# Proposal for Engineering’s New Field

### Quantum Cryptography and its subset Quantum Recursiveness

Quantum Cryptography is a newly emerging field in engineering, with post-quantum cryptography algorithms already being processed for standardization. This has “spawned” from Quantum Engineering. However, in this day in age there needs to be a past theoretical approach into looking at post Quantum-level encryption. With Quantum Cryptography, you are making room for Quantum Recursiveness, which something I found interesting was K. Svozil’s Quantum recursion theory which he published in 2009.

My intake in Quantum Cryptography, is that we need to go beyond the realm of explaining this in classical terminology. We are talking about a whole new method and apparatus of data processing in general. This is why we need to look into recursive Qubit compatible hardware encryption through pure mathematics, computational physics, and what is possible in the realm of modern day computing.

#### My proposed hashing sequence: 4n!/(2!)^n

##### At N = 0

##### At N = ∞

I am proposing this sequence for the purpose of multi-path layer mathematical recursion/continued hashing for Post-Qauntum networks. Reason (4n) as in representation of the original Qubit encryption layer. Wanted to come up with a new sequence similar to Bernoulli numbers but non-existent.

Old Proposal OEIS (Pending/Draft): https://oeis.org/A309669

###### Forgot that this is a non-integer sequence so made the equation: (4^n^2)+n! for multilayer hashing with a -∞ infinity proof at n = -1 (Infinity is can be viewed as is or isn’t an integer)

New Proposal: https://oeis.org/A309675

Current Hashing Methods: (Source: Wikipedia)

```
Lattice-based cryptography
Multivariate cryptography
Hash-based cryptography
Code-based cryptography
Supersingular elliptic curve isogeny cryptography
Symmetric key quantum resistance
```

This variation would be Merkle based inspired by my current Hardware cryptography solution for classical computing i.e. HippaSafe2.0 and utilize theoretical hashing. For offset N = -1, you are set with the lowest value of -∞. I wanted to make a non-existent sequence for hashing sort of inspired by Bernoulli numbers.

#### Another possible expansion was the new equation (4n!/(2!)^n*2)^n:

Anyways, I think applying these sequential techniques mathematically into Quantum Cryptography to create recursive post-Quantum hardware key encryption is the way to go. I also think these types of formalities offer insight into recursive and sequential hashing for Qubit based processing.