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 Post subject: Not understanding Public Key Encryption...
PostPosted: Wed Jun 30, 2004 11:17 am 
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Not that this is really specific to windows, but i figured someone would have a more comprehensive explanation. I see how it works... Public key paired with Private key, so that all can Encrypt but only some can decryt, but how is that possible!?

If you have a public key that follows a given algorithm to convert from plaintext to ciphertext, why can't you just reverse engineer the key to get back to plaintext... What am i not seeing? It just seems like you would do the antialgorithm given to you in the public key to be able to decrypt.

All explanations are appreciated. :)


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 Post subject: Re: Not understanding Public Key Encryption...
PostPosted: Wed Jun 30, 2004 11:49 am 
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virtualchaos wrote:
Not that this is really specific to windows, but i figured someone would have a more comprehensive explanation. I see how it works... Public key paired with Private key, so that all can Encrypt but only some can decryt, but how is that possible!?

If you have a public key that follows a given algorithm to convert from plaintext to ciphertext, why can't you just reverse engineer the key to get back to plaintext... What am i not seeing? It just seems like you would do the antialgorithm given to you in the public key to be able to decrypt.

All explanations are appreciated. :)


I have been fooling with this a bit in a little python applet. The algorythm is multi layered, so there is no easy way to reverse encryption bacause it is done in layers - kinda like cyphring a message that is already cyphered - once you take a layer off - how do you know its off?. Only you change things randomly so you use a different cypher each time. This means the only way (I can think of) to reverse the cypher it to try every key. At 128 bit that 3.4X10^38 keys (I think). Also, added to the key is a user password upto 10 characters (in my case). Its not part of the key stored on the system - so even if you got the private key - you are looking at brute forcing the password.

It could be done - but it would take forever and a powerful system. The algorythm is of little help in the effort.

And my little app is considered simple I am told :)

Manta


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 Post subject: Re: Not understanding Public Key Encryption...
PostPosted: Wed Jun 30, 2004 12:28 pm 
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MantaBase wrote:
Only you change things randomly so you use a different cypher each time.


I'm not sure i understand that part... what exactly are you changing randomly?


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 Post subject: Re: Not understanding Public Key Encryption...
PostPosted: Wed Jun 30, 2004 12:51 pm 
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virtualchaos wrote:
MantaBase wrote:
Only you change things randomly so you use a different cypher each time.


I'm not sure i understand that part... what exactly are you changing randomly?


Sorry, the cypher method.

Here is a silly example:

First pass - cypher all charaters to numbers (method selection was picked at random - and put in privatekey)

Second pass - cypher all number to other numbers (again - picked at random)

3rd - cypher all numbers to letters (random method pick)

output

kljasldkjlkasfhlakhfioehrporpov d,mcxvn,z

but the cypher is actually a cypher of a previously picked cypher - and the method at each pass is random.

Thats not real world -- but close

Does that help?

BTW - this is not exactly what you are talking about - I am only trying to explain why the method works and is hard to de-encrypt with only the algorythm

Manta


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 Post subject: Re: Not understanding Public Key Encryption...
PostPosted: Wed Jun 30, 2004 4:31 pm 
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virtualchaos wrote:
If you have a public key that follows a given algorithm to convert from plaintext to ciphertext, why can't you just reverse engineer the key to get back to plaintext... What am i not seeing? It just seems like you would do the antialgorithm given to you in the public key to be able to decrypt.

All explanations are appreciated. :)


It is basically mathematically very difficult to do. Some are vulnerable to different types of attacks, depending on how big their keys are, how the keys are made, and how the messages are encrypted.

Here's what happens with public key systems. If I want to send you a signed and secured message, I first encrypt the message with my private key, then with your public key. You receive the message, and decrypt it with *your* private key, then my public key. The public and private keys are mathematically related, but you can't just get one from the other. It takes a public key to decrypt a private key encrypted message, and vice-versa.

Asymmetric (two-key) methods include:
I'd recommend reading up on some of them to find out how they really work, and how they really are mathematically "difficult" (I hesitate to say "impossible") to break and essentially impossible to get private keys from with the public key and ciphertext or plaintext.

Generic links on asymmetric crypto:
The other option are symmetric methods, where I give you the key and we both "know" about it. DES, 3DES, and AES are this kind of system.

