"""
Module with useful functions to experiment with public key cryptography.
To use in sage, apply the load() function.
"""

def to_number(message):
    """
    Maps the lower case letters from 'a' to 'z'
    to the numbers 1 to 26, the space is mapped to 0.
    With this map, the message gets converted to 
    one big number, and the number is returned.
    """
    alphabet = [chr(k) for k in range(ord('a'), ord('z')+1)]
    alphabet.insert(0, ' ')
    numbvals = [n for n in range(0, 27)]
    items = [t for t in zip(alphabet, numbvals)]
    str2num = dict(items)
    vals = [str2num[c] for c in message]
    return ZZ(list(reversed(vals)), base=100)

def to_string(number):
    """
    Given a positive number, returns the corresponding
    string of characters, inverting the to_number:
    to_string(to_number(message)) == message.
    """
    alphabet = [chr(k) for k in range(ord('a'), ord('z')+1)]
    alphabet.insert(0, ' ')
    numbvals = [n for n in range(0, 27)]
    items = [t for t in zip(numbvals, alphabet)]
    num2str = dict(items)
    vals = ZZ(number).digits(base=100)
    # letters = [num2str[x] for x in vals]
    letters = []
    for val in vals:
        try:
            letters.append(num2str[val])
        except KeyError:
            letters.append('?')
    letters.reverse()
    return ''.join(letters)

def modexp(message, expkey, modkey):
    """
    Applies modular exponentiation on the numerical message,
    using exponent expkey modulo the modkey.
    """
    result = 0
    wrk = message
    shift = 1
    while wrk > 0:
        rest = wrk % modkey
        result = power_mod(rest, expkey, modkey)*shift + result
        wrk = (wrk - rest)/modkey
        shift = shift*modkey
    return result