substitution cryptosystems: converting a key from alphabetic to numerical values

[sagetrac-mvngu]

The class SubstitutionCryptosystem accepts keys whose values are alphabetic characters. We should implement a method to allow a key
to be converted between alphabetic characters and numerical values. For example, here is what I have in mind:

sage: A = AlphabeticStrings()
sage: S = SubstitutionCryptosystem(A)
sage: key = S.random_key()
ABC
sage: S.alphabet_to_numbers(key)
012
sage: S.numbers_to_alphabet([0, 1, 2])
ABC

Generalizing from this, we can also have methods to do the following conversions:

• from alphabetic characters to binary values and vice versa

• from alphabetic characters to hexadecimal values and vice versa

• from alphabetic characters to mod 26 values and vice versa

• from alphabetic characters to ASCII values and vice versa

Component: cryptography

Keywords: substitution cryptosystem

Reviewer: Travis Scholl

Issue created by migration from https://trac.sagemath.org/ticket/6565

[tscholl2]

comment:6

I think it would be better to add some kind of conversion/coercion for string monoids instead of specifically for substitution cryptosystem strings. Also I don't believe there is an ASCII/byte value monoid. In either case, that would be a different ticket (see #9118). If someone still wants that they should open a new ticket.

This is also pretty easy to do by hand if someone wants to. For example, to take and element from an alphabetic monoid to a list of ascii values you can use this:

    sage: A = AlphabeticStrings()
    sage: a = A.encoding("THISISATURTLE")
    sage: map(lambda x: ord(str(x)),a)
    [84, 72, 73, 83, 73, 83, 65, 84, 85, 82, 84, 76, 69]

I'm going to set this as won't fix and give it positive review.

[tscholl2]

Reviewer: Travis Scholl