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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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FranG
Boot

Joined: 23 May 2006
Posts: 35

Gee, Guys, I didn't think it would start a controversy. It was just a little dig at themandotcom's arithmetic.


Quote:
So, WBBMC HGFIB LXCQY WEZFL ITHPJ LFHWY ETKWY LJOTY YNGYJ+
IFENT ROPYW INSTH ENOUT WARDL OOKSS HOULD LEAVE YOUCO ect.

So for the first block would be
(WBBMC HGFIB)
23 2 2 13 3 8 7 6 9 2
9 6 5 14 20 18 15 16 25 23
6 8 7 2 23 26 22 22 8 25 EQUALS
fhgbwzvvhy


He didn't have any problem with 23+9=6; he just miscalculated 13+14 and got 2 instead of 1.

I don't think you need to worry about 0 in this case. Just number the letters from 1 to 26 and add them normally. Then subract 26 until the remainder is less than 27 and that's the answer.

23+9=32 & 32-26=6 (f). 13+14=27 & 27-26=1 (a), not 2 (b)

PostPosted: Wed Jul 05, 2006 2:09 am
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Jim
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Re: Off Tangent

Sh1ft wrote:

Given our past experience with the more difficult cards and the context of the text, my question is, to narrow the scope of what possible passphrase could be "buried" in the "if entropy wins" phrase what should we exclude? Are quotes from famous Earth people appropriate? The text written on the card indicates (to me) that this is a Perplexian matter, and I have tailored my passphrase attempts to vague phrases that are appropriate to the "if entropy wins" phrase.

Because Solitaire/Pontifex is a "earth" equivalent of a keystream generator, should we be looking for quotes from famous earth people as a possible passphrase? I have avoided even the word "Boolean" as this seems far to "earthy" for Garnet and his unknown benefactor. Is this short-sidedness? Should we include words derived from famous earth mathematicians and philsophers names and/or their direct quotes to try and come up with a passphrase appropriate to the "if entropy wins" phrase?


I would include earth quotes. The pack of cards that Garnet was given somehow found its way from Earth to Perplex City. So there may be some link between Earth and this puzzle.

PostPosted: Wed Jul 05, 2006 9:36 am
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Guin
Unfettered


Joined: 11 Jan 2006
Posts: 400
Location: Antartica

Re: Add?

Sh1ft wrote:
I could be wrong, but I thought 13+13=26=Z, I only thought you subtracted when you exceeded 26.


It does Smile
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So long and thanks for all the fish! Trout

PostPosted: Wed Jul 05, 2006 11:31 am
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Sh1ft
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Joined: 12 Nov 2003
Posts: 110
Location: Salt Lake City, Utah

pcx wrote:

There have been 260 failed attempts at solving this card.


Well, nothing new to report, but just in case we are missing something obvious, I am thinking we should use our collective brain power to try and find out how:

Schneier wrote:

It's your job to figure out how the key is buried in the phrase.


So, let us assume that "if entropy wins outward looks should leave you cold" is a cryptic crossword clue (as has been previously been mentioned many times) and try and find out how the key is buried in the phrase.

As a lame attempt at 'rallying the troops', post up your best interpretation of "if entropy wins, outward looks should leave you cold"!!!!!!

FYI, 'degree of uncertainty' passphrase doesn't decrypt anything discernable from resonable starting deck orders.

PostPosted: Tue Jul 11, 2006 3:55 am
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Guest
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As we already know that entropy has many meanings on this card, I think there is a main reason why it feautures on this card.

The focus I think is on the word "wins":

By saying "if entropy wins outward looks should leave you cold" I think it means that if you shuffle the cards/text first you wont be able to get any further. Maybe it wants you to do something else first then shuffle, possibly using the SHUFFLED FOURTH PRIME somewhere. There could be another cipher at work here.

Also in terms of cryptic clues:

"...outward looks should leave you cold"

This could mean that when decrypted, if you look at the ends, you end up with the first and last letters being:

co..........ld or some variation

So another meaning of the clue could be telling you that when you have shuffled the first and last letters are as above giving you a starting point.

There is not just one way of reading it and I think the clue is not clear enough to guide you to an answer unless there is another purpose for it.

