faux_polar_ecc.rs

faux_polar_ecc.rs

use std::f64::consts::PI;

// Note: This implementation uses f64 (floating-point) for the polar coordinates (r, theta)
// and trigonometric functions (sin, cos). This approach is for **geometric demonstration** // and is NOT how Elliptic Curve Cryptography (ECC) is performed, as ECC requires 
// all arithmetic to be done with **integers** in a finite field (modulo P).

// The equation evaluated is: 
// r^2 * sin^2(θ) = (A_std * r^3 * cos^3(θ) + B_std * r * cos(θ) + C_std) mod P

/// Evaluates the polar form of the Elliptic Curve equation.
///
/// Due to the mix of float and integer math, this function returns a pair:
/// (LHS_value_mod_P, RHS_value_mod_P)
///
/// # Arguments
/// * `r` - The radial distance (must be a float).
/// * `theta` - The angle in radians (must be a float).
/// * `a_std`, `b_std`, `c_std` - Elliptic curve coefficients (u128).
/// * `p` - The prime modulus P (u128).
///
/// # Returns
/// A tuple `(lhs_mod_p, rhs_mod_p)` where both are u128.
fn evaluate_ecc_polar(
    r: f64,
    theta: f64,
    a_std: u128,
    b_std: u128,
    c_std: u128,
    p: u128,
) -> (u128, u128) {
    let cos_theta = theta.cos();
    let sin_theta = theta.sin();

    // --- 1. Calculate the Right-Hand Side (RHS) ---
    // RHS = A_std * r^3 * cos^3(θ) + B_std * r * cos(θ) + C_std
    
    // x-coordinate in Cartesian terms: x = r * cos(θ)
    let x_float = r * cos_theta;

    // Calculate terms using f64 first
    let term1_float = a_std as f64 * x_float.powi(3);
    let term2_float = b_std as f64 * x_float;
    let rhs_float = term1_float + term2_float + c_std as f64;

    // Convert RHS back to integer and apply modulo P
    // NOTE: This conversion involves significant precision loss/rounding.
    let rhs_integer = rhs_float.round().abs() as u128; // abs() because f64 can be negative
    let rhs_mod_p = rhs_integer % p;


    // --- 2. Calculate the Left-Hand Side (LHS) ---
    // LHS = r^2 * sin^2(θ)
    
    // y-coordinate in Cartesian terms: y = r * sin(θ)
    let y_float = r * sin_theta;
    let lhs_float = y_float.powi(2);

    // Convert LHS back to integer and apply modulo P
    let lhs_integer = lhs_float.round().abs() as u128;
    let lhs_mod_p = lhs_integer % p;

    (lhs_mod_p, rhs_mod_p)
}

fn main() {
    println!("--- Conceptual ECC Polar Evaluation (f64 + u128 Modulo) ---");
    
    // ECC Parameters (same as previous example)
    let p: u128 = 34028236692093846346337460743176821145; 
    let a_std: u128 = 25; 
    let b_std: u128 = 100; 
    let c_std: u128 = 15;
    
    // --- Test Point (r, theta) ---
    // This example chooses a point that, when converted to Cartesian, 
    // is roughly close to the previous x_coord for scale comparison.
    let test_r: f64 = 1.8e37; 
    let test_theta: f64 = PI / 4.0; // 45 degrees
    
    // --- EVALUATION ---
    
    let (lhs_result, rhs_result) = evaluate_ecc_polar(
        test_r, test_theta, a_std, b_std, c_std, p
    );
    
    // Calculate the Cartesian x/y coordinates from the polar input
    let cartesian_x = test_r * test_theta.cos();
    let cartesian_y = test_r * test_theta.sin();

    println!("\nCurve Equation: r^2*sin^2(θ) = {}*r^3*cos^3(θ) + {}*r*cos(θ) + {} (mod P)", a_std, b_std, c_std);
    println!("P (Modulus): {}", p);
    println!("Test Point (r, θ): r={:.2e}, θ={:.4} rad", test_r, test_theta);
    println!("(Approx. Cartesian x, y): x={:.2e}, y={:.2e}", cartesian_x, cartesian_y);

    println!("\n--- Result ---");
    println!("LHS (r^2*sin^2(θ)) mod P: {}", lhs_result);
    println!("RHS (A*x^3 + B*x + C) mod P: {}", rhs_result);

    // The point is on the curve IF lhs_result == rhs_result.
    let on_curve = if lhs_result == rhs_result { "YES" } else { "NO" };
    println!("\nPoint is on the curve (LHS == RHS)? {}", on_curve);
}

https://play.rust-lang.org/?version=stable&mode=debug&edition=2024&gist=5bd6c3f398d920f84cadb2ffd7412d75