Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7Lesson 3 -
Improved 2-Letter Shift Encoding Program For Words Up To 8 Letters
Long
Note: To use the Javascript programs
in these lessons, you will need to use a
FireFox browser or other non-Internet Explorer browser due to the
"feature" in the IE browser
disallowing Javascript prompts.
Introduction
To understand the basics of how this encoding program works, you
should first read through the
Simple 2-Letter Shift Encoding Program page and also try out the
Simple Letter Shift Code Creator
and read through the documentation on the Code Creator page.
The Problem With The Old Formula
In the simple 2-Letter Shift, each letter was assigned a number and
then the number was increased by 2. The new number was then
reassigned back to a letter. Basically, the equivalent of the
function y = x + 2 was used. The problem with this formula was that
the letters Y and Z were assigned the values 25 and 26, which were
then increased to 27 and 28. 27 and 28 could not be reassigned
to any letter. In essence, our function y = x + 2 did not have
an inverse for all x-values. When this is the case we say the
function is not one-to-one.
A New Formula That Provides a Solution!
Instead of simply adding 2, we need to add 2 and then apply modular
arithmetic. In modular arithmetic, you divide by the modular base and
the remainder after dividing is your answer. We use modular
arithmetic in base 12 nearly every day. For example, if it is
10:00 now, in 4 hours it will be 2:00. To get 2:00, we are adding 4 to
10 to get 14 and then using the modular base of 12 to get 2 since 14
÷ 12 has a remainder of 2. We would writhe
this as
2 = (10 + 4)(mod 12)
In our coding example we use the new formula
y = (X+2) (mod 26)
This means that when we increase "Z" by 2, it's numerical
equivalent does not become 28, but rather the remainder of the
division 28 ÷ 26, which is 2.
Modular Arithmetic and Abstract Algebra
Modular arithmetic is something covered in great depth in Abstract
Algebra, a generalized math course taken mostly by math majors and
graduate students at the college level. Also, the concept of
one-to-one is studied in depth in an Abstract Algebra course as
well.
Can You See Why This Code Would Be Easy to "Break"
This coding scheme is very easy to break. Try out
this code generator and find
why.
GO TO LESSON 4
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