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jdege
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I'd be happy to answer questions, to the extent I can, but I'm not quite sure where to start.

Do you understand what we mean by "alphabet" when we talk about polyalphabetic substitution?

A substitution cipher is one in which chunks of the plaintext are replaced by different chunks to form the ciphertext. Most commonly, the chunks are individual letters. These are what we call monoliteral ciphers. In other ciphers, the chunks can be pairs of letters, or larger groups of letters, or individual bits. Playfair is a multiliteral cipher, operating on pairs of letters. So is the Hill cipher, which operates on pairs of letters when using a 2x2 matrix, triplets when using a 3x3 matrix, etc. Modern computer stream ciphers operate on individual bits, modern computer block ciphers operate on blocks of 64, 128, or 256 bits.

But most ciphers, throughout history, have been monoliteral, operating on individual letters, as have those that you have offered us, so we'll focus on them.

In a simple substitution cipher, there are two alphabets, The plaintext alphabet and the ciphertext alphabet. The plaintext alphabet is the ordinary, standard alphabet that you use to write the message. The ciphertext alphabet is something else. It may involve unique symbols, it may simply be the letters of the standard alphabet in a different order. It doesn't much matter. What matters is that there is a one-to-one correspondence between each letter of the plaintext alphabet and the ciphertext alphabet.

So, when you transform a plaintext to a ciphertext by replacing every letter in the plaintext with its corresponding letter from the ciphertext alphabet you're doing a simple substitution cipher.

Simple substitution ciphers aren't terribly secure. Newspapers print them in their comics sections, alongside the crossword puzzles, as a form of recreation. There are statistical clues about the plaintext that leak through simple substitution ciphers that make them very easy to break.

What you need to understand is that piling substitution on top of substitution doesn't increase security at all. Applying a substitution cipher to the output of a previous substitution cipher just gives you a different substitution cipher.

When you encode A as 01, B as 02, C as 03, etc., you're doing a substitution. When you go through again, substitution 10 for 01, 20 for 02, 30 for 03, etc., you're doing another substitution. It's exactly the same as if you'd done A as 10, B as 20, C as 30, etc., in the first place. Adding more of these sorts of transformations, no matter how many of them you add, don't do anything at all towards making the cipher more secure.

Do you understand this?
When cryptography is outlawed, bayl bhgynjf jvyy unir cevinpl.
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