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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Silver Puzzle Cards
[Puzzle] #243 Silver - Shuffled Part 2 (Read 1st Post!)
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb
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mattyjh
Kl00

Joined: 23 Jan 2006
Posts: 42
Location: Uk - Leeds/Hull

Quote:
Its a long shot but my thinking was five of cups, cups are often used in magic tricks


I like this idea; there are alot more decks used in magic tricks like the one you mentioned...

I remember some specific ones from my youth that did special things if you dealt them properly... For example one would give everyone in a circle a really good 5-card poker hand but ultimately you as the dealer had a royal flush. This deck could also be used for loads of other tricks too.

I might start having a look through my old card trick books!

It's a very long shot but at this stage I think every idea is!!

PostPosted: Fri Aug 25, 2006 12:58 pm
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James Siegesmund
Boot

Joined: 02 Aug 2006
Posts: 26
Location: Denver, CO

PerplexHero wrote:
James: Are you thinking that the mystery letters are the deck order, the enciphered text, or both? If it is the deck order, that implies that the deck is 128 cards + 2 jokers. Since this isn't a nice multiple of 52, it's definitely a non-standard 2.25-ish decks.
-PerplexHero


I think the letters on the deck are just the message, possibly with noise letters (letters that will only 'decrypt' to more garbage, but yet must be decrypted so that the keystream properly matches the actual message).

PerplexHero wrote:

You need both the end-condition deck order and the enciphered text to work out the solution as Bruce describes.
-PerplexHero


Correct. My theory : the end-condition deck order is identical to the order in which the cards come out of the box, and the enciphered text is there on the card.

When working backwards, the first step gives the last letter of the keystream. You start with the end-condition deck, figure out what the last keystream letter was, work Solitaire one round back, figure out what the second-to-last keystream letter is, etc. I don't have my notes with me, but suppose you did this and found a keystream that would end "XXXXX". One nice thing about this method is that "XXXXX" will be the always be the last five letters of a keystream that ends with that end-condition deck, no matter how long the keystream ends up being (it will be as long as the encrypted text).

Putting the same thing differently: for any given end-condition deck and keystream length, there is a unique keystream that leaves that end-condition deck. Let x and n be two keystreams of different lengths for a particular end-condition deck, with x>n (e.g. keystream n has length 3, keystream x has length Cool. The final n letters of keystream x will always be identical to keystream n.

So if you do fifteen steps of backwards Solitaire, you generate roughly the last 15 letters of a keystream. Those fifteen could be "subtracted" from the last 15 letters of the message, whatever length you think the message (and, by extension, the whole keystream) is. Thus the same keystream end-fragment could be tested against the end of a 128 letter message, or 108 letters, or 55 letters, or whatever.

PostPosted: Fri Aug 25, 2006 12:59 pm
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BrianEnigmaModerator
Entrenched


Joined: 05 Oct 2003
Posts: 1199
Location: Pacific Northwest

Okay, so I have started to revisit Shuffled. Waaaayyyyy back when (wave 1 or 2), I wrote a program that attempted to figure out a correct deck order, given the playing card symbols on the cards we knew. It attempted to find the various permutations of the remaining cards in the remaining prime numbered "holes."

After talking with a few people in IRC and revisiting the wiki, I am starting to believe that the deck started in a "standard" order. In this case, I am taking "standard" to mean not how the cards are stacked at the factory in any given deck, but the mathematical start of the Solitaire cipher (i.e. card 1 is in position 1, card 2 is in position 2, etc.) More specifically, and stepping into meta out-of-game territory for a second, it is very likely that the puzzle's designer went over to Schneier's site, grabbed his Solitaire Perl program, then ran his message through it with a password/phrase. Schneier's program does not have a particular starting deck--it starts with everything in order (as I said above, card 1 in position 1, etc.)

This got me thinking that all we need is a password/phrase, and the message is ours for the taking! A slightly inefficient shell script later, I was throwing the standard Unix dictionary at the encryption. I've attached my results, if you're interested. I scanned them for obvious crib words (djinn, virus, worm, perplex, sente, kiteway, claire, castille, etc.) but nothing intelligible came out. You're free to try yourself. What bothers me a bit is why some of the lines are missing a letter. There is a quirk of some kind in the decryptor that eats an extra letter on certain words. For example compare "./sol.pl -d abas message.txt" versus "./sol.pl -d abase message.txt" and you will see the former decode is one letter short.