In general, there are several attacks that are done to attempt to "break" encryption in general:
    1. known-plaintext: you know what the original text looks like through other means
    2. chosen-plaintext: you choose the plaintext to encrypt yourself
    3. chosen-ciphertext: you can choose the output, but not the plaintext
    4. dictionary attack: the frequency of some words (a the is of) can help you break encryption based on a repetitive element in the ciphertext
    5. birthday attack: the probability that any two people in a room have the same birthday is low (apply this to the cryptosystem instead of birthdays ;))
    6. man in the middle attack: intercept a session and "pretend" you are the receiving end
    7. ciphertext only: this basically just means you've gathered the ciphertext of several messages and you need to figure out the key to decrypt them

Each algorithm may have its own vulnerabilities (some of which aren't in my list), for example if you read up on RSA you will find that it is vulnerable to timing attacks, where I can figure out your hardware's timing and "predict" what's going to happen.


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 Post subject: Re: Not understanding Public Key Encryption...
PostPosted: Thu Jul 01, 2004 12:35 am 
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virtualchaos wrote:
Not that this is really specific to windows, but i figured someone would have a more comprehensive explanation. I see how it works... Public key paired with Private key, so that all can Encrypt but only some can decryt, but how is that possible!?


If I want to send you an encrypted message, I use my private key and your public key to encrypt the message. BOTH keys are used to encrypt the message. Your private key is then needed to decrypt the message. Does that make sense? Public/Private key ciphers are important because they solve the 'key distribution' problem.


virtualchaos wrote:
If you have a public key that follows a given algorithm to convert from plaintext to ciphertext, why can't you just reverse engineer the key to get back to plaintext... What am i not seeing? It just seems like you would do the antialgorithm given to you in the public key to be able to decrypt.

All explanations are appreciated. :)


As Colby mentioned, certain mathematic operations are hard to reverse. The classic example, X % 5 = 2. Can you solve for X?

However, the reason you can't simply use an 'antialgorithm' is because you sill need to know the key. One of the oldest ciphers is called a monoalphabetic substitution cipher. You can create a cipheralphabet using a key....

key = hairball
cipheralphabet = hairblcdefgjkmnopqstuvwxyz
regularalhabet = abcdefghijklmnopqrstuvwxyz

Then, for each letter in the plaintext, substitute the regular alphabet letter with the cipheralphabet letter, so

commence the attack on the eleventh of september.

becomes,

INKKBMIB TDB HTTHIG NM TDB BJBVBMTD NL SBOTBKABQ.

Think about this for a minute. If you don't know the key, how can you reverse the algorithm? This cipher is weak though - but for a different reason. it vulnerable to a form of attack called frequency analysis and is a common puzzle refered to as a 'cryptogram'.

Here's one for you to cut your teeth on....

IUN TM C QNSNLT ROCSN SQCBTR FLTQURFML, TEN ULFTNI MQDCLFRKR MB RCTUQL ECVN INSJCQNI WCQ ML TEN SFTFZNLR MB NCQTE.


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 Post subject: Re: Not understanding Public Key Encryption...
PostPosted: Thu Jul 01, 2004 12:38 am 
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Colby wrote:
Here's what happens with public key systems. If I want to send you a signed and secured message, I first encrypt the message with my private key, then with your public key. You receive the message, and decrypt it with *your* private key, then my public key. The public and private keys are mathematically related, but you can't just get one from the other. It takes a public key to decrypt a private key encrypted message, and vice-versa.


And I missed that whole paragraph. :)

How have you been? Still working for the same company?


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 Post subject: Re: Not understanding Public Key Encryption...
PostPosted: Thu Jul 01, 2004 6:41 am 
iron colbinator
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Gadget wrote:
How have you been? Still working for the same company?


I've been busy, working pretty long hours lately. The company and I are doing well, though :)

How about you? How's school?


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 Post subject:
PostPosted: Thu Jul 01, 2004 10:10 am 
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the beauty of public key encryption (aka asymmetric encryption) is that you encrypt with one key and decrypt with another. and those two keys are different.

one of the most important thing in encryption is that the security should rely on the key, not the algorithm. if it relies on the algorithm, then like you said, people can simple reverse engineer it and crack the hell out of everything.

most encryption algorithms are well published (RSA, 3DES), so the algorithm itself bears no secret at all. The secret is in the key people hold. Fundamentally, it is all mathematics...


