A Prototype for Quantum-Secure, Mathematically Uncrackable Encryption Streams

By felix / 18 August 2024

Alternative title: Why One Time Pads are impossible within the universe.

Abstract

We present a prototype of a novel encryption scheme, designed to be a quantum-secure and mathematically uncrackable (given a perfect random seed) scheme that can prolong a One Time Pad (OTP) indefinitely by reconstructing new keys using contextual knowledge available to the receiving party. The scheme leverages a unique combination of one-time pad encryption and a reconstructive hashing mechanism to create a stream cipher where the hashed key is brute-forced and verified on the client side using existing knowledge. The sacrifice is in the potential for infinite false positives leading to the need for infinite computing resouce to decrypt, not the security, and the general need for more resource and bandwidth for the connection (3*data). It’s security significantly not compromised by potential false positives in decryption given even as few as 3 random seed chars. Therefore, the insecurity of the scheme is closer to the metaphysical domain than any viable mathematically definable dimension. However, the same insecurity is true for any OTP possible within the universe, unless it is transmitting purely random data. False positives are mitigated to a potentially usable level through contextual knowledge, continually saved until the message is complete. For any non-infinite message there is always the possibility to decrypt, given appropriate resources. This makes any message that is under a certain size always possible to decrypt even with imperfect error checking, and this might mean false positives are potentially infinitely unlikely in this context: This encryption paradigm aligns with emerging concepts in mainstream science regarding the physical nature of knowledge (potential action), and potentially opens the discussion about a mathematical proof that the universe can last forever.

Introduction

The advent of quantum computing poses a significant threat to traditional encryption methods. This necessitates the development of new cryptographic schemes resistant to attacks from quantum computers. One type of encryption that is provably uncrackable, and therefore quantum secure is OTP. OTPs are impossible within the universe, because they require perfectly random data, which is not possible in the universe unless the data is infinite. We propose a prototype for such a scheme that provides quantum-secure and mathematically uncrackable encryption, that only takes 3 perfectly random characters as a seed to start the ciper. This is achieved by sending the key within the encrypted message using reconstructive compression of key data. I.E., using hashes that rely on there being a context on the client side. The context is metaphysical, and generally understood to be inaccessiable to humans, but may be vulnerable to some form of quantum algorithm designed by an AI due to the dimensionality of the encrypted value not matching the randomness when english is used. If english is used the relationships between the words are not reflected in the key, providing an avenue of attack on all physical OTPs used to transmit non-random data.

Methodology

Original scheme operates on the following format:

<data><hashed:<data><new key char*final message length>>

This is equivalent to:

D<DKKK> = DHH

The hashed component is derived from a copy of the data itself, and a new key of a length that matches the final message length. The hashed length of the hash potion of the data is equivalent to less data than is transmitted. It’s worth noting that the hash (not the scheme itself) needs to make it double as difficult to bruteforce as a hash of the same length as the data and key, not 100x more difficult to bruteforce.

After encrypting server-side as an OTP with the known psk, saving the new key, transmitting, receiving, the process of decrypting the resulting DHH frame clientside begins. The hash will be used on the client side to reconstruct a new key of a sufficient length to fully replace the used key on the clientside aswell, by bruteforcing the hash (checking all the options) comparing the redundant copy of the data in the hash, to the unhashed copy and saving all viable options where they match.

False positives can occur in the decryption process, and it is therefore interesting to think about how likely it is for this decryption process to be wrong for various lengths of data, possible optimisations and if it is possible for it to be wrong forever or just infinitely unlikely. If it is infinitely unlikely this suggests parrallels with the relationship between space and time. It’s notable how wrong it would have to be to exhaust available computing resource also.

Therefore the only compromise is in the uncertainty of reliably getting the correct value for the decrypted data, not with the mathematics of the ciphertext. The final size of the transmitted data with this scheme is 3*data length. The fact that something physical exists (knowledge) in the receiving location allows the new key to be reconstructed with brute force or reconstructive compression using generative AIs, making it possible to send less information but still receive the benefits of precisely matching the length and type of randomness with the transmitted data.

Security Analysis

The scheme’s strength lies in how it is a perfect one-time pad. However its important to note the size of the randomness available to computers (random characters) perhaps does not represent the complexity or dimensionality of any non-random message (language), and the scope for an attack vector where an AI generated quantum algorithm can decrypt an possible OTP exists, potentially even a digital attack vector using an AI language model. This attack vector exists not just for OTPs or the technique described in this paper, but all possible encryption that transmits non-random data, that is intercepted. It’s unclear how significant the resources would need to be to decrypt any known messages would be, and therefore the encryption described in this paper is still one of the most secure streaming algorithms known in the world.

The metaphysical relationships between the values of the data such as the meaning of the words within the key can mean we have no known way to express the dimensionality in any form of code. The same is true for any imperfect OTP possible in the universe. The security of the scheme relies on the secrecy of the pre-shared key (PSK), and a mechanism of sharing the key is not presented as part of this paper but a psk of even just 3 totally random characters means that you are able to establish a connection that self replenishes with completely new randomness.

The initial random characters practically matching the dimensionality of the data, means that every option for the 3 character string, and therefore every possible combination for the new key and every following key is possible, and the only current, known, practical attack vector is the length. It’s significant to note the cryptographic integrity is not degraded over time if the PSK value is kept secret. However it is distinctly obvious how the referential dimensionality of the data can pose an attack surface in every encryption scheme, from this paper.

Implications

This scheme could have profound implications. It’s mathematically provable as an uncrackable, quantum-secure, OTP-based algorithm, given perfect randomness. But as well as this, the potentially infinitely low probability of false positives over time, given context, suggests a mathematical proof that the universe could exist indefinitely is possible. It ties nicely into the emerging scientific concept that knowledge has a physical presence.

Conclusion

We have presented a prototype concept for a quantum-secure and mathematically uncrackable encryption scheme. While further analysis, and auditing are needed, the initial results are promising. This scheme could represent a significant step forward in developing post-quantum cryptography as well as our understanding of physics. This paper makes is possible for a whole new branch of computing regarding explanatory hashing, and reconstructive compression.

https://circuspam.coffee/2024/08/18/a-prototype-for-quantum-secure-mathematically-uncrackable-encryption-streams/