555-EN, 7. The Moment When SegWit and AggWit Converge, and the Compression of Space
The Emergence of a Decodable Imprint in SHA-256 - A Possible Message Left by Satoshi
Author: The Two Goddesses
7. The Two Witnesses - The Moment When Segregated Witness (SegWit) and Aggregated Witness (AggWit) Converge, and the Compression of Space
Building upon the implementation of CSHA256, this chapter examines the moment when the two witnesses - Segregated Witness (SegWit) and Aggregated Witness (AggWit) - converge, as imprinted within the structure of SHA-256 itself.
Originally, SHA-256 was designed as a purely cryptographic hash function.
Yet, the presence of such an archetypal structure - two witnesses - raises an essential question:
Why would a mathematical construct intended for randomness and security bear this symbolic duality?
One of them, Segregated Witness, has already appeared in the real world as a functioning protocol implementation.
The fundamental role of SHA-256 is to compress information and yield an output that is unpredictable by any deterministic means.
In other words, the concept of compression lies at the very core of its mathematical nature.
From this perspective, one could interpret that every future event - data, structure, and transformation alike - is ultimately compressed under the dominion of these two witnesses.
This remains a hypothesis, but it is by no means implausible.
What, then, is this compression of space - a phenomenon that even evokes biblical resonance?
It is a structure governed by number theory, one that permits no deviation, a system that inevitably converges toward a fixed, predetermined value.
Cryptocurrency itself arises from the same mathematical constraint:
each parameter is bound by arithmetic law and cannot be altered by human will.
Thus, seemingly unrelated domains - cryptography, economics, and theology - become interconnected through a single mathematical chain.
Within this web of numerical restrictions, the two witnesses and the architecture of currency are inseparably linked.
From an abstract standpoint, this relationship may indeed represent the true essence of cryptographic currency.
The moment when these two witnesses stand together may therefore symbolize the completion of the cryptographic monetary system itself.
Yet, at that very instant, an unexpected presence intervenes - the quantum.
Because the Aggregated Witness is founded on signature aggregation (Schnorr), its foundation necessarily involves the mathematics of elliptic curves.
As a close examination of its implementation reveals, the security of this scheme depends upon the relation
P = kG
which must remain computationally irreversible - that is, "k" must never be derived from "P".
If this mapping were ever inverted, Shor's algorithm could be applied to recover the secret scalar "k", allowing any adversary to generate valid digital signatures and broadcast unauthorized transactions.
The entire cryptographic framework would collapse instantly.
Here lies the fundamental dilemma.
To bring the Aggregated Witness into existence - even as a symbolic realization - it must embody the concept of aggregation.
As established in earlier chapters, this property is intrinsic to its design.
Consequently, there exists a practical imperative:
an aggregation-capable signature scheme must be implemented within the coming year.
Yet at present, no known post-quantum cryptographic (PQC) scheme provides both secure and efficient aggregation.
Does this mean that the Aggregated Witness will emerge in its elliptic-curve form after all?
If so, quantum resistance would be sacrificed.
Indeed, several recent studies estimate a probability of roughly 50 percent that elliptic-curve cryptosystems of practical bit length could be compromised within the next five years.
To standardize an aggregation mechanism on elliptic curves under such conditions would be, both theoretically and operationally, an exceedingly perilous choice.
And still - it appears inevitable.
There may be forces at work here that lie beyond resistance:
institutional, historical, or perhaps structural necessity itself.
The convergence of the two witnesses and the emergence of spatial compression thus represent more than a mere technical unification.
They mark a phase transition in the history of cryptography - the closing of the classical era and the dawn of the quantum age.
In the next chapter, we turn to number theory itself, examining the most fundamental form of this spatial compression through the general expression,
|3n - m|.