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 Post subject: Re: Not understanding Public Key Encryption...
PostPosted: Thu Jul 01, 2004 1:20 pm 
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colby wrote:
Gadget wrote:
How have you been? Still working for the same company?


I've been busy, working pretty long hours lately. The company and I are doing well, though :)

How about you? How's school?


No summer school this time around! :D

As for school plans, I am still trying to decide whether I want to finish my Masters then work in industry (since things were suppose to be good by now), and when things slow down again, finish a phd and teach at a uni (aka the original plan), or just go ahead and get the phd now. The job market isn’t terrible, but I would still be competing with a lot of vets w/ 10+ years of experience. I am in a 'wait and see' mode right now – I’ll send some phd apps out in a couple of months and see what happens.

I took a job at Cal State Fullerton this past semester. It is ok. Pay sucks, too many meetings, and any crap that Dr. Whoever doesn't want to deal with tends to find itself on my desk. I've spent way too much time doing things that have nothing to do with software engineering – I guess I am a bit bitter now. Fortunately, I am making contacts with a number of people in industry; hopefully, greener pastures are just around the corner.


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 Post subject:
PostPosted: Fri Jul 02, 2004 10:57 am 
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You used the word organisys?

There is no confirmation for "Y"

Manta


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 Post subject:
PostPosted: Fri Jul 02, 2004 11:05 am 
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MantaBase wrote:
You used the word organisys?

There is no confirmation for "Y"

Manta


Is that for me? If you refering to the 'here's one to cut your teeth on' problem. No. I'll give you a hint though. The first three letter of the ciperalphabet are 'cas'.

I should turn a couple of my crypto apps into applets or jws applications so people can screw around with them and get a better idea about how some of the classic crypto works.


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 Post subject:
PostPosted: Fri Jul 02, 2004 11:12 am 
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Gadget wrote:
MantaBase wrote:
You used the word organisys?

There is no confirmation for "Y"

Manta


Is that for me? If you refering to the 'here's one to cut your teeth on' problem. No. I'll give you a hint though. The first three letter of the ciperalphabet are 'cas'.

I should turn a couple of my crypto apps into applets or jws applications so people can screw around with them and get a better idea about how some of the classic crypto works.


I already solved it except for that one word - what is K? in the cypherbet?

Manta


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 Post subject:
PostPosted: Fri Jul 02, 2004 11:23 am 
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MantaBase wrote:
Gadget wrote:
MantaBase wrote:
You used the word organisys?

There is no confirmation for "Y"

Manta


Is that for me? If you refering to the 'here's one to cut your teeth on' problem. No. I'll give you a hint though. The first three letter of the ciperalphabet are 'cas'.

I should turn a couple of my crypto apps into applets or jws applications so people can screw around with them and get a better idea about how some of the classic crypto works.


I already solved it except for that one word - what is K? in the cypherbet?

Manta


Damn.... I did it on my home machine. Give me a minute.


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 Post subject:
PostPosted: Fri Jul 02, 2004 12:05 pm 
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The key was cassinni (the spelling won't matter)

Here is how the cipheralphabet is formed.
  1. remove any duplicate letter from the key. key = casin
  2. remove any letters in the key from the alphabet
    alphabet = bdefghjklmopqrtuvwxyz
  3. append the alphabet to the key
    cipheralphabet = casinbdefghjklmopqrtuvwxyz

Code:
cipherbet = casinbdefghjklmopqrtuvwxyz  (this should be in caps, btw)
alpherbet = abcdefghijklmnopqrstuvwxyz

so K = m.

This is just one method of forming the key. I'll let you notify the world about the impending doom.


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 Post subject:
PostPosted: Fri Jul 02, 2004 12:31 pm 
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Well, I didn't have duplicate of "K" so I wasn't sure. I didn't reconstruct the key or I might have seen it.

I tend to use x,y, or z or something like when an entry is rare

I won't post it till someone else gets it.


Try this:

Comeup with three different methods of ciphering (alphabet, asciibet, HTML codebet.)

Then write a script that randomly uses them on the same message 10 times and always does an 11th into alpha-numeric cipher

a key is generated that allows you to decipher.

Then, the key is cyphered based on a password.

You need the password to decipher the key - and the key to decipher the message.

Key should be less than 21 digits.

Its not government proof - but its fun.

