Code shared from the Rust Playground

playground.rs

// Note: In real ECC, the modulus P is a large prime (256 bits or more), 
// which requires an external crate like `num-bigint` or `crypto-bigint`.
// This example uses u128, which is only 128 bits, for demonstration purposes.

// We will map the general equation to the standard Weierstrass form over a finite field:
// LHS: R * sin^2(θ)  -> y_squared
// RHS: A*(r/cos(θ))^3 + B*(r/cos(θ))^1 + C -> A_std * x^3 + B_std * x + C_std

/// Evaluates the right-hand side of the Elliptic Curve equation (Weierstrass form)
/// over a finite field, using only Rust's standard library integer types (u128).
/// 
/// The equation evaluated is: result = (A_std * x^3 + B_std * x + C_std) mod P
///
/// # Arguments
/// * `x` - The x-coordinate (derived from r/cos(θ)).
/// * `a_std` - The coefficient A (from your equation).
/// * `b_std` - The coefficient B (from your equation).
/// * `c_std` - The coefficient C (from your equation).
/// * `p` - The prime modulus P.
///
/// # Returns
/// The result of the calculation: (RHS) mod P.
fn evaluate_ecc_rhs(
    x: u128,
    a_std: u128,
    b_std: u128,
    c_std: u128,
    p: u128,
) -> u128 {
    // 1. Calculate the raw right-hand side (RHS) without modulo.
    // We use temporary u128s, but MUST be careful of overflow before the final modulo P.
    // In real ECC, this is why a BigInt library is mandatory.

    // Calculate x^3. This is the main overflow risk point.
    let x_cubed = x.saturating_mul(x).saturating_mul(x);

    // Calculate A_std * x^3
    let term1 = a_std.saturating_mul(x_cubed);

    // Calculate B_std * x
    let term2 = b_std.saturating_mul(x);

    // Add all terms together. This calculation represents (RHS_raw)
    let rhs_sum = term1.saturating_add(term2).saturating_add(c_std);

    // 2. Apply the modulo P
    // The modulus operation must handle potential wrapping, but for positive numbers,
    // the built-in % operator performs the modulo arithmetic correctly.
    // We assume the intermediate sum fits within u128, which is a strong limitation here.
    let result_mod_p = rhs_sum % p;

    result_mod_p
}

fn main() {
    println!("--- Conceptual ECC Evaluation (Stdlib u128) ---");
    
    // Define parameters. P must be large, but must fit in u128.
    // For a real ECC curve, these would be large, randomly chosen integers.
    let p: u128 = 34028236692093846346337460743176821145; // A large prime near u128::MAX/5
    let a_std: u128 = 25;  // Coefficient A
    let b_std: u128 = 100; // Coefficient B
    let c_std: u128 = 15;  // Coefficient C (The 'B' term in standard ECC form)
    
    // Choose an x-coordinate to test.
    let x_coord: u128 = 123456789012345678901234567890123456789;
    
    // --- EVALUATION ---
    
    let y_squared_mod_p = evaluate_ecc_rhs(x_coord, a_std, b_std, c_std, p);

    println!("\nCurve Equation: y^2 = {}*x^3 + {}*x + {} (mod P)", a_std, b_std, c_std);
    println!("P (Modulus): {}", p);
    println!("Test Point x: {}", x_coord);
    
    println!("\n--- Result ---");
    println!("The value of y^2 (mod P) for the given x is: {}", y_squared_mod_p);

    // NOTE: The LHS (R * sin^2(θ)) is equal to the result y_squared_mod_p 
    // if the point is on the curve. This result is the value it must equal.
}