Anyway, this line of reasoning (assuming it's a 1..52 deck order and sol.pl), leads to the password being not a standard word, but a non-dictionary word or a longer phrase. I tried the obvious ("if entropy...") as well as a few names (variations on Garnet's name, given that the message was written for him), etc. The mnemonic letters of "if entropy..." anagram out to "ice slowly," so I tried that, too.

At this point, I am not sure what else to try and whether I should drop this line of query for a little while.

Okay, not an attachment because it's 16M, but here's the output: http://perplexcitycardcatalog.com/notes/shuffled-wordlist-output.zip
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PostPosted: Fri Aug 25, 2006 2:46 pm
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Mindez
Decorated

Joined: 26 Feb 2006
Posts: 165

Ugh.

I just went through the whole thing and read every line with "The".

And I found nothing =(

Does your output include the outside letters, though?

Perhaps try again with/without the outside letters?
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PostPosted: Fri Aug 25, 2006 3:03 pm
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themandotcom
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Joined: 28 Apr 2006
Posts: 136
Location: Syosset, New York, USA, Earth, Milky Way Galaxy, Universe

Bri, in your output, I did a control-f on sente. There is acutally one that says." Sentehi." Coincidnce? I don't know, just lettin' ya know.
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PostPosted: Fri Aug 25, 2006 3:10 pm
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Sh1ft
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Joined: 12 Nov 2003
Posts: 110
Location: Salt Lake City, Utah

BriEnigma wrote:
What bothers me a bit is why some of the lines are missing a letter. There is a quirk of some kind in the decryptor that eats an extra letter on certain words. For example compare "./sol.pl -d abas message.txt" versus "./sol.pl -d abase message.txt" and you will see the former decode is one letter short.



This is nothing more than the author assuming the output has padded X's at the end of the line and truncating them. This means the decrypts that are missing 3 characters must have had 3 X's at the end of the line. (As the solitaire instructions say to add X's to bring your char count up to a multiple of 5.)

Comment the following line in sol.pl to see the X's:

Code:

## If we're decrypting, remove trailing X's from the newly found plaintext
$o =~ s/X*$// if $d;


PostPosted: Fri Aug 25, 2006 3:47 pm
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BrianEnigmaModerator
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Joined: 05 Oct 2003
Posts: 1199
Location: Pacific Northwest

Mindez wrote:
I just went through the whole thing and read every line with "The". And I found nothing =(

You have quite a lot more patience than I.

Mindez wrote:
Does your output include the outside letters, though?

Given Von's hint ("If you're feeling cold, you're overly sensitive") and given the letters disappear when heat is applied, I ran it without the outside letters. I suppose you are correct and that I should try again with them included, just in case.
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PostPosted: Fri Aug 25, 2006 3:48 pm
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PerplexHero
Boot


Joined: 16 Jun 2006
Posts: 30

James Siegesmund wrote:


I think the letters on the deck are just the message, possibly with noise letters (letters that will only 'decrypt' to more garbage, but yet must be decrypted so that the keystream properly matches the actual message).

PerplexHero wrote:

You need both the end-condition deck order and the enciphered text to work out the solution as Bruce describes.
-PerplexHero


Correct. My theory : the end-condition deck order is identical to the order in which the cards come out of the box, and the enciphered text is there on the card.

That's a great idea! I'll see if I can modify my code this weekend to try that out.

-PerplexHero

PostPosted: Fri Aug 25, 2006 11:35 pm
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brokasaphasia
Boot

Joined: 31 May 2006
Posts: 26

James Siegesmund wrote:
Then my cards were stolen (along with my briefcase). Cursing

...snip...

4. Solitaire is reversible.

...snip...

I think we have an already shuffled deck disguised as a new deck.

Sorry to hear about the theft... that sucks man.

Regarding your idea, have you read this webpage?
http://www.ciphergoth.org/crypto/solitaire/

It states that Solitaire CANNOT be reversed. Here is the pertinent quote from that page:
Quote:
The CPRNG state machine is not reversible, contrary to what the operational notes claim: the initial step in which a joker is moved to the top if it is on the bottom cannot be reversed.


