It's quite clever, but I think the pedagogical function is questionable, because I don't think that the geometric interpretation will be particularly clear to players who haven't read these articles.
The idea of the game seems to be to show people that public-key cryptography exists and can work, yet the actual method of creating the public and private keys (and the fact that the public key can be created easily given the private key and not vice versa) won't be especially obvious.
Indeed it was our idea; with the opportunity for the most curious players to learn more about Crypto, Algorithms and Math. The articles (and the whole "documentation" menu) are for the curious kids (of all ages...)
After 24h hours the game is already a success. I will for sure put a lot of effort in getting the game translated !
I think it's excellent to try to find new ways to explain these concepts. Do you think there is a path for an ordinary player of this game to come to perceive more about the properties of public and private keys, and especially how the two are related to one another?
Add this to that the fact that we need to try not to lose the player's attention so he won't get too confused by too much information.
In the dialogs, we first explain to the player that we need to create him a username, a private key and a public one. Now the player gets too chose his username, and right after that we generate a random private key (well not exactly random, in fact we randomize a pre-generated private key so we can be sure of it's properties, otherwise the player could get hard times decrypting).
Once the private key is generated, we get the player to create his public key through scrambling and mixing the private key.
During the normal game, we add an extra check to make sure the private/public keys matches the ideal properties we need for our demonstration: we want the player to play with a simple public key and the AI to play with a strong (kind of) public key, in the game this translates to one column significantly 'bigger' than the others for the private key and more than one 'big' columns for the public key.
We only constrain the public key during the game's story mode, in arcade one can chose to create a 'weaker' public key ("Arcade" > "création des clés"), then let him play the arcade boards with it.
Additionally, we allow the player to chose who plays with what, so both the player and the AI can play with private/public keys.
So I really think all the building blocks are already in the game + arcade mode. But we need to admit that most people just skip dialogs, no matter what.
Well, the fact is the player builds itself the public key from the private key at the beginning of the game, somehow choosing itself the randomness used in the key generation process. I was hopnig this gives a bit of an idea that public key is derived from private key.
In that sense the public key is a "mix" of the private key. Then the cipher is the message plus a "mix" of the public key. By transitivity the cipher is the message plus a "mix" of the private key; and the private key is simple enough so that it can be "unmixed"...
Somehow playing a variant of tetris explains public key crypto.