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Cipher Challenge: The Secret Code for the Wish Box | technology


Centuries ago, Tercia Land was divided into five kingdoms, Kingdom 1, Kingdom 2, Kingdom 3, Kingdom 4, Kingdom 5. The borders between their lands crossed at the cube top, inside the magical forest, guarded by a forest wizard. After many years of constant war between the two kingdoms, a long period of peace finally followed, as the wizard of the forest created a magical potion that would grant anyone who tasted it any wish. To protect this dangerous force, insert the dose into a box, and close it with a digital lock that can only be opened by entering a secret number. Then he called the heads of the five kingdoms, and spoke to them thus:

“Inside this box I placed a potion that grants desire to whoever drinks from it. To open the box, it is necessary to know a secret number, I will now give you a number fragment for each other. Every time someone drinks, I’ll come over to change the pin and give you new shards.

Hope to cooperate; Because it is necessary to combine at least two parts to find the password:

Look, my friend, we have a crossroads ahead

Vertical one, from top to bottom

Another horizontal, left to right

Your crossing is a double zero.

Let’s start from your point of view,

Let’s meet on the vertical path,

And let us consider how far the crossroads lies; He said the distance will open this chest

And so he gave each kingdom a part, which was no more than a pair of numbers: for kingdom 1, the part (1,4) corresponds to kingdom 2 (2,1), to kingdom 3, (3, -2) ), to Kingdom 4 in (4, -5) and to Kingdom 5 in (5, -8).

Within several months, the wish box had not been opened. During this time, more than one commander, hungry for a certain desire, cunningly tried to get the secret from his sliver on his own … but without success. However, the fateful day came when we coincided in Kingdom 2 and Kingdom 5, two evil leaders. Both sent mathematicians to Cubic Peak, who soon found a way to calculate the secret number: the parts were points on the XY plane, which, of course, marked one line. If the two kingdoms are there, the parts (2,1) and (5,-8) mark the straight line y = -3x + 7. This “secret” straight line cuts the ordinate axis (the vertical path, the OY axis, where x-values ​​equal 0 ) at the point (0,7). Therefore, according to them, the secret number that would open the chest was 7, because 7 was the distance of the secret line point from the origin, which was only the point (0,0).

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In fact, they tried number 7 and unlocking. The leader of Kingdom 2 took a drink from the potion and asked to keep the harvest of Kingdom 3.

Then the wizard of the forest appeared to close the box with the potion and change the secret code of the lock. Then, the leaders gave the new parts: to kingdom 1 part (1.15), to kingdom 2 (2.17), to kingdom 3 (3.19), to kingdom 4 (4.21) and to kingdom 5 (5.23).

The leaders of Kingdoms 1, 3, and 4 moved quickly and agreed to make use of the Wish Box before the malicious Kingdoms 2 and 5 did so again. Collecting the fragments of Kingdom 1 and Kingdom 3, they find the number secret and ask that the chest not be opened again by the alliance of Kingdoms 2 and 5.

The wizard of the forest immediately appeared, summoned the leaders of the Five Kingdoms and spoke to them as follows: “From today you will need to combine at least three parts to find the secret number and thus be able to open the wish box.”

He gave Kingdom 1 part (1,22), Kingdom 2 (2,29), Kingdom 3 (3,32), Kingdom 4 (4,31), and Kingdom 5 (5). , 26).

Over time, Kingdoms 2 and 5 overthrew their evil rulers. The leaders of Kingdoms 1, 3 and 4, thinking about creating a global alliance, decided to climb the cube top again and ask the Wish Box that from now on, it will be necessary to merge the five parts of the Five Kingdoms in order to open the chest.

What secret code did kingdoms 1 and 3 use to open the chest and claim that the evil leaders of kingdoms 2 and 5 can’t do that anymore? What secret code will the three cooperating kingdoms use the last time to open the wish box? How would the wizard of the forest now be able to order five pieces to open the chest?

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Crypto challenges will be posted every 15 days (although we were late in this latest batch, we apologize ;-)). Readers can leave their solutions and discuss the problem in the comments on this page, so anyone who wants to solve it on their own is advised not to read it until the puzzle is solved. You can also email your responses [email protected]. In each new challenge, we will post the previous solution, along with a comment with some of the original or inspiring ideas we received.


Javier Herans He is a researcher at the MAK Group and Professor of Applied Mathematics at the Polytechnic University of Catalonia.


A solution to the previous challenge

The previous challenge was related to visual coding, an area initiated by Israeli Adi Shamir (S for RSA Encryption System) in 1994.

The answer to the first question – what message is obtained by overlaying the first transparency with the second proposed – is that instead of a white A on a black background, a black L on a white background is obtained. In fact, with a certain transparency, any image (with the same definition quality) can be obtained using an appropriate second transparency.

In the second exercise, the image that is restored if 1 and 4 or 2 and 3 transparencies are grouped together is:

Our readers, like (usually) Joaquín and Javier, arrived at the solution without using the “analog mechanism” suggested in the text, using different code to combine and then enhance the images.

On the other hand, something similar to what was suggested with the images in this audio challenge could be done (as suggested to us by Ramiro in the mail, and Salva Fuster from the comments section). Indeed, we are reproducing his musical challenge, in case someone still dares to solve it:

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An inescapable word with a small musical touch (sometimes dissonant) in two sounds:

To: GDBAB – DBDGD – BABDB – DGECB – CECEG – ECBCE – CEGFC – BCFCF – GFCBC – FCFGG – BABGB

B: FEEBA – EEGFG – ABEGE – ECAFE – FFBAF – FBCBF – BFFGF – EBBBB – FGFCB – GFBFC – ABAAA

– What melody acts as a key (keep in mind that the letter F in the key is actually an F)?

– What is the hidden word?

– What is the system that allows the message to be encrypted/decrypted?

The phonetic method is also described in the article Audio and optical coding, proposed by Desmedt et al., at the ASIACRYPT 98 conference. The reader also has an online demo linked to the scheme described in this article at this link: https://crypto.cs.jmu.edu/visualaudiocrypto/AudioCryptography. html

index:

-101 Computing: https://www.101computing.net/visual-cryptography/

-Douglas R. Stenson: An Explanation of Secret Sharing Plans. dis. Cryptogr tokens. 2 (4): 357–390 (1992)

– Paolo Darko, Roberto de Brisco: Visual Cryptography – Models, Issues, Applications, and New Directions. SECITC 2016: 20-39

Giuseppe Atenes, Carlo Blondeau, Alfredo de Santis, Douglas R. Stinson: Visual cryptography for public access structures. informations. 129 (2): 86-106 (1996)

– Moni Naor, Uday Shamir: Optical coding. EUROCRYPT 1994: 1-12

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