Despite this (and because I didn't totally understand it), I tried your idea with a perl program. Working the full 128-character cipher-text BACKWARDS with a starting deck that matches the most common "out of the box" deck order (1..54 = C1..C13,D1..D13,H1..H13,S1..S13,JA,JB) I yield the following plain text:

ZZRUHPOFVZPHJZZAQJEICETTHAASQBFJSMKSARQSKLAEPARROFICYASVNAOYDAULELDHJYYTZIIMZBNAETWODETXHPGONLIDOLBPEYIQJSPKHRRXANAJMZWUHDQRJVJN

The final deck order after this "un-encryption" is:

13,28,1,42,43,19,6,7,44,47,38,20,30,33,10,45,41,26,4,50,54,35,36,40,48,3,9,27,18,25,2,16,24,32,17,49,12,8,21,34,31,22,5,46,39,52,53,23,15,37,51,29,11,14

As a test, I then loaded this deck order back into my perl program and forward encrypted it with the plain text shown above. The resulting cipher text is:

EODMFXRUTHWBBMCHGFIBLXCQYWEZFLITHPJLFHWYETKWYLJOTYYNGYJBIOGIFUVMRXIHGURAGXHNQHRSXAWJUFJTAMSMMOSMVBAAKPGVVWXOVMYKZPLLULFHURGIFULK

The astute reader will note that this is totally correct EXCEPT FOR THE LAST LETTER.

Also, I note that my ending deck order after encryption is:

51,53,54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,52

Which is, of course, NOT back to where I started... Either I made an error in my program, or the non-reversibility of Solitaire (which I still don't understand) is causing this.

Anyway, hope this helps put your mind at rest Smile Good idea! I had not considered it before this.

PostPosted: Sat Aug 26, 2006 7:05 am
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PerplexHero
Boot


Joined: 16 Jun 2006
Posts: 30

brokasaphasia wrote:
EODMFXRUTHWBBMCHGFIBLXCQYWEZFLITHPJLFHWYETKWYLJOTYYNGYJBIOGIFUVMRXIHGURAGXHNQHRSXAWJUFJTAMSMMOSMVBAAKPGVVWXOVMYKZPLLULFHURGIFULK

The astute reader will note that this is totally correct EXCEPT FOR THE LAST LETTER.


Did you try decrypting without the first/last 10 characters?

PostPosted: Sat Aug 26, 2006 7:03 pm
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brokasaphasia
Boot

Joined: 31 May 2006
Posts: 26

PerplexHero wrote:
Did you try decrypting without the first/last 10 characters?


un-encrypted plaintext:
NISPLLCYTRINNNZDZJZFOLXXAANKRFOICYHFOABOWTFXWPDOJMMNOXSWRBCCYTGCQMALYVLCXGKWCDBBMVOJGINXMFDCHTKUPCMZLWJYPMSJ

ending deck order:
46,20,29,12,11,49,36,5,18,16,25,45,41,2,32,17,10,4,24,34,38,54,33,1,23,53,50,35,15,37,48,27,26,8,21,22,14,40,28,30,31,42,43,9,52,3,19,6,7,44,47,39,13,51

re-encrypted ciphertext:
WBBMCHGFIBLXCQYWEZFLITHPJLFHWYETKWYLJOTYYNGYJBIOGIFUVMRXIHGURAGXHNQHRSXAWJUFJTAMSMMOSMVBAAKPGVVWXOVMYKZPLLUG

ending deck order:
51,53,54,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,52

PostPosted: Sun Aug 27, 2006 3:03 am
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arnezami
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Joined: 14 Apr 2006
Posts: 136

@brokasaphasia: could you post the source of your program so we can look if there is a bug in it. Because solitaire should be perfectly reversable (if you have the resulting deckorder). Its also possible there is a bug in the original source of the decryption code.

Looks like a small problem though since your ending deck is very close to the original deck. Maybe when reversing you could also output the keystream/decrypted text and compare this later when you start decrypting forwards (in other words: outputting the backwards decryption).

Btw: I suspect step 5 may not have been reversed properly somewhere (because of a joker).

