In the of the analysis, we will bring back the that play on the ZKP stage. The part is dedicated to showing the “ ” of the ZPK scene. And , we will appeal of “possible” luck from the intruder. Now, let’s present the nature of the abstract and let’s unfold its mysteries. first part actors second magic thirdly rare probabilities Abstract We’ll be using an as the on how to open a mystical door. The nature of the abstract is to turn (such as left/right) into . The mechanism movers are unique to each instance of opening. The the of the structure to the shared . The abstract works when tangible and intangible . The abstract is an which ties them both together to form the . If you play with and have of the ones, you will have chances of the key. Imagine guessing the position of an respective to an . abstract shared knowledge decision gates mechanism movers abstract connects tangible rules intangible knowledge only both exist upper system tangible rules no knowledge intangible close to 0 guessing unknown number x unknown group of y numbers Part 1: The actors As the curtain rises, it reveals to us 3 actors. The is the and , is the and and is . When describing them, the aim is to provide a clear and structural analysis of them, any information regarding the . I will only refer to it but not provide any information until the second part. door giver of access holder of the lock Lisa opener bearer of the key, Bob the verifier outside structure of the lock The door The door is the of the abstract . In its internal knowledge, we find the logic and of the lock. The refers to the required to open each to the by the . Those locks after each opening, ensuring that any given by Lisa can be used for the (which will be passed after a failed/successful attempt). bearer lock hard-coded structure abstract system comparing internal steps individual lock information presented opener iterate successful information strictly current lock If a is reached, because Lisa made a and the , will begin and Lisa will have to provide a based on her knowledge of the . Based on its , the door will depict whether Lisa holds or not the key to enter. critical point mistake passed opening point another lock iteration new key overall (abstract) system internal gears Lisa Lisa, as the bearer of the key, holds knowledge of the and the structure. She knows the of the lock and will her knowledge of that in the form of to the door. She will the lock as if it in front of her. Stating movements such as l which will be the the door will receive and the of the lock accordingly. Once Lisa is sure the lock is in the position, she will state the and . internal system current lock’s limits present logical reasoning imagine opening sits eft/right input adjust internal gears open current key end communication value Bob Bob, as the verifier, can form the of a . Let’s say that Lisa comes and a conversation with the door. She will further state: Left, Right, Left, Left, Right, Right, Right, . After which, she will . Bob now knows how to open of the door. However, has a distinct route to be taken. image potential lock initiates Key end communication iteration 1 iteration 2 As the day passes Bob gathers the information about how to open all . Now, the comes into play and all the 500 iterations. The next day, becomes of the . Now, the will play a crucial role in of guessing. 500 iterations system shuffles Iteration 1 any other 499 logic of shuffling reducing the probability Remember when I said “One could always check the security by checking the memory. Then, questions about gibberish memory come into play to scare off the intruders who may want to bypass. Alluding later to the sense of courage and self-esteem as you broke down 1TB of key complexity.”? For this system to work, it requires that and the have a kind of inside them. of the Door allows for each lock to be and later . Now, the shuffling can come each day or based on . So the door also has to have some kind of (which I will further call the reason of the system) of . both Lisa Door computer Memory uniquely stored shuffled manually algorithmic logic logic shuffling Lisa and all other authorized personnel could very well gather their knowledge of from a “Headquarters”. today’s lock system Or they could have as the Door inside their heads in the case we to create a headquarters. similar shuffling reasoning do not want This allows for both and storage and interactions. A headquarters will allow to gain access. No headquarters would mean that only would be able to open the door. centralized decentralized new personnel limited predefined personnel Both avenues open deeper implementation as a as it could allow to be granted access by providing her with a . decentralized system, newcomers by Lisa unique encrypted key But now I may get too far ahead of myself. Let’s see how the is made. abstract lock Part 2: The lock Maybe is the simplest part to understand. proving it is, however, out of my reach and expertise, but I will try to provide a clear and structural analysis that could allow for mathematical understanding and implementation. the lock Mathematically 1. The prime-nonprime lock system. 