# Equations for Key Processes

Here are key equations that explain the underlying processes of KYC, authentication, encryption, risk management, and transaction throughput.<br>

### &#x20;KYC (Know Your Customer) Risk Scoring:

The risk score $$R\_{\text{KYC}}$$ is a weighted sum of risk factors:

$$
R\_{\text{KYC}} = w\_1 \cdot R\_{\text{location}} + w\_2 \cdot R\_{\text{transaction\_history}} + w\_3 \cdot R\_{\text{account\_activity}} + \dots
$$

Where:

* $$w\_1, w\_2, w\_3$$  are the weights for each factor.
* $$R\_{\text{location}}, R\_{\text{transaction\_history}}, R\_{\text{account\_activity}}$$ re the risk scores for each category.

### Authentication: Multi-Factor Authentication (MFA):

The probability $$P\_{\text{auth}}$$ of successful authentication:

$$
P\_{\text{auth}} = P\_{\text{password}} \times P\_{\text{MFA\_token}} \times P\_{\text{biometric}}
$$

Where:

* $$P\_{\text{password}}$$ is the probability of correct password entry.
* $$P\_{\text{MFA\_token}}$$ is the probability of valid MFA token entry.
* $$P\_{\text{biometric}}$$ is the probability of successful biometric verification.

### Encryption: Symmetric Encryption:

Encryption and decryption processes:

$$
C = E(K, P)
$$

$$
P = D(K, C)
$$

Where:

* E  is the encryption algorithm,  D  is the decryption algorithm.
* K  is the symmetric key,  P  is the plaintext, and  C  is the ciphertext.

### Transaction Processing Time (TP):

The time $$T\_{\text{processing}}$$ to process a transaction:

$$
T\_{\text{processing}} = T\_{\text{validation}} + T\_{\text{confirmation}}
$$

Where:

* $$T\_{\text{validation}}$$ is the time to validate the transaction.
* $$T\_{\text{confirmation}}$$ is the time for block confirmation.

&#x20;Risk Management in Trading:

The expected value E  of a trade:

$$
E = P\_{\text{gain}} \cdot V\_{\text{gain}} - P\_{\text{loss}} \cdot V\_{\text{loss}}
$$

Where:

* $$P\_{\text{gain}}$$ is the probability of gain, $$V\_{\text{gain}}$$ is the value of the gain.
* $$P\_{\text{loss}}$$ is the probability of loss, $$V\_{\text{loss}}$$ is the value of the loss.

### Hash Function for Block Generation:

The hash of a block $$H\_{\text{block}}$$ :&#x20;

$$
H\_{\text{block}} = H(D\_{\text{block}} + N)
$$

Where:

* H  is the hash function (e.g., SHA-256),
* $$D\_{\text{block}}$$ is the block data,
* N  is the nonce value.

### Throughput of the System (Transactions Per Second - TPS):

System throughput TPS :&#x20;

$$
TPS = \frac{N\_{\text{transactions}}}{T\_{\text{time}}}
$$

Where:

* $$N\_{\text{transactions}} $$ is the number of transactions,
* $$T\_{\text{time}} $$ is the time taken to process them.

This document represents a comprehensive guide on how GCB implements its technical architecture, security protocols, and regulatory strategies, including critical equations to explain the system’s key processes.

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