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I think so. At least a big enough version should work. Since floating point numbers are ultimately discrete bits being switched on and off.

The and-or is applied only as the state is updated, so only two rows are involved. In the code, I use use a 64-bit integer s and run it through one of two functions parameterized by the "gate code."

I actually have experimented with XOR gates, and I thought of building the circuit entirely using NANDS. My primary constraint is that I want to use unsigned 64 bit integers to represent a layer of little gates. I started with XOR gates (1 is negation and 0 lets the input bit pass thru) and the AND-OR gates shown above (where 0 applies an OR to the 2 associated input bits while 1 applies an AND.) So I guess that NOR and NAND are implicit in that setup, because the XOR gates and AND-OR gates alternate. What inspires me is the theory of circuit complexity. As we add layers we add to the number of functions from 64 bits to 64 bits that might be computed by a random key (selection of gate bits.) If we interpret the input bits and output bits as floating point numbers, we are generating random functions on real-ish number. Anyway, the idea above could be presented via Raylib in pixels, with much more detail and more complex circuits.

Emerging Complexity requires balance, or being close to it, AND on a 50:50 infinite binary input here balanced, because for any 1 to "survive" to the next iteration it has to has another one next to it, right or left, and probability of it is also 50:50. same ill be in XOR, but then you won't see grouping of 1s, it will look more like a white noise

its allice and bob bro.

Not that I know of. I think mostly people use the same few systems, mostly to encrypt files. Like AES. Not sure what kind of things spies are doing these days, though I'm reading up on the history of cryptography.

@@f_u_m_a_r_o do you think its crackable without a quantum computer

I think this system only makes sense if you've looked into cellular automata, such as Wolfram's Rule 30. Basically it's a 1D version of something like Conway's Game of Life.

IMO, probably not, but I do think philosophy of math and logic is connected in surprising ways to theology. Godel thought quite a bit about math and God and logic.

That makes sense to me. You basically choose some number of bits for the specification of a single color (256 being a natural choice) and include enough bits for 3 color values per pixel. The only problem would be the computational expense as images get large. But on modern computers that should not be a big deal. At some point I may even code it up just to see a picture scrambled and then unscrambled. I looked up Moti. Interesting fellow. As I mentioned elsewhere, My own crypto learning is just a couple of independent studies while a math student, so I am far from an expert. But I'm a fan of the stuff and I like coming up with systems. Lately I started to think about Public Key cryptography. Very challenging. Much harder IMO than symmetric cryptography.

​@@f_u_m_a_r_o Such a system has some practical usage. In criminal investigations, specifically those relating to CSAM, this form of encryption could be used to maintain integrity of offensive and illegal materials. Using non symmetric public key architecture, the same database could be used to store both the data needed to continue criminal investigations and a honeypot to monitor malicious actors attempting to access the materials. Inspired by some of Moti's work, the system could even be built in such a way to appear symmetric to unauthorized users but instead is a tool to monitor traffic. I know most of this is just for fun, but I think you have a highly purposeful and useful system here.

@@f_u_m_a_r_o Ive been meaning to reply to this but never did. There is novel use in the application of such encryption. I would like to work for HSI, and one of the horrible parts of the job is handling CSAM(child sexual abuse material) Such an image encryption system could allow images to sit in a public database and only those with specific keys could decrypt images correctly. Asymmetric encryption would also allow specific keys access to materials to be monitored for threat actors. 2-in-1 system for public immutable evidence protection and a means to catch people who should not be attempting access. I think you have a genius idea.

I checked it out. Very cool. I've been wrestling with using CA, and I think the periodicity is a good way to get an inversion or descrambling. I'm guessing it's hard to find rules that invert, since usually information is thrown away in any kind of neighborhood rule. Thanks for sharing !

@@f_u_m_a_r_o I hear that reversibility is important for energy efficiency. And also that calculations relying on quantum mechanical effects must be reversible. But I do not yet understand how to implement reversible CA on my platform. It should be possible with the very rich rule-space (which includes access to the previous generation's states configuration), but probably none of my CA so far are reversible, as evident from the observation of multiple seeds producing the same pattern upon iteration.