PostPosted: Tue Jul 11, 2006 11:00 am
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sirichj
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Joined: 15 May 2006
Posts: 85

Entropy

Trout if you want but I'm not reading through ten hours of pages to see if this has been mentioned Cool

Could it have something to do with thermodynamics?

From what I understand of it (which is very little) according to the 2nd law of thermodynamics entropy will always win, order will always revert to chaos. If you put this into context, the cards are all ordered when you begin i.e. in suits, if you shuffle them obviously they are not ordered and entropy has won because the order has gone and chaos has ensued. I'm not quite sure what I'm getting at and how this could related to outward looks leaving you cold but I did find these on different websites :

The universe itself, for instance, is a thermodynamically closed system. No new free energy can enter it from the outside, so its entropy inevitably increases. In fact, entropy will inevitably destroy it, sapping and using up all of its free energy and reducing it to a cold inert realm where there is no energy flow, a condition known as "heat death".

Broadly speaking, entropy is the amount of disorder and information in a system. Take, for example, a fresh, unshuffled deck of cards. In that state it has low entropy and contains little information. Just two pieces of data (the hierarchy of suits and the relative ranks of the cards) tell you where to find every card in the deck without looking. Give it a good shuffle and look again. The deck has a lot of entropy and a lot of information. If you want to locate a particular card, you have to hunt through the entire deck. There is only one perfectly ordered state but about 1068 disordered ones, which is why you will never, ever accidentally shuffle the deck back into its original order.


I just wondered if anyone had tried anything to do with 'heat death' as a passphrase ? Sorry if this doesn't make sense but I am trying !

PostPosted: Fri Jul 14, 2006 12:32 pm
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Nerd
Boot

Joined: 07 May 2006
Posts: 31
Location: Wokingham, Berkshire, UK

this is excellent, and it has set me off in a direction for understanding the design of the cards Smile..i'll read more into it then post some stuff

PostPosted: Fri Jul 14, 2006 7:04 pm
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Nerd
Boot

Joined: 07 May 2006
Posts: 31
Location: Wokingham, Berkshire, UK

i think the images on the card has alot to do with space and time, but cnt think how this relates the the message..

PostPosted: Fri Jul 14, 2006 8:06 pm
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Si richj
Guest


Is this any help

Hi

I found this somewhere after a lot of searching and just wondered if this was any help?



Solitaire


CRyptography Applications Bistro

8 April 2004



Tuesday:

High-tech crypto with sophisticated, expensive equipment using the principles of quantum mechanics to solve a problem most people don't have
Today:

Low-tech crypto with ordinary, inexpensive equipment using the principles of shuffling to solve a problem most people don't have


Solitaire


Output-feedback mode stream cipher
Designed by Bruce Schneier in 1999
Implemented using a deck of cards
Featured in Neal Stephenson's novel Cryptonomicon


Tin-foil hat time


You want to communicate securely with other people
You don't want the secret police to be able to decode your messages
You don't want to have to keep around incriminating evidence, such as a computer with PGP
You want to be able to do this without electricity


Requirements


Cannot rely on security-through-obscurity
Must be secure even against a well-funded adversary
Must be simple enough that someone can remember it
Must not require incriminating equipment
Must be entertaining enough to go in a Neal Stephenson novel


Overview of Solitaire


The key consists of a shuffled deck, with two jokers: A and B
A sequence of cuts and rearrangements generates a pseudo-random keystream
The keystream is added to the plaintext, modulo 26, to encrypt
The keystream is subtracted from the ciphertext to decrypt


The Algorithm


Move the A-joker one card down
Move the B-joker two cards down
Perform the triple-cut
Perform a count-cut, using the card on the bottom to count with
Find the output card, using the card on the top to count with


