How to decode and what is the use?(Math!)

"No. The special feature about the one-time pad is that you use a key length equivalent to the length of the message (or even longer, but that wouldn't change the outcome). This is what sets apart "digits of pi" (it is, for practical purposes, a key of infinite length) from other polyalphabetical ciphers.

And further - i know i am wrong, as you have already pointed out, but i'd like to stick to my erroneous beliefs - the weakness of every polyalphabetic cipher is that the relationship between unencoded and encoded signs is 1:1. That means if you encode one character the result will always be one (other) character (or, as @Otienimous correctly mentioned in #35: the length of the message is preserved)."

This is generally, not true. We are using very simple examples in the thread to make the posts readable by others, but the reality is far from being that simple.
We may add extra spaces and other symbols in the encoded message which don't matter for its decryption, although some extra work is required.

#39 "Actually, you should publish a semi-prime number (such that is a product of two primes)."
Yes, thank you for pointing out this error.

Re #40 post @krasnaya "No. The special feature about the one-time pad is that you use a key length equivalent to the length of the message (or even longer, but that wouldn't change the outcome). This is what sets apart "digits of pi" (it is, for practical purposes, a key of infinite length) from other polyalphabetical ciphers. And further - i know i am wrong, as you have already pointed out, but i'd like to stick to my erroneous beliefs - the weakness of every polyalphabetic cipher is that the relationship between unencoded and encoded signs is 1:1. That means if you encode one character the result will always be one (other) character (or, as @Otienimous correctly mentioned in #35: the length of the message is preserved)." This is generally, not true. We are using very simple examples in the thread to make the posts readable by others, but the reality is far from being that simple. We may add extra spaces and other symbols in the encoded message which don't matter for its decryption, although some extra work is required. #39 "Actually, you should publish a semi-prime number (such that is a product of two primes)." Yes, thank you for pointing out this error.

krasnaya

#42

@tromeus said (#41):

We may add extra spaces and other symbols in the encoded message
which don't matter for its decryption, although some extra work is required.

You can do that, but then it would not be a "polyalphabetic cipher" any more - at least, it wouldn't be only that. Of course you can use several encryption methods on top of one another, but that still doesn't take away from any one of them having certain characteristics. And the alphabetic cipher (monoalphabetical being just a polyalphabetical one with a keyword length of 1) has the weakness that it encodes any letter with a - small number of - other letters.

A monoalphabetical chiffre (i.e. rot13) transforms a given letter to exactly one other letter. A polyalphabetical chiffre transforms a given letter to one of X other letters, where X is the length of the "keyword" you use. The keyword "monkey" basically means that a sequence of "aaaaaa" is transformed to "monkey" by it, so you use rot13, rot15, rot14, rot11, rot5 and rot25 on subsequent characters and then start over again. But the letter "a" will always be transformed to one of "e", "k", "m", "n", "o" or "y", nothing else. So, while making decryption more complicated, it still doesn't make it impossible. Especially, because the message, if it is much longer than the keyword, has the keyword (or, rather, the pattern of various monoalphabetic encryptions) being repeated over and over again.

Now, if you use an "infinitely long keyword" - like the digits of pi - you have no such repeating pattern and therefore decryption is again made more difficult. And this - using an infinitely long key - is what sets apart a one-time pad from a simple polyalphabetic encryption. The practical problem for one-time pads is that you need to transport the key the same way you need to transport the message and if the message can be intercepted so can the key.

