# Can you solve this Playfair cryptogram and set a new world record?

Today I’m presenting a 24 letter message that has been encrypted with a Playfair cipher. Such a short Playfair cryptogram has never been solved before.

In December, I reported on Konstantin Hamidullin’s solution of a Playfair challenge I had published four weeks earlier. With only 26 letters, this cryptogram is the shortest Playfair message that has ever been broken.

### Playfair cipher records

Konstantin’s deciphering success was already the fifth Playfair world record set by my blog readers. Here are the four previous ones:

In all of these cases, a Playfair cipher with a random matrix (i.e., not based on a keyword) was used. US cryptanalyst Alf Monge broke a 30 letter Playfair back in the 1930s, but this one was keyword-based, which made things easier.

According to George Lasry, the unicity distance for a Playfair cipher applied on an English text is 22. This means that a ciphertext of 22 letters or shorter does not have an unambiguous solution. If the ciphertext is longer, a unique solution exists and can be found – at least in theory.

Hill climbing appears to be a good method for breaking a Playfair encryption. George, Nils, and Magnus used this technique for their record-breaking cryptanalysis successes. Their work has considerably improved the hill climbing methods applied in codebreaking. To my big surprise, Konstantin didn’t use hill climbing when he set the current record. Instead, he conducted an exhaustive search with several optimizations. Each solution candidate was checked with a fitness function.

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I’m excited to announce I’ll be speaking at RSAConference 2020 on UNDERSTANDING AND EXPLAINING POST-QUANTUM CRYPTO WITH CARTOONS.
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### How the Playfair works

I’m sure that meanwhile most readers of this blog know how the Playfair cipher works. For those who don’t, this section gives an introduction.

The Playfair cipher substitutes letter pairs. So, the cleartext needs to be written as a sequence of letter pairs (the following cleartext is a Shakespeare quote taken from Robert Thouless’ life-after-death experiment):

BA LM OF HU RT MI ND SG RE AT NA TU RE SS EC ON DC OU RS EC HI EF NO UR IS HE RI NL IF ES FE AS T

The Playfair cipher requires that no letter pair consist of two equal letters. Therefore, we add an X between the two Ss:

BA LM OF HU RT MI ND SG RE AT NA TU RE SX SE CO ND CO UR SE CH IE FN OU RI SH ER IN LI FE SF EA ST

If the number of letters in the cleartext is odd, another X needs to be added at the last position, but this is not the case here. Next, we set up a 5×5 matrix containing the letters of the alphabet in a random order (we identify the J with the I, in order to get a 25 letter alphabet):

```S U R P I
E A B C D
F G H K L
M N O Q T
V W X Y Z```

As you might have noticed, the letter order in the matrix has been derived with the keyword SURPRISE. It would be more secure to use a completely random order of the letters.

Now, we replace the cleartext letter pairs (BA, LM, OF, HU, …) according to the three Playfair rules. Here are the rules in a diagram:

Here are the same rules in text form (I refer to the letter pair to be replaced as XY):

1. If X and Y are not in the same column and not in the same row (this is the most frequent case), form a rectangle and replace the two letters by the other two corner letters (the upper cleartext letter is replaced by the other upper letter in the rectangle, the lower cleartext letter by the lower one). For instance, LM becomes FT.
2. If the two letters stand in the same row, each one is replaced by its right neighbor. Here, BA becomes CB.
3. If the two letters stand in the same column, each one is replaced by its lower neighbor. In our example, AN becomes GW.

When we apply the Playfair rules on our cleartext with our 5×5 matrix, we get the following ciphertext:

CB FT MH GR IO TS TA UF SB DN WG NI SB RV EF BQ TA BQ RP EF BK SD GM NR PS RF BS UT TD MF EM AB IM

### A new challenge

After my 26 letter ciphertext had been solved by Konstantin Hamidullin, I created a new challenge based on an even shorter message. This time, I chose a ciphertext consisting of 24 letters. As usual, I used the Playfair function of the software CrypTool for encryption.

Here’s the ciphertext I received:

VYRSTKSVSDQLARMWTLRZNVUC

Can you decipher this message? If so, you will set a new world record.

Edited to add: The ciphertext I presented first (BZR…) was wrong. It contained a J, which is not possible in the standard Playfair cipher.

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## Kommentare (10)

1. #1 Betacam
30. Januar 2020

OFT HILL THAT ED THE SAND TOSH

2. #2 Klaus Schmeh
30. Januar 2020

@Betacam: This is not correct. Sorry.

3. #3 Narga
27. Januar 2021

Happy birthday, 24-letter Playfair challenge! 🙂

Here are some highlights from my output file:
``` KEY - SOLUTION```

``` ```

