: 6 Number: 0
Place: 7 Number: 0
Place: 8 Number: 0
Place: 9 Number: 0
Place: 10 Number: 0
Place: 11 Number: 0
Place: 12 Number: 0
Place: 13 Number: 0
Place: 14 Number: 0