On The Commutation of The Ordination of The Origination of COVID - jalToorey/IdealMoney GitHub Wiki

Re-Visiting Public Key Cryptography

Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key.

Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions.

Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security.

In a public-key encryption system, anyone with a public key can encrypt a message, yielding a ciphertext, but only those who know the corresponding private key can decrypt the ciphertext to obtain the original message.

For example, a journalist can publish the public key of an encryption key pair on a web site so that sources can send secret messages to the news organization in ciphertext.

Only the journalist who knows the corresponding private key can decrypt the ciphertexts to obtain the sources' messages—an eavesdropper reading email on its way to the journalist cannot decrypt the ciphertexts

On Genealogy of Hierarchical Deterministic Key Pairs

Of cryptocurrency wallets we note the evolution to hierarchical determinism:

A sequential deterministic wallet utilizes a simple method of generating addresses from a known starting string or "seed". This would utilize a cryptographic hash function, e.g. SHA-256 (seed + n), where n is an ASCII-coded number that starts from 1 and increments as additional keys are needed.[43]

The hierarchical deterministic (HD) wallet was publicly described in BIP32.44(https://en.wikipedia.org/wiki/Cryptocurrency_wallet#cite_note-44) As a deterministic wallet, it also derives keys from a single master root seed, but instead of having a single "chain" of keypairs, an HD wallet supports multiple key pair chains.

On The Relevant Generalization of a One-Way Function

In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems.

Here for our generalization we note there can be zero complexity distance between the concept of a very computationally hard inversion and an impossible or implausible backward deduction/inversion etc.

"Asymmetric encryption". IONOS Digitalguide. Retrieved 9 June 2022.

This one-way function is the main idea behind the asymmetric cryptosystem. The two keys are completely independent from one another. Even if an attacker has access to the public key, they cannot use it to draw any conclusions about the private key.

On Commutative Nature of Some Blinded Signatures

Meet the greatest simple equation since e=mc2 ~ Szabo

Szabo explains ‘blind signatures’ encapsulated in this formula:

gSf(m) = S(m)

The example is commutative encryption. The idea is each encryption layer is indifferent to each other layer. The order doesn’t matter. Szabo give the example of tricking someone into signing a blank check:

The genius behind this discovery: cryptography guru David Chaum. The brilliance lies in step 3: Chaum discovered that some signatures have the property of being "commutative" with the blinding functions: Alice can strip off the blinding in the reverse order which the blinding and signature were applied, leaving just Alice's signature of n. It is as if Alice put a piece of carbon paper inside the envelope!