1. Moving the A joker


If the joker is on the bottom, move it to one below the top card


9


2


6


*A


10


9


9


2


*A


6


10


9



2. Moving the B joker


If the joker is on the bottom, wrap around like we did with the A joker


2


8


J


*B


3


Q


2


8


Q


J


3


*B



A


3. The Triple-Cut


A


A


A


A


*B


A


A


A


6


*A


A


A


A


2


A


A


A


2


*B


A


A


A


6


*A


A


A


A


A


A



4. The Count Cut


5


5


5


5


J


5


5


5


5


5


5


5


5


5


5


3


5


5


5


5


5


J


5


5


5


5


5


3


5


5


5


5


J


5


= 0 + n

= 13 + n

= 26 + n

= 39 + n
*A = *B = 53



5. Finding the output card


7


5


5


5


J


5


2


J


5


5


5


5


5


5


5


3


5


= 0 + n

= 13 + n

= 26 + n

= 39 + n
*A = *B = 53


Convert the top card to a number
Count down that many from the top
The next card is the output card
If the output card is a joker, go back to step 1
The deck does not change


J = 13 + 11 = 24



PLGRM BZIVF JGH


A 1 J 10 S 19

B 2 K 11 T 20

C 3 L 12 U 21

D 4 M 13 V 22

E 5 N 14 W 23

F 6 O 15 X 24

G 7 P 16 Y 25

H 8 Q 17 Z 26

I 9 R 18



Key Distribution


Solitaire is a symmetric cipher, so we must have a key known to both parties
Use identically shuffled decks: 54! 2237
requires distributing decks
requires good shuffling
Use a bridge ordering: 52!/(13!)4 295
need way to position jokers
the secret police read newspapers too
Use a passphrase to key the deck


Keying the Deck with a Passphrase


Move the A-joker down one card
Move the B-joker down two cards
Perform the triple cut
Perform the count cut based on top card
Perform a second count cut based on a letter from the passphrase


How many shuffles does it take to be "random"?


In an ideal riffle shuffle, we split the deck in halves, then interleave the halves
Cards in the same half are not reordered
This yields 54!/(27! 27!) 250
We'd need five shuffles to reach 2237


Shuffling, in practice


In practice, the 250 interleavings are not equally likely
cards near each other don't separate much
Keller [1995] claims seven shuffles are needed


How many bits are in a passphrase?


English text is highly redundant
some studies claim you get 1.4 bits per character
You need at least 80 characters


Bias in Solitaire


One would expect that, if Solitaire is a good CPRNG, the probability of getting the same keystream letter twice in a row would be 1/26
Crowley [2001], through simulations, found that this is not the case: it appears to be about 1/22.5
This information could, in theory, be exploited to form an attack


Non-reversibility


The cipher was designed to be reversible
You should be able to reconstruct the previous deck state from the current deck state
However, the rules allowing the jokers to move from the bottom to the top of the deck are not reversible:
* 1 2 3 4 5 6 ... 51 52 1 * 2 3 4 5 6 ... 51 52

1 2 3 4 5 6 ... 51 52 * 1 * 2 3 4 5 6 ... 51 52

Reversibility is not necessarily a problem, but reversible ciphers are easier to analyze


Practical Issues


Solitaire uses output-feedback mode:
A single bit error in the ciphertext results in a single-bit error in the plaintext (good)
Not self-synchronizing: drop a bit of ciphertext and everything after it is lost (bad)
The keystream can be generated in advance of receiving the message
Encryption and decryption are slow
Key distribution is difficult
Potential attacks based on lack of randomness


Future Work


Develop attacks on Solitaire
Develop a hand-computable asymmetric algorithm
This would address key distribution problem
You could, in theory, compute RSA by hand, but not with reasonable key sizes
(for further details, see Dave's license tag)



Other Games


A deck of cards doesn't have enough entropy for an assymetric key (237 bits)
Two decks might be enough (474 or 578 bits)
An 8x8 chessboard has 64!/(32!8!8!2!2!2!2!2!2!) 2141 states
a group in CS588 designed a chess-based cipher last year
A 19x19 go board has 3361 2572 states
Cellular automata might be computable by hand as well

PostPosted: Sat Jul 15, 2006 6:07 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

Si richj Welcome to the Shuffled thread. I guess you havent been here and unficiton long (or ever?) but that has been discused in Super great detail throught out 2 threads, please consult the Wiki for more info this is definatly trout worthy :Trout:
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PostPosted: Sat Jul 15, 2006 11:53 pm
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BBuck
Decorated

Joined: 13 Dec 2005
Posts: 184

A trout is a teeny bit harsh: can't remember seeing this site before (it's a good summary, even if it doesn't add much new).