Thanks for all the work btw Smile.

arnezami

PS. Just to be sure this should also be tried: use the deck order on the primary cards as end-deck and then reverse it (= do the backwards decryption). Keep in mind after reversing there could be some "logic" to the resulting (and originally starting) deck which we might have been able to guess without the primary cards. Which would mean we didn't need the primary cards...
PPS. Its also possible the reversing doesn't take 108 steps but 10 or 20 or 118 or 128. And maybe you have to decrypt the whole 128 text while only the middle 108 makes sense after decryption.
PPPS. What would finally explain the existence of the 10 characters at both ends would be this method: reverse the deck 128 steps (entropy wins because the deck is shuffled). Then decrypt only the 108 characters (outward looks should leave you cold). This way both 10-texts would effectively be additional security measures. And of course there may be other possibilities I haven't mentioned/thought of yet.

PostPosted: Sun Aug 27, 2006 4:48 am
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brokasaphasia
Boot

Joined: 31 May 2006
Posts: 26

Actually, I believe that my code is correct.

I believe that it is IMPOSSIBLE for Solitaire to leave the deck perfectly ordered 1..54 at the end of any number of encryption steps:

If the deck ENDS UP like this:
Code:
DECK 1:
C C C C C C C C C C C C C D D D D D D D D D D D D D H H H H H H H H H H H H H S S S S S S S S S S S S S J J
1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K A B


Then just prior to that a count cut was performed from this deck:
Code:
DECK 2:
C C C C C C C C C C C C C D D D D D D D D D D D D D H H H H H H H H H H H H H S S S S S S S S S S S S S J J
1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K A B

(remember, when a joker is on the bottom, count cut will leave the deck unchanged)

So, just prior to that a triple cut was performed from this deck:
Code:
DECK 3:
J J C C C C C C C C C C C C C D D D D D D D D D D D D D H H H H H H H H H H H H H S S S S S S S S S S S S S
A B 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K


So, just prior to that, the B Joker was shifted down from this deck:
Code:
DECK 4:
J C C C C C C C C C C C C C D D D D D D D D D D D D D H H H H H H H H H H H H H S S S S S S S S S S S S J S
A 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q B K


So, just prior to that, the A Joker was shifted down from this deck:
Code:
DECK 5:
C C C C C C C C C C C C C D D D D D D D D D D D D D H H H H H H H H H H H H H S S S S S S S S S S S S J J S
1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q B A K


But wait... if we RE-DO the A Joker shift right now, we do NOT end up back to DECK 4... we actually end up with something different:
Code:
DECK 6:
C C C C C C C C C C C C C D D D D D D D D D D D D D H H H H H H H H H H H H H S S S S S S S S S S S S J S J
1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q K 1 2 3 4 5 6 7 8 9 0 J Q B K A


So, Solitaire may be reversible, but you will not find the deck in a perfect 1..54 at the end.

PostPosted: Sun Aug 27, 2006 11:16 pm
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arnezami
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Joined: 14 Apr 2006
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brokasaphasia wrote:
Actually, I believe that my code is correct.

I believe that it is IMPOSSIBLE for Solitaire to leave the deck perfectly ordered 1..54 at the end of any number of encryption steps:

So, Solitaire may be reversible, but you will not find the deck in a perfect 1..54 at the end.

You are right Smile.

Solitiare IS completely reversible BUT that does not mean it can end up in any deck order. Only deck orders that are the result of solitaire en/decryption can always be reversed. And solitaire never results in a "fresh" deck.

Sadly though it means this idea (of reversing a deck) has been debunked. At least the idea of reversing a "fresh" deck. Reversing the "prime numbered deck" still has a chance.

Good work and thinking!

arnezami

PostPosted: Mon Aug 28, 2006 4:58 am
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RedZed333
Boot


Joined: 13 Jul 2006
Posts: 24
Location: Sunderland

I know Von has told us 'as for the code, everything you need is there' and, according to Perplex City Customer Services, 'You do not need any other puzzle cards in order to solve card 243-shuffled.'

Do you think it's worth asking if these hints mean we can solve this card as it stands and we don't need knowledge of any 3rd party codes/ciphers ie solitaire.

If so, who could we ask?

PostPosted: Mon Aug 28, 2006 11:38 am
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