krasnaya

@tromeus said (#41): > We may add extra spaces and other symbols in the encoded message > which don't matter for its decryption, although some extra work is required. You can do that, but then it would not be a "polyalphabetic cipher" any more - at least, it wouldn't be *only* that. Of course you can use several encryption methods on top of one another, but that still doesn't take away from any one of them having certain characteristics. And the alphabetic cipher (monoalphabetical being just a polyalphabetical one with a keyword length of 1) has the weakness that it encodes any letter with a - small number of - other letters. A monoalphabetical chiffre (i.e. rot13) transforms a given letter to exactly one other letter. A polyalphabetical chiffre transforms a given letter to one of X other letters, where X is the length of the "keyword" you use. The keyword "monkey" basically means that a sequence of "aaaaaa" is transformed to "monkey" by it, so you use rot13, rot15, rot14, rot11, rot5 and rot25 on subsequent characters and then start over again. But the letter "a" will always be transformed to one of "e", "k", "m", "n", "o" or "y", nothing else. So, while making decryption more complicated, it still doesn't make it impossible. Especially, because the message, if it is much longer than the keyword, has the keyword (or, rather, the pattern of various monoalphabetic encryptions) being repeated over and over again. Now, if you use an "infinitely long keyword" - like the digits of pi - you have no such repeating pattern and therefore decryption is again made more difficult. And this - using an infinitely long key - is what sets apart a one-time pad from a simple polyalphabetic encryption. The practical problem for one-time pads is that you need to transport the key the same way you need to transport the message and if the message can be intercepted so can the key. krasnaya

tromeus

#43

@krasnaya

Quite much as I value your posts in other topics like music or philosophy, I believe that you need to broaden your knowledge in cryptography before you answer any more posts here...

Now everything, that you are saying in #42 post is wrong. For example what do you mean by: "A polyalphabetical chiffre transforms a given letter to one of X other letters, where X is the length of the "keyword" you use."
A polyalphabetical chiffre transfoms a given letter to anyone of the fixed letters of the alphabet you're using.

In the next paragraph below this you're stating that "But the letter "a" will always be transformed to one of "e", "k", "m", "n", "o" or "y", nothing else."
Absolutely not! As the running key continues the encoding key will not be "NLMPVBH" anymore but something else like "VITAMIN" or "DGFGGUU", so you will not be encoding the word MONKEYS as AAAAAAA anymore. Any future occurence of the letter A in the message you're sending will depend on the letter it encounters in the running key code to be translated to. So certainly, it won't be one of "e", "k", "m", "n", "o" or "y", at all! All the letters of the alphabet are potential candidates for this.

And most definitely, absolutely nowhere you're using "an "infinitely long keyword" - like the digits of pi" or infinitely long key."
You're just using some sequence of consecutive Pi digits which has a beginning and an end.

Now, I am surprised where you're picking this information from.

@krasnaya Quite much as I value your posts in other topics like music or philosophy, I believe that you need to broaden your knowledge in cryptography before you answer any more posts here... Now everything, that you are saying in #42 post is wrong. For example what do you mean by: "A polyalphabetical chiffre transforms a given letter to one of X other letters, where X is the length of the "keyword" you use." A polyalphabetical chiffre transfoms a given letter to anyone of the fixed letters of the alphabet you're using. In the next paragraph below this you're stating that "But the letter "a" will always be transformed to one of "e", "k", "m", "n", "o" or "y", nothing else." Absolutely not! As the running key continues the encoding key will not be "NLMPVBH" anymore but something else like "VITAMIN" or "DGFGGUU", so you will not be encoding the word MONKEYS as AAAAAAA anymore. Any future occurence of the letter A in the message you're sending will depend on the letter it encounters in the running key code to be translated to. So certainly, it won't be one of "e", "k", "m", "n", "o" or "y", at all! All the letters of the alphabet are potential candidates for this. And most definitely, absolutely nowhere you're using "an "infinitely long keyword" - like the digits of pi" or infinitely long key." You're just using some sequence of consecutive Pi digits which has a beginning and an end. Now, I am surprised where you're picking this information from.

Otienimous

#44

I'm sorry, but because of other occupations I won't be able to participate in this fascinating discussion anymore. In fact, there is every chance I won't even log into Lichess for the next two weeks or something like that. Thank you very much, it was a pleasure!

deweyduck edited

#45

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BossOfBosses

#46

Most the posts are long, did anyone notice....?

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