1.1 Prime-nonprime lock cipher The cipher at play is made out of . two sets A set of only numbers and a set of only . prime non-primes Both sets have an . equal number of elements Each set can start at an number as long as the . arbitrary previous rule holds true , the set will obtain ‘ ’ as its , whereas the set will obtain ‘ ’ as its . After they are formed prime 3 last element non-prime 2 first element So we have: Prime=[prime, next prime, next next prime…(30 times),3] Non Prime= [2, NP, next NP, next next NP… (30 times)] And pretty much this is the lock. 1.2 Cipher interaction Let’s suppose Lisa comes and tries to unlock the door. We assume that she knows the and (except 3) are in the set. As well as non primes. She knows (except 2) and we find out she how many non-primes there are (we do not want to waste information on what is locally known from the primes set). first prime how many primes the first non prime already knows So the of each or will require knowledge of the from and the from (All the primes and non-primes that exist in math). To later it to the required which to the set of the (which only the authorized personnel will know of). internal knowledge opener intruder set of primes x to y set of non-primes x to y adjust parts correspond actual cipher So Lisa knows supposedly all primes and non-primes. Both up to infinity and divided in the required by the . respective set current lock She, as the authorized personnel, will know that of the starts with the and has (+3 at the end) and the starts with the (+2 at the beginning) and holds 100 (+1) non-primes in total. iteration 1 prime set 30th prime 100 primes non prime set 100th non-prime For a very basic interaction, I will present to you and their interactions with . The text is what know of. The is what is , what Bob can hear. both sets Lisa bolded only the door and the authorized personnel italicized text given outside Iteration 1: Prime set = [5,7,11,13,17,19,(3)] Non Prime set = [(2),4,6,8,9,10,12] Lisa comes to the door and states: ‘ ’. This is the . Now, the door knows that Lisa is aware of . 2,3 initiation both locks inside The process of opening starts. The ‘selected’ prime is 3. The ‘selected’ non-prime is 2. (This is a rule of the internal logic) Lisa says: ‘3, left’. Now, the gears of the prime selection turn to 19. ‘2, right’ The gears of the non prime point now 4. ‘3, left’ (17) ‘2, right’ (6) ‘3, left’ (13) ‘2, right’ (8) Lisa says: Now, the lock has reached a middle place, 13 is selected as the prime and 8 as the non-prime. Lisa has to state their difference (5) and end communication with the door for the door to run its own rules and check. ‘5; 3,2’. Now the door will run internally and check the difference between the middle numbers of each set, if it corresponds to the number specified by Lisa, access is granted. If Lisa however fails, another iteration begins and Lisa has to take a different route. This new deeper layer of failure requires both centralized and decentralized systems. If Lisa was sent from the headquarters and only knew how to open iteration 1, she would have to return to regain information about the second. If the iteration is based on a rule of background iterations (in the case of repeated failed opening), then the iteration will turn instead of 2 to 1.1 iteration. Assuming that Lisa also gained knowledge from the headquarters on how the lock will change in case she fails to open it. (Assuming the cycle doesn’t repeat) At iteration 1.3 (after 3 failed attempts) the pace of the “left/right” decision could turn from 1 step to 3 steps and the newly introduced sets will have a total number of 3n+1. Ensuring that no matter how hard you try, you can never select the middle point of the sets. Who knows however if this is necessary. If we allow the locks to repeat themselves we could envision such a protection: After you state “left” when you are positioning the prime selection and you are located at the first prime, you will be sent back at 3. This would assume you are also positioned at the last position of non-primes and thus, stating “right” would turn you to 2. (Or we could never tell the opener that they failed so they will infinitely try to guess, but that of course, would give of no knowledge of whether someone tried to enter and failed or not.) The ‘3,2’ state was achieved and no key was mentioned so the input was wrong, access was denied and the iteration moved to the next lock. 2. Metaphysics (Creativity/Imagination/ ) vs Mathematics (Present state) Possibility The and seem to . What does that mean? It means that we could use and to stop any “ ” or avenues that aim to break the system. It’s not a problem of , but one of of the set limits. Even if you know you can do, you can never know if that 1TB holds 1000 sets of 20 to 1000 numbers of 100 sets of 10.000 numbers. And thus, Especially since those 10.000 numbers could very well be sets that follow one another. possibilities of interaction security measures stop at the power of imagination (endless routes could be taken) reason hidden information creative newly taken computational problem prior knowledge all the actions you will never know your starting point. I will present a view on “cipher interaction” depicted with the help of ChatGPT. (I will lend my personal view in bold and italicized) “The mention of "the power of imagination" in the context of interaction and security measures implies that the system's robustness relies on the ability to anticipate and counteract potential creative or innovative attempts to breach its security . (Any route taken, no matter of creative or smart it is, is not tied to the “ground-truth” knowledge of the system) It suggests that the system designers have incorporated elements that make it resistant to unconventional or unexpected approaches by leveraging reasoning and hidden information. In practical terms, this means that the system is designed in such a way that even if an attacker tries to think outside the box or employ novel strategies to break the system, there are safeguards in place to mitigate such attempts. These safeguards may include: : The system's structure and rules are sufficiently complex and dynamic, making it difficult for an attacker to predict or exploit weaknesses effectively. Complexity : Certain critical information about the system's configuration or operation is kept hidden or encrypted, preventing attackers from gaining a comprehensive understanding of the system's vulnerabilities. Hidden Information : The system can adapt or evolve in response to emerging threats or attack strategies, ensuring that it remains resilient over time. Adaptive Security Measures : Attackers are constrained by their prior knowledge of the system's set limits, preventing them from exploiting vulnerabilities that they are not aware of or cannot anticipate.”