@@hex-automata My understanding is that, indeed, Wolfram style CAs are not reversible, which makes sense, because they map 3 bits to 1 bit, so you are losing information. But I thought maybe you found a periodic cellular automata. Not sure I understood you correctly. But assuming one has a periodic CA, then one has found a functional inverse. Let x be a set of bits. Let f_n(x) be the application of the fule f to the seed x performed n times in a row. Then if you can find some m such that f_m(x) = x, you can decompose f into functions g and g_inverse. If I understood correctly, you encoded "hello" with such a periodic function. That appeals to me because I am very interested in using Wolfram style CAs in crypto. The ones used above are not Wolfram style, because they map n bits to n bits. I have thought of some systems that use Wolfram style CAs. And they work. But they don't work by inverting the update rule. But theoretically there are rules out there (which maybe you've found in the hex situation) that have some fixed period. Ideally they'd need the same fixed period for every input x. One could search possible rules for this periodicity, but it would be computationally expensive. You might be stuck with messages of maybe 16 bits.

I think other systems do already have that feature. But I liked finding another approach to the same clever idea. In larger versions of this system, you could encode an unknown number of plaintext messages in the same ciphertext. So you could potentially have 2 or 3 "fake decryptions" available, which you might choose from depending who was forcing you to decrypt your file. Basically the only constraint is memory. But for small files (like text files) this wouldn't be a problem at all. You are basically increasing the file size by a factor of n (so only a linear increase).

Very interesting. I was thinking on "how can we make the encryption less expensive than the decryption". But then I realized that we are picking arbitrary spots from this matrix. Those voluntary spots would act like the "private key". We then advance time for a given large enough "N". Since the spots picked and time skipped "N" are not known, it increases the computation required to decrypt by an exponential lot. To advance the time on the Automata requires as input all the elements of the current time. So it can't be parallelized that easily. Meaning a quantum computer may have a hard time computing something with large enough parameters. But there is also the risk that something too hard for quantum computers to decrypt may also be too expensive for computers to encrypt. It definitely is a step in an interesting direction though. I wonder how do we advance this further? I'm not an expert on the topic of encryption and quantum computation. Just worked on it for a while.

@@rumplstiltztinkerstein Actually we aren't picking spots, though that would be an interesting approach. ( I may be misunderstanding you though. ) Here we just load the cube with whatever the plaintext is. The key is just the set of update functions for each dimension. An update function is just a random 1-1 invertible function on the integer values of rows, cols, etc. We basically apply these individual functions in an intensely entangled way. After N steps, we have the cipher text on the cube. Then someone with the key is able to undo all the transformations, run the CA backward. I think of these update functions as the "reversible CA rule." I agree that it looks hard to make parallel. Which I think is a good thing as far as untangling the cipher text goes. If someone REALLY wanted to use a system like this at high speed, I suppose they could build "tesseract chips" that compute an entire dimension in one sweep. Because you CAN parallelize that part. The rows are updated independently. But then the column update diffuses the rows into one another, and so on. I think a specialized chip could encode in 4 steps per round. But I'm not an expert on this stuff. I went to school for math, took a couple of independent studies with a specialist, but that's it. How to advance this further ? I THINK this particular framework can be generalized to n dimensions. What might be fun (if possible) is bringing in complex numbers (Gaussian integers) or maybe even quaternion integers. It would also be easy to switch to some other base, like base 3 or base 10 or hexadecimal. quatarnians

@@f_u_m_a_r_o Interesting. I'm a software engineer only so I'm not very familiar with the mathematical concepts themselves.

@@rumplstiltztinkerstein I'm more of a math person who codes on the side, mostly to see certain ideas worked out at high speed. nice thing about crypto is that the math is very concrete.

Basically it's one more symmetric system among others. So you could encrypt files, trade secret messages. This "toy size" version encrypts 256 bits at a time. You could something like this to process blocks and create an encrypted chain of blocks, so that you can encode large files. But you'd want a bigger version of this idea, so that there are too many possible keys for a brute force attack.

Yes. One could use it to encrypt files locally or to exchange encrypted messages with friends. Basically you create a key, and whoever has that key can encrypt whatever messages were encrypted with that same key. ( You'd want to use a bigger version than this "proof of concept" demo. )

Thanks ! I'll check it out.

xD

I was going for something vague and suggestive. Horror is in there, but I was also going for a transcendent / detached vibe. Maybe the videos are (lots of them) metaphors for the cosmos as a kind of machine or wheel.