```YOQWBXFDTRHIUMLPCNSAGVKEZ - GOT A DECENT BULB TERM BACK IN ZUTEYBMSLWDNARKGCVQIFOHXP - ITALY AT A BAR ENABLES DEACON EZOSVYWLDNKXCPMBFIHQRGUTA - ENTER POSTS IN TAX NUDGE VAIL YWBIQCADMSRHXEOUGKFZTVPLN - TWO CPU AN MAIN CHAIN POULTRY EYBVPOCKFHWAQDGXRITLNSZMU - BEAR IF MY MAGIC AND IT IS MESH WVFIPTQBELOUZKMDSNYACRXGH - ISSUE OUR DATE SHOP LEXUS FOR KZYXUGWLEDANVPIFBMQHTROSC - LOT OF TOP CEMENT BLOG BRANCH GBVEYNFOWMZXQHIDCTSRKPAUL - BEST DATE TRIAL TWO RADIO GPS RGNLVAUHDCYXZQIKWOMBSPTEF - RISKS OF READER SO KENNY GLAD NLVITPDBMKYCOWEZASUHGRFQX - NO FAX TO FABRIC AIMING AT LAW PTGWCIQZAXYVBREKOMSUFLHND - YEAR POOR UNTO WAS GLOBAL RED BVRIGMOSUPQCZNHDKWFXYEATL - BE A REFORM WHY WAS DATA SCION INVLARXESTZGMDPQBWKHUYOCF - NOTE SHELL SKI ITEMS AIR INFO HXCFQGTSVENDOULPIKYWBZMAR - FUMES IT STORE MARKED A BUG OF TAMXOSLGIYREDFKBQWPZCUNVH - HISTORIC GREAT END ASK BUNCH YEVWLPXIMQRCSGFODUKAZBNHT - ELF CHAIN CULT OF WHAT POUNDS KFYQIBLHOVWEDSCAZXMRTUGPN - HIM CAT CODE FORM A SUBMARINE ILDBQVTASRMGHZFOYWPNKECUX - TO SAVE A RABBITS HOLES FORCE UQTAXIBKGWDMVHEYSOCZPNRLF - DONOR TO MY MANTLE BAR FOR MAY WZBXOVHSEADKIFUPLYGRTNCQM - SPY AND HAVING OUT ON PLOT HIM IXLCYQHPDABKORSGFZUVMEWNT - STORES AS RAPID STEW YOU TURN BEDYCWUGITSVMRAZFQPXHLOKN - REMAIN AS MB FORMS GUNS PLATE ZXEPCDOGLRNMUKITSVAWFQHBY - WHO WANTS TO BOWL IS ADD CUTIE MVUGOKETSRIHXDNFQPBWYALZC - MASTER EGG SPACE OF UP SCHOOL WDTLYUASRKNZHXGEFVCIOBPMQ - IT SAYS THAT MY US OLD TAX HERE XKMNPELQBOSARTCYHFIVUZDWG - I VACANCY RULES AND A BAD PIGS EGSMVWHRBZCIFQODKNYUPATLX - MUSTANG MEN BY THE BATH BUS DO NYOVGAMRQKWPZHESXBITLUDCF - ON A BEGIN BLACK MAPS FOR GOLD QKPZNDOYCTEVBFSLAXIRHGUMW - BOSTON FEET HELIUM DRINKS MY ```

but no convincing winner so far 🙂
I think those won’t score far from the actual solution’s value (with standard scoring solutions) and thus there are many high local hills for algorithms to climb (or basins to hop into) instead of the correct one.

4. #4 farmerjohn
27. Januar 2021

Happy birthday:)
Here are some of my favorites:

and perhaps he’s collecting
they say the liquor had gone
the name of springtime leaf
he counted companion boats
you’re confusing dark grapes
dear me did not fall heavily
Basil has a very short space
he counted companion goats
you’ve met the pointed boots
I came to an English diabolo
I do wish those forms of wine
say nothing but a form advice

5. #5 Klaus Schmeh
28. Januar 2021

Interesting guesses, but none is correct.

6. #6 Narga
28. Januar 2021

@farmerjohn: Those are so much better than mine. And fun to read, too! Plus the short length adds a whole new “plausible denial” feature to Playfair encryption: “Tanks and planes? No officer, it’s just an order for Port and Sauternes. Your key is all wrong.”

7. #7 Gerd
28. Januar 2021

Very interesting results. Isn’t that a proof that it is ambiguous even with 24 letters instead of 22 ?

8. #8 farmerjohn
Riga
5. Februar 2021

@Gerd
Probably yes, and so a very good scoring function working at word level is needed. For example, clearly legitimate result “Thank you Iacob. We’re in Rome” was way too far from the top in my list…

9. #9 Richard Bean
Newcastle
26. April 2023

Here are some of my guesses. At this length, even choosing only “stand-alone” messages with an imperative tone and generic phrases, there are many plausible possibilities. I think the starred ones are more likely.

your emotional after Athens
dispatch the networks eggs ***
host emotional after Athens
want presenting person ask ***
yes Alice protesting halls
again stations arent match

offense strategy in the sun ***
featured as no longer lives
never described him it shows
hope might have asked aloud
woman said the Pacific poem
boy back burned the details
iust ask Simon the Catholic
never described for its God
hope might have asked proof
abide said the Soviet group
policies began after all ok
behind is the glowing asset
you tended the larger units
yes human rights your point
use phone instead of tableau
CIA record one was pleasing

page of equipment in the vase
game plan on the first iudge
improve if you had to Marvin
someone say their in the KGB
knew had all the white money
trying it is the monster two
someone said help in the kai
pascal here on the first key
gesture perhaps he cant do it ***
gesture perhaps we cant do it ***
guarantee soft and in a bunch

10. #10 Richard Bean
Newcastle
17. Mai 2023

And a few more

Yes had completion in the MiG
West in terms of the said bank
It’s okay in the building shop ***
I cut something up and admire
Belong to this works for some
HIV positive chances Andrew
I stone people who are not big *** amusing
Case asked for the girls a boy
No it’s list of the best change
On orders of the same to vinyl
Spy out of action winter pays