- ChatGPT Limits of Prior Knowledge Imagine that you are playing chess. However, you can’t see your opponent’s pieces in exchange for him not seeing yours. This play state could be akin to You do not intend to be offensive at all, in the exchange of being private and aware of your flaws. everybody minding their own business. If during the state of the game, any player sees only once the position of the pieces, then that player will gain relevant irreversible information of position. Without it… who knows how many chess boards are between his pieces and your king. Part 3. The Luck of opening such a system I want to first mention that everything I wrote is simply an idea. Until I see it in action, I will disbelieve it as true. And even if I see it in action, who knows if I will believe it to be the true case. I will still require knowledge of the background sets to know what the opener has done. Now, what do I mean by “Luck”? Let’s turn back to another story. “What can we say about “efficiency” when it comes to our safety? Our long-term health and well-being? Why does “efficient” sound a little too rushy here? Because here, we need proof. We have to be sure as our health is at play.” It indeed seems like has a aspect to it. How could we tie efficiency to our locks? efficiency rushy Well… let’s say that the door only requires the key ‘ ’ and the ‘ ’ ending to open. All the internal structure will itself to the middle of the sets and check. This way, we would the number in novel ways. Lisa could simply state “ ” which for the door would mean “ ” and if the difference between the middle points is indeed 51, access is granted. X 3, 2 run encrypt abc 51 I assume that this approach could offer the same kind of information as before. But then, wouldn’t there be the possibility for someone to get that information out of Lisa? I mean, if they know towards which door she is going they could simply go there, and… maybe we could even implement more doors in this case. What if the quantum world is guided in the end by the classics? I don’t know if it’s just me, but I believe that there exists a . A specific Mathematical that, as long as it is , could drive us into of paving a path for . Like the distribution of primes. Each time you get to a , the pattern , but, it . specific system process kept hidden endless ways true privacy new prime overall changes the slightest changes Based on what we see, 2,3,5,7, and so on, those , of numbers out of the . first prime numbers cut a lot natural number line The the primes we find, the the numbers they . Yet, when talking about , isn’t the same as the part? bigger less influence infinity half 1000th Personal Infinity Could we form a “ ” that works as our ? personal bounded infinity workspace The is and to that . If know those , then only we can depict that to at the to it. overall change static tied infinity only we boundaries overall change stop last prime required exhibit The of someone the is very low since they have to take into account the (Which are at and (but serve as guiding rules) in the process of ). The simplest form of drawing a line is placing 2 points and connecting them. chance exhibiting exact median change starting and end points given among authorized parts creation hidden interaction Now the question comes: Could this be some kind of axiom in math? Or a rule that quantum mathematics could follow? When I say quantum mathematics I mean the interaction between two distinct points of view. Those we have to find the between them, knowing about the , or of the in which they sit. (Those points however cannot move as it would require a meeting and re-organizing among the authorized personnel) two points measured distance nothing shape size, color space Part 4: The synergy Now, extended to people, this space could be comprehended and understood. When it comes to AI or any other computational rule, it can only be analyzed. But what if there is nothing else to analyze except the existence of those two points? Even people peaking into the play cannot see the system. This could be a point where we could ensure protection through a form of “limited” consciousness. Understanding of the system itself (which is different from self-understanding). Mathematical rules of a circle, reflection, inner, out, and so on, all enveloped to form a limited self-awareness. With the lack of human power (acknowledging it can be more) the system will remain forever overall static. Even if the rules that guide it are moving and shaping interactions and outcomes. If those two points were to be humans, their unique perspectives would allow them to potentially observe one another and find smart ways to guess the difference between them. Maybe, they could never guess the exact classical value. But that act of guessing could be akin to seeing the rules. Bots would remain stuck there. But humans could draw. Even if we use sophisticated AI for Lisa, the Door, and Bob, they will still not be able to arrive at a conclusive judgment as there will always be insufficient information. If I am to sum up the whole article in a single phrase, I will say: Bots in the end could create the fastest algorithms we’ve had, but they could never surpass our creativity. I mean… it’s important to keep dreaming. The future looks amazing. But there’s still a lot of work to do x.x (This article is dedicated to Dan. Without your help, my schedule (and also my mood) wouldn’t have allowed to me focus on all those points. Thank you!)

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