However, in future, please either add a link using the Insert URL command or use the Code command to ensure the formatting doesn't go completely screwy. This will help keep the (second) Shuffled thread manageable. Preview is also a useful thing.

PostPosted: Sun Jul 16, 2006 7:08 am
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Grizy
Veteran

Joined: 19 Nov 2005
Posts: 89
Location: Preston, UK

Si richj,

Welcome to PXC.
If you register and login on Unfiction it gives you the option
to edit your posts.

Wink

Grizy

PostPosted: Sun Jul 16, 2006 10:43 am
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yggdrasila
Boot


Joined: 12 Jul 2006
Posts: 13
Location: Brooklyn, NY

A quick thought, that I don't believe I've seen elsewhere, and hopefully not too clueless, as I am far from a crypto and having quite a time trying to wrap my head around the Solitaire cipher. Is it possible to do the Solitaire cipher with two decks, rather than one?

I ask because on the card, the little widgety thing in the middle of the card pack graphic points precisely north-south, almost exactly from one corner of the deck to the other, and it occurs to me that a way to make two decks out of one (and thus solving the 108-character problem) would be to cut the cards in half. Presuming that Garnet was in possession of scissors.

(another possibility would be a compass direction, since that's the design, but a., the line is not on a specific compass point as depicted, and b., I don't see how that might fit in.)

One other little thing: I do note that the whispered text contains a remarkable number of the letters of the alphabet, including all the vowels. The only letters not in the sentence are "bgjkmqvxz" - it seems possible that the whispered sentence contains all the letters present in the message itself.

hopefully trout-less,
ygg

PostPosted: Sun Jul 16, 2006 2:55 pm
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justdig
Boot

Joined: 14 Aug 2005
Posts: 29

Well, my theory is that the 108 characters of text are not, in fact, decryptable with solitaire, and instead use a keystream generated by the cards. Yeah, you've got 54 cards and 108 characters. And, guess what, every card can be described by two characters. 10 of hearts is TH or HT, jack of clubs is JC or CJ, etc.

Clues supporting the theory:
-"Outside looks will leave you cold", "if you're feeling cold you're oversensitive". Sounds like seeing the outside text may actually be a bad thing. This theory uses only the inside text.

-Solution that uses playing cards.

-Will actually be solvable, no password guessing.

-Desipite all the focus on the solitaire cipher and attempts to get passwords from the whispered text, no progress has been made. That suggests that an alternative method may be needed.


Clues going against the theory:
-A 54-card deck has two jokers. My assumption is that these would be wild-cards. Or possibly JO. Something like that.

-One of the jokers had a star. This points to the Solitaire cipher. One possibility is that the text decoded using the main theory will give a clue as to a key for the solitaire cipher, which will then be used to decode the outside text. Either that or it'll just tell us about the solitaire cipher, and the eck order used for decrypting the text will be used as the deck order for deciphering.

-The existance of the outside text. This could either just be a plain red herring, as I said in my first point in favour of the theory, or it could be the text which would be deciphered using the solitaire cipher as per my previous point.



I've made a useless, messy spreadsheet which didn't really get anywhere and tried to do some statistical analysis which also didn't really get anywhere. Attempts to make a start manually were pretty useless, and I don't have the programming knowledge to do it that way. Anybody want to try a brute-forcer which will search for dictionary words and/or specific words such as "DJINN" or "WORM" or "PASS", or whatever?

PostPosted: Sun Jul 16, 2006 7:01 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

Justdig, I'm not sure that i get your theory.... Isn't solitare a keystream generated by a deck of cards? Yeah... i think it is, but decrypting with 2 decks.... hmm interesting, I would have to say no, because how would we know how mind candy did the cut count, triple cut ect. and what about the extra 2 jokers in there? unused i presume? i guess it would be a cool idea if someone could think of a way to implement it... good idea thou, i knwo i havent heard of it..


Just a quick thought, maybe due to the fact that the deck has 54 cards, and there is 108 characters, can we try to solve iit that way. Like the 54th letter, M and the 108th letter L are encrypted with the same keystream number. So can we try to crack it that way, and maybe get the keystream?? I'm not sure that'll work?
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PostPosted: Sun Jul 16, 2006 7:18 pm
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