Official help for 8b

[Anonymous]

I think it’s AES this year

[Anonymous]

The view of a parent coaching their 12 year old son…

I might be missing the point here, but I feel this challenge has gravitated toward the likes of The Times’ cryptic crossword, which requires a particular type of cerebral “wiring”, possibly at the expense of enthusing those with a desire to learn more about mathematics, cryptanalysis and algorithm design.

Please don’t get me wrong, my son has *loved* working on the challenges thus far and is keen to understand how the mechanics of the various ciphers work. I also take my hat off to those that have devised the challenges, the ciphers and the back-story.

However, taking 8B as an example, without the extensive clues in the forum, I can’t see how anyone could make the assertion that a Hill cipher is at play. Even now, it’s not 100% clear, as there’s a reasonable amount of misdirection in the unofficial posts. Assuming for one moment that a Hill cipher is being used for 8B, where does Joan’s clue of “12 is a number you may be interested in” possibly fit in? There’s also a suggestion of two ciphers being used, but the relatively flat frequency analysis of the cipher text makes it impossible to know where to start.

Back to the Hill cipher… today, I took my son through how a Hill cipher works. We then looked at matrix multiplication, GCD calculations, adjugate matrices and multiplicative inverses. Finally, we wrote some code to brute-force the cipher text using a 2×2 matrix (hey, we need to start somewhere).

The result … nothing. 456,976 possible keys (26^4), of which 157,248 have an inverse matrix and 144,144 of these can work with a Hill Cipher with a 26 character alphabet. But, non of the resultant “plain” text contains any discernible words. Back to the drawing board then.

I guess what I’m trying to say is that trying to “guess” the ciphers being used detracts from the opportunities of learning the ciphers and their underlying mathematics/algorithms themselves.

Having said all that, please keep up the awesome work of running the challenge!

</rant>

[Anonymous]

@OldManSmithers Thank you for your comments. I will make sure that Harry sees them. This challenge is made to be fun and accessible to a wide range of ages and abilities, but at some point we also have to identify the best code breakers for the prizes. 8B is always very, very tough with few clues given till the end. We hope that your son will continue to enjoy this challenge for many years.

[Anonymous]

OFFICIAL CLUE: As we are getting near the end, here are some absolutes for you. Yes there are 2 ciphers. 1 is reversal, the other can be viewed as a Hill cipher, but can also be solved without using matrices. This one has a period of 12. To solve each letter you need to know the letter immediately preceding it. Good luck, and some more clues will come out soon.

[Anonymous]

Nice to have some absolutes, surely with this I’ve got to be able to solve!

[Anonymous]

@Koala a matrix is defined as a rectangular array (basically table) of m rows by n columns.

[Anonymous]

@Koala matrices* – basically tables with numbers. I would recommend looking up videos from khanacademy to learn how they work. From what I’ve found, they are mainly used in computer science for graphics and locations (vectors can be taken as matrices).
Matrices are also ‘made up’, in the sense that we made them to help us calculate numbers faster, as opposed to 1 + 1 = 2, which is a law of the universe, and has always existed, and always will (it might change with bases such as binary, you would get 10, but the actual value is the same).

[Anonymous]

It seems to me that every 12th letter is correct due to ioc and frequency analysis (if we start counting from 0); but i still can’t figure out the function done using it to encrypt the next letter

[Anonymous]

OFFICIAL HELP: @michael1212 great observation – others, read his message above for a great clue. First reverse all the words. Then use michael1212’s observation, the word structure, words you expect to appear and the knowledge that you only need the current letter and the one before it to encipher each letter (and hence the same to decipher it).

[Anonymous]

you can use the ONE letter words very profitably as well as the likely three’s – for us, the second word was the Big Moment (as it were), although the “every 12th letter” idea had to follow a bit later

[Anonymous]

Now the difficulty is finding this secret message!

[Anonymous]

Will there be any clues about the secret message?

[Anonymous]

Don’t need clues Joan. Only needed to stop and think. Nothing more to do. Except to say thank you. It was a brilliant challenge. Thanks Harry, Joan and elves!

[Anonymous]

I completely agree! It was my first one and I was astonished at how good everything was, from the storyline to the deciphering itself, and the management has been superb!

[Anonymous]

Ok, i figured our the cipher completely now, without using matrices. Could someone explain how you would do it USING matrices? (after the competition finishes, for obvious reasons).
Thank you!

Now to find the secret message…

[Author]

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