4.1 Recap - Where are we, and where are we going?

The previous section ended with the following key observations:

• We say that the original frequencies of plaintext are unscrambled.
• Enciphering rearranges, or scrambles, frequencies.
• Deciphering restores the original arrangement of, or unscrambles, frequencies.

We can restate the last observation as, if ciphertext is deciphered, then frequencies will be ``unscrambled'', i.e. frequencies will be restored to the original positions they had for plaintext. Three questions now arise:

1.

Can we turn that if-then statement around? That is, does unscrambling ciphertext frequencies suffice to decipher ciphertext?

2.

If so, given that we don't know the plaintext, how do we recognize/identify that a table of frequencies is unscrambled?

3.

When we rearrange frequencies to unscramble them, what kinds of rearrangements are both legal and effective?

To answer these questions, we need to know more about frequencies of actual plaintexts and to study the effects of encryption on frequencies. To help you keep track of things, we will periodically summarize where we are and where we are going with a Roadmap.

Roadmap
Section 3.7	Encipher plaintext $\Rightarrow$ scramble frequencies.
Section 3.7	Decipher ciphertext $\Rightarrow$ unscramble frequencies.
$\rightarrow$     Section 4.2	Q: Does ``unscramble ciphertext frequencies'' suffice to ``decipher ciphertext''?
Section 4.3	Q: How do we recognize that a table of frequencies is unscrambled?
Section 5	Q: What are legal and effective ways to rearrange frequencies?