Equations for Key Processes

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

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.

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 $H_{\text{block}}$ :

$$H_{\text{block}} = H(D_{\text{block}} + N)$$

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 :

$$TPS = \frac{N_{\text{transactions}}}{T_{\text{time}}}$$

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.