#7123: cryptanalysis of the shift cipher
----------------------------+-----------------------------------------------
Reporter: mvngu | Owner: somebody
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.1.3
Component: cryptography | Keywords:
Work_issues: | Author: Minh Van Nguyen
Reviewer: | Merged:
----------------------------+-----------------------------------------------
Comment(by rbeezer):
Hi Minh,
Finally have a chance to comment carefully on the various ways to measure
the distributions.
1. For a chi-square used for goodness-of-fit between distributions see
Hogg and Tannis, Probbilit and Stastical Inference, 6th Ed., Section 8.4.
Use the actual counts of each letter in a candidate decipher and call
these "observed." Then multiply frequences from
{{{frequency_distribution()}}} times the length of the message. Call
these theoretical counts the "expected" and carry them as non-integers,
even if we know they should be integral. Then the statistic is the sum
over all the letters of
{{{(observed - expected)^2/expected}}}
I would use the keyword "chisquare" for this.
2. The sum of squared differences should probably be computed as the sum
over all letters using counts, not frequencies, ie
{{{(observed - expected)^2}}}
This is equivalent in this case to the coefficient of determination, or
more informally "r-squared." Another name is "residual sum of squares."
3. Not at all clear to me how [SavHar99] justifies the use of their
expression and naming it a chi-square statistic. If anything, it looks to
me like a noncentral chisquare statistic. But it may do a good job of
"scoring" candidate decipherments. Can you be sure if they mean to square
just the numerator of each term ({{{FD^2/CD}}}), or square the whole
fraction ({{{FD/CF}}})?
Rob
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7123#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
