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[Quantum-resistant: L1 implemented]
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On Quantum Resistance in Blockchain

Introduction

Quantum computers are primarily specialized in determining periodicity.

They possess the capability to transform computational tasks that would typically require exponential time-taking decades to trillions of years even with the fastest supercomputers-into polynomial-time calculations that can be solved in a matter of minutes.

Quantum Computers and Shor's Algorithm

Quantum computers process information using quantum bits (qubits). This allows them to perform calculations much faster than classical computers. Shor's algorithm is one of the algorithms executed on quantum computers, efficiently factoring large numbers.

\[ | \psi \rangle = \cos\left(\frac{\theta}{2}\right) | 0 \rangle + e^{i\phi} \sin\left(\frac{\theta}{2}\right) | 1 \rangle \]

Modern public key cryptography(RSA) relies on the fact that factoring large numbers is not computationally feasible in a realistic timeframe. However, quantum computers can factor large numbers in a realistic timeframe using Shor's algorithm.

Originally, the phase information φ of a quantum bit in superposition cannot be directly observed. However, by utilizing quantum Fourier transform, this phase information can be converted into the frequency domain, making it possible to transform it into an observable probability amplitude of the quantum bit's particle nature.

\[ f(x) = a^x \mod N, \;\gcd(a, N) = 1 \] \[ |x\rangle = H\; \otimes \;H\; \otimes \cdots \otimes \;H \;|00 \cdots 0\rangle = \sum_k |k\rangle \rightarrow f(x) \rightarrow |x\rangle\; \otimes \;|f(x)\rangle \] \[ |f(x)\rangle = \sum_k |k\rangle \rightarrow \text{Collapse} \rightarrow |f(x)\rangle \rightarrow f(j),\ j: \text{the chosen solution} \] \[ \therefore\;|j\rangle = \frac{1}{\sqrt{n}} ( |m_1\rangle + |m_2\rangle + \ldots + |m_n\rangle ) \] \[ \text{n: the number of superposed states on the input register} \] \[ m_1 \cdots m_n: \text{the respective states} \]

\[ \therefore\;QFT\_{2^n}\;|j\rangle \rightarrow \frac{1}{\sqrt{2^n}} \sum_{k=0}^{2^n - 1} e^{2\pi i j k / 2^n} |k\rangle \]

On Quantum Computers and Probability Amplitudes

In the example above, we were able to significantly increase the probability amplitude for maintaining the frequency domain. However, such cases are rare, and quantum computers are weak at tasks like finding the preimage of a hash designed to lack periodicity. This is because, without periodicity, there is no effective method to significantly increase the probability amplitude of the value to be observed.

While there are methods to gradually increase the probability amplitude, they only scale by approximately the square root and are therefore impractical. Consequently, by incorporating mathematical elements that make it difficult to enhance probability amplitudes into the signatures of public-key cryptographic systems, it is possible to achieve quantum resistance for blockchain systems.

The following image represents the quantum resistance integrated into SORA L1. It incorporates signatures that utilize this property.

Balances separated between ECDSA and Quantum resistance

The SORA Quantum-Resistant Blockchain automatically separates the balances of the widely adopted ECDSA cryptography, used in Bitcoin and similar systems, and the quantum-resistant cryptography uniquely enhanced and implemented by SORA. Users can utilize both ECDSA and quantum-resistant cryptography without being aware of the differences. Specialized knowledge, such as multisig, is "not required." Simply using the blockchain as usual allows you to enjoy the benefits of quantum resistance.

Please refer to the image below. The numbers displayed at the bottom represent the separated balances.
[ECDSA: 9.90 SORA + Quantum resistance: 256.00 SORA = Available: 265.90 SORA]

AI-NFT

Support for ownership management, metaverse, drive(HDD/SSD/NVMe) inspection and advanced scientific analysis ... etc.

Web3 - Blockchain - Multidimensional NFT by SORA Network. We aim to popularize multidimensional NFTs that can be built by direct product based on Web3 - blockchain technology. The base development has already been completed, and 1-dim NFT, 2-dim NFT, and 4-dim NFT are operating normally on SORA Network.

What kind of use is there? For example, when analyzing meteorological observation data with a blockchain. If the "wind direction" and "wind strength" at a certain point are used as data, it will be a 2-dim NFT.

This 2-dim NFT operate to record data on the SORA-blockchain. And if you give a special NFT to blockchain with action by direct product or comparison, you can get the result from the blockchain.

By the way, regarding the first goal of the SORA project, "Achieving drive inspection statistics on the blockchain", we achieved with the 4-dim NFT (i-sector). Now it can operate SSD/NVMe safely.

\[ a_0 \cdots a_n \in \text{AI-NFT} \] \[ T_{ij} = a_0 \otimes a_1 \otimes a_2 \otimes \cdots \otimes a_n \]

16 passphrase, restore wallet completely

With this kind of feeling, you can build an NFT that can directly product the conventional tokens with smart contract and raise the dimension. Smartly adapts to any application ... Reborn as a general blockchain!

Then, No need a hard-ware wallet, No need a paper wallet, No need a buckup, in SORA Network. No need, those backup, hardware wallet, paper wallet, and so on. Why? because Using 16 passphrase, restore wallet completely (Coins and NFTs are safe).

\[ f: D^{16} \longrightarrow C \]

SORA L1 Quantum Resistance in Blockchain Core

We have implemented quantum resistance directly on L1, eliminating the need for a bridge.

The traditional public-key cryptography method, ECDSA, widely used in Bitcoin and other systems, uses addresses that start with "S." In contrast, quantum-resistant transactions incorporating SORA's proprietary quantum-resistant signature use addresses that start with "sora1."

The implementation is remarkably simple!

SORA L2 Quantum Resistance in Blockchain AI-NFT

On SORA L2, we are developing blockchain-based applications. Please feel free to make use of them as well.

In the following image, blockchain is integrated with other functionalities, operating inspection features and more with AI in the background.

About the Specifications

SORA Discord wallet: Bot

Only once registered in "#mainnet-discord-wallet", you can immediately use functions like "deposit", "withdraw", "catch" etc. Commands starting with "qai" indicate quantum resistance.

Roadmap 2018 - 2024

Implemented SORA L1 Quantum resistance

Implemented SORA L1 SORA-QAI

Implemented SORA L1 sora1 address / Schnorr signature

Implemented SORA L1 Crypto message

Implemented SORA L2 Sorascan

Implemented SORA L2 AI-NFT

Implemented SORA L2 Blockchain Solutions

Implemented SORA L2 Crypto memo

Implemented SORA L1 Automatic checkpoints

Inplemented SORA L1 Benchmark

Launched SorachanCoin project, SorachanCoin-qt ver1.0