Manta


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 Post subject:
PostPosted: Fri Jul 02, 2004 1:55 pm 
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MantaBase wrote:
Comeup with three different methods of ciphering (alphabet, asciibet, HTML codebet.)

Then write a script that randomly uses them on the same message 10 times and always does an 11th into alpha-numeric cipher

a key is generated that allows you to decipher.

Then, the key is cyphered based on a password.

Do you have examples of these 4 ciphers?

The key contains the information about which ciphers were used, right? (else you're going to have one hell of a time writing a script to decipher!)


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 Post subject:
PostPosted: Fri Jul 02, 2004 7:51 pm 
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Ok maybe this will be better:

I am very tired BTW - trying to get this in before the bell tolls

Psudo code kinda

Take Password
Use password to generate 10x10 array with entries of 00-99
this is reprodusable

Then, 10 supercypher methods. - These are not really cyphers - things like droppin the message to ascii, or HTLM % code etc......

these are represented as the first digit in an array entry (0-9)

10 Subcyphers - like how do I "scramble" the alphabet. Ten different methods for each supercypher.

Then take message and randomly decide an array co-ordinate to use.
generate the entry into a key (like 92 - superset 9 subset 2). Cypher message - do this 10 times randomly.

To decypher, script need password (to replicate table) and key.

Does it make more sense now??


Oh yeah - you have to cypher the last layer to alphanumneric to obfiscate the last cypher (incase its ascii or something)

Sorry, I am late for bed :)

Manta


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 Post subject:
PostPosted: Fri Jul 02, 2004 11:26 pm 
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Let's redifine things a little:

the password is what the user needs to know to decrypt the message
the key may, or may not, be the same as the password, but it is also needed to decipher the msg.
the rand, short for random, is the information about which cipher was used to initially encipher the plaintext

Let's start with the second method you suggested - it is easier to attack.

In order for someone to decipher the message, they need to have the encrypted message, the password, and the rand (actually, they don't need to 'know' the rand - the information concerning the rand is just passed to them - I'll discuss not knowing the rand later). So where do we put the rand? It can't go in the password - the rand is random! It has to be located within the encrypted message.

So where do we put the rand. We can't do something obvious like encrypting the rand with some known cipher and putting it at the front or end of the message. It would be easy for someone to reverse engineer their own message and find the location. After they figured out which cipher is used to encrypt the rand, you're back to using just a single cipher. Worse yet, they may now know the key!

Don't waste neurons thinking about it though. We don't need transmit the rand. Since we have the password/key, we just go through the first decryption algorithm and then use that result and try each of the 100 remaining possible ciphers. On average, it will take 50 tries to get it. No biggie - computers are fast at this. A good marketing guy will spin doctor this and have people thinking the extra time is just making their data more secure. This is much better then trying to transmit the encrypted rand (at least of the possibilities that I considered).

We could even take this a step further and disregard the rand in your first example. If we had 5 weak ciphers and randomly enciphered the plaintext 3 times with any of the ciphers, we would have a 5^3 combinations of ciphers. 125 is within working range, if you know the key, and it might be possible to use an alpha-beta algorithm to reduce the problem space further.

This technique of enciphering a message multiple time doesn't always improve things though. For example, some ciphers don't provide any extra security when they're used multiple times. You could use a Caesar shift, monoalphabetic substitution or transposition cipher on a message a 1000 times an it wouldn't make a bit of difference. The original weakness just shines right through. Occassionaly, it makes things worse. If anything, I suspect these techniques buy a little more time and help foil automated attacks.


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PostPosted: Sat Jul 03, 2004 12:44 am 
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Ok. Had to take a break and switch comps. Gonna test the idea that a super cipher will fool automated attacks. Our super cipher is a monoalphabetic substitiution cipher followed by a caesar shift. Before you read any further, you might want to think about whether this will increase, decrease, or not change the strength of the original cipher.

