I'd like to get opinions on the following from the experts -- I am in
the process
of preparing for a cryptography course, for which I've previously used
a Magma
package that I wrote and would like to use SAGE.
Python has some special octal ('\ooo') and hexadecimal ('\xhh') string
constructors, e.g. one can see hexadecimals in action here in SAGE:
import Crypto
for i in range(256):
x = Crypto.Util.number.long_to_bytes(i)
print "%s: %s %s [%s]" % (i, repr(x), x, len(x))
Note that repr(x) uses hexadecimal printing for strings in some, but
not all,
ranges of the ASCII alphabet.
Thus Python strings represent the monoid \union_n {0,..,255}^n, with
special
constructors for the subsets of octals in \union_n {0,..7} and
hexadecimals in
\union_n {0,..,15}^n.
What would you think of having SAGE classes for binary, octal,
hexadecimal,
radix64 (used by GPG) and other string monoids, which are not Python
strings?
Advantages: differentiated printing, clear morphisms, efficient
embeddings
(i.e. length n binary strings can use n + O(log(n)) rather than 256n
bits),
and more general string monoids (like with alphabets {"AA",..,"ZZ"}).
Disadvantages: performance and introduction of non-standard Python
classes.
The alternative is to always embedd cryptographic strings in Python
strings.
In Magma I did create a Hackobj cryptographic string type (CryptTxt)
for
exclusive use with my cryptography package.
V := VigenereCryptosystem(8);
M := Encoding(V,"ABCDEFGH");
ABCDEFGH
Type(M);
CryptTxt
This was meant to overcome certain disadvantages with Magma strings,
give verifiable type-checking, etc.
What do you think of such classes in SAGE would be merited?
Is there possibly any existing string library which provides similar
features?
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