⚫X Function

The Erratic random function model.

➥ What is X Function?

The X function ensures that all profits obtained in Erratic Finance are entirely random within a predetermined range. This ensures absolute fairness within the Erratic ecosystem, preventing any undue profit monopolization.

As an example, today you could collect 100 E-Points from Daily Check-in, while tomorrow you might gather 600 E-Points or 1000 E-Points, and so on.

Typically, mathematical pseudo-random numbers use a simple Linear Congruential Generator (LCG) as their internal random number generator. The random numbers generated by this package are sufficient for simulations, games, or scenarios that do not require high randomness. However, they are not suitable for security-sensitive applications such as cryptographic operations or key generation. The reason is that while their randomness is statistically uniformly distributed, theoretically, if the generator's internal state is known, future outputs can be predicted.

➥ Feature

• High randomness

• Security and fairness

• Dynamic iterative optimization

➥ Implementation

Considering these security issues, the random numbers we designed rely on cryptographically secure random sources provided by the operating system, such as /dev/urandom or /dev/random on Unix-like systems. These random sources draw noise from physical processes (e.g., clock interrupts, network activity) to fill the entropy pool, from which random data is then extracted. Since the data in the entropy pool is unpredictable, the random numbers generated are secure.

Based on the following three aspects, we ensure security and true randomness:

• Entropy Source: The random numbers use high-entropy sources provided by the operating system, meaning they are based on unpredictable events from the physical world, making the numbers difficult to predict.

Express the entropy source as:

$H(t) = A \cdot N(t) + B \cdot P(t) + C \cdot W(t)$

$A,B,C$: Weighting coefficients that adjust the contribution of each component

$N(t)$: Gaussian noise

$P(t)$: Poisson process

$W(t)$: Random walk, defined as $W(t) = W(t-1) + X_t$

• Reseeding: Each time random numbers are requested, data is drawn from the entropy pool, which is continuously refilled by environmental uncertainties, ensuring a constant supply of randomness.

Model Definition

1.Entropy Pool: $E(t)$: represent the entropy pool at time $t$

2.Environmental Inputs:

$U(t)$: environmental uncertainties

$U_s(t)$: System events

$U_h(t)$: Hardware noise

$U_n(t)$: Network activity

Express the Environmental Inputs as:

$U(t)=U_s(t)+U_h(t)+U_n(t)$

3.Reseeding Function: Use $R(t)$ to update the entropy pool

$E(t)=E(t-1)+R(U(t))$

4.Random Number Generation: When random numbers are requested, data is drawn from the entropy pool:

$RNG(t)=F(E(t))$

• Blocking and Non-blocking Modes: The system can be configured to block and wait until sufficient entropy is available before generating random numbers, ensuring high-quality random numbers even in low-entropy environments.