The automated attack tool is part of CrypTool, which is an interesting program designed to teach encryption. It is a very good tutorial, but not a very good cryptoanalysis tool. It completely floundered w/ the encrypted text I had posted previously. Too short. Confused the poor machine... :)

Enciphering this paragraph taken from Colby's post.

plaintext wrote:
Here's what happens with public key systems. If I want to send you a signed and secured message, I first encrypt the message with my private key, then with your public key. You receive the message, and decrypt it with *your* private key, then my public key. The public and private keys are mathematically related, but you can't just get one from the other. It takes a public key to decrypt a private key encrypted message, and vice-versa.

ciphertext wrote:
QFPF'R WQAS QAMMFIR WGSQ MTLEGD CFY RYRSFHR. GV G WAIS SJ RFIK YJT A RGNIFK AIK RFDTPFK HFRRANF, G VGPRS FIDPYMS SQF HFRRANF WGSQ HY MPGUASF CFY, SQFI WGSQ YJTP MTLEGD CFY. YJT PFDFGUF SQF HFRRANF, AIK KFDPYMS GS WGSQ *YJTP* MPGUASF CFY, SQFI HY MTLEGD CFY. SQF MTLEGD AIK MPGUASF CFYR APF HASQFHASGDAEEY PFEASFK, LTS YJT DAI'S BTRS NFS JIF VPJH SQF JSQFP. GS SACFR A MTLEGD CFY SJ KFDPYMS A MPGUASF CFY FIDPYMSFK HFRRANF, AIK UGDF-UFPRA.

CrypTool's solution wrote:
NEVER BNAK NASSECR BLKN SHOULD GET RTRKEIR Lv L BACK Kj RECk TjH A RLnCEk ACk REDHVEk IERRAnE L vLVRK ECDVTSK KNE IERRAnE BLKN IT SVLuAKE GET KNEC BLKN TjHV SHOULD GET TjH VEDELuE KNE IERRAnE ACk kEDVTSK LK BLKN TjHV SVLuAKE GET KNEC IT SHOULD GET KNE SHOULD ACk SVLuAKE GETR AVE IAKNEIAKLDAUUT VEUAKEk OHK TjH DACK bHRK nEK jCE vVjI KNE jKNEV LK KAGER A SHOULD GET Kj kEDVTSK A SVLuAKE GET ECDVTSKEk IERRAnE ACk uLDEuEVRA

Again, the attack failed miserably. In fact, it failed several times using different assumptions for the attack and with different implementations of a monoalphabetic substiution cipher (I even removed all non-letters). Each time the automated attack resulted in exactly the same jibberish, proving beyond any doubt, that Colby's writing contains a subliminal cipher that when combined with even a simple substitution cipher results in an encrypted message that would baffle the NSA's best people. She is that good folks.

Anways, I copied a different text.

plaintext wrote:
Kerry is in the middle of a three-day, 546-mile Fourth of July weekend bus tour through rural Minnesota, Wisconsin and Iowa, just over three weeks before he accepts his party's nomination at the Democratic National Convention.

He planned to meet Saturday with family farmers and ranchers in nearby Independence, Wis., before heading to Dubuque, Iowa, to watch fireworks along the Mississippi River.

On Friday, Kerry attended outdoor rallies in Cloquet, Minn., population 11,200, and Bloomer, Wis., population 3,300, to tout proposals he said would benefit rural Americans.

He talked up his plans to repeal tax cuts for those making more than $200,000, prohibit unfair farming practices such as corporate meatpackers owning livestock more than two weeks before slaughter, and increase renewable fuels from corn, soybeans and other sources.

And, he planned on Saturday to stress his proposals to require food labels to include the product's country of origin and to expand programs that provide financial assistance to farmers to encourage conservation.

"It's time we fought for family farmers," Kerry said in prepared remarks. "The American family farmer grows the safest, lowest priced and finest food on the planet. Our policies should foster an economic climate that helps them compete and succeed in today's global marketplace."

CrypTool's solution wrote:
dERRy IS Ii THE gIDDLE OF A THREEDAy gILE FOURTH OF MULy WEEdEiD BUS TOUR THROUGH RURAL gIiiESOTA WISoOiSIi AiD IOWA MUST OuER THREE WEEdS BEFORE HE AooEkTS HIS kARTyS iOgIiATIOi AT THE DEgOoRATIo iATIOiAL oOiuEiTIOi HE kLAiiED TO gEET SATURDAy WITH PARHELIA IS THE GREATEST VIDEO CARD EVER! FARgERS AiD RAioHERS Ii iEARBy IiDEkEiDEioE WIS BEFORE HEADIiG TO DUBUlUE IOWA TO WAToH FIREWORdS ALOiG THE gISSISSIkkI RIuER Oi FRIDAy dERRy ATTEiDED OUTDOOR RALLIES Ii oLOlUET gIii kOkULATIOi AiD BLOOgER WIS kOkULATIOi TO TOUT kROkOSALS HE SAID WOULD BEiEFIT RURAL AgERIoAiS HE TALdED Uk HIS kLAiS TO REkEAL TAw oUTS FOR THOSE gAdIiG gORE THAi kROHIBIT UiFAIR FARgIiG kRAoTIoES SUoH AS oORkORATE gEATkAodERS OWiIiG LIuESTOod gORE THAi TWO WEEdS BEFORE SLAUGHTER AiD IioREASE REiEWABLE FUELS FROg oORi SOyBEAiS AiD OTHER SOURoES AiD HE kLAiiED Oi SATURDAy TO STRESS HIS kROkOSALS TO RElUIRE FOOD LABELS TO IioLUDE THE kRODUoTS oOUiTRy OF ORIGIi AiD TO EwkAiD kROGRAgS THAT kROuIDE FIiAioIAL ASSISTAioE TO FARgERS TO EioOURAGE oOiSERuATIOi ITS TIgE WE FOUGHT FOR PARHELIA IS THE GREATEST VIDEO CARD EVER! FARgERS dERRy SAID Ii kREkARED REgARdS THE AgERIoAi PARHELIA IS THE GREATEST VIDEO CARD EVER! FARgER GROWS THE SAFEST LOWEST kRIoED AiD FIiEST FOOD Oi THE kLAiET OUR kOLIoIES SHOULD FOSTER Ai EoOiOgIo oLIgATE THAT HELkS THEg oOgkETE AiD SUooEED Ii TODAyS GLOBAL gARdETkLAoE

Not bad - this can be finished off quickly. I then took the encrypted text and ran it through a caesar shift and used the automated attack again. Even though I didn't expect this cipher to improve things (see my previous post), I am still surprised - the irrational mind at work.

CrypTool's solution to the super cipher wrote:
rERRm IS Iw THE uIDDLE OF A THREEDAm uILE FOURTH OF MULm WEErEwD BUS TOUR THROUGH RURAL uIwwESOTA WIScOwSIw AwD IOWA MUST OiER THREE WEErS BEFORE HE AccEyTS HIS yARTmS wOuIwATIOw AT THE DEuOcRATIc wATIOwAL cOwiEwTIOw HE yLAwwED TO uEET SATURDAm WITH FAuILm FARuERS AwD RAwcHERS Iw wEARBm IwDEyEwDEwcE WIS BEFORE HEADIwG TO DUBUzUE IOWA TO WATcH FIREWORrS ALOwG THE uISSISSIyyI RIiER Ow FRIDAm rERRm ATTEwDED OUTDOOR RALLIES Iw cLOzUET uIww yOyULATIOw AwD BLOOuER WIS yOyULATIOw TO TOUT yROyOSALS HE SAID WOULD BEwEFIT RURAL AuERIcAwS HE TALrED Uy HIS yLAwS TO REyEAL TAk cUTS FOR THOSE uArIwG uORE THAw yROHIBIT UwFAIR FARuIwG yRAcTIcES SUcH AS cORyORATE uEATyAcrERS OWwIwG LIiESTOcr uORE THAw TWO WEErS BEFORE SLAUGHTER AwD IwcREASE REwEWABLE FUELS FROu cORw SOmBEAwS AwD OTHER SOURcES AwD HE yLAwwED Ow SATURDAm TO STRESS HIS yROyOSALS TO REzUIRE FOOD LABELS TO IwcLUDE THE yRODUcTS cOUwTRm OF ORIGIw AwD TO EkyAwD yROGRAuS THAT yROiIDE FIwAwcIAL ASSISTAwcE TO FARuERS TO EwcOURAGE cOwSERiATIOw ITS TIuE WE FOUGHT FOR FAuILm FARuERS rERRm SAID Iw yREyARED REuARrS THE AuERIcAw FAuILm FARuER GROWS THE SAFEST LOWEST yRIcED AwD FIwEST FOOD Ow THE yLAwET OUR yOLIcIES SHOULD FOSTER Aw EcOwOuIc cLIuATE THAT HELyS THEu cOuyETE AwD SUccEED Iw TODAmS GLOBAL uARrETyLAcE


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