P = p·Gtaproot internal public keyp = a·btaproot internal private key
Alice and Bob reveal each other their pubkey for the session, and then both can generate the same address.
A = a·GAlice (buyer of UTXO)
| // 1. Declarative Macro Definition | |
| // This macro takes a field identifier ($field:ident) and generates a public | |
| // getter method with the same name. | |
| macro_rules! create_getter { | |
| ($field:ident) => { | |
| // The generated code: | |
| pub fn $field(&self) -> &str { | |
| // Assumes the field is a String, and returns a string slice (&str) | |
| &self.$field | |
| } |
| 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. |
| // 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). |
| //// src/main.rs | |
| use std::collections::HashMap; | |
| // --- PLACEHOLDER TYPES (Replacing ECC Types) --- | |
| // In a real implementation, these would be Elliptic Curve Points or Scalars. | |
| type MintPrivateKey = u64; // k | |
| type MintPublicKey = u64; // K = k * G | |
| type UserSecret = u64; // x | |
| type RandomPoint = u64; // Y = hash_to_curve(x) |
| //// The prime modulus for the finite field GF(17) | |
| const P: i64 = 17; | |
| // Curve parameters: y^2 = x^3 + A*x + B (mod P) | |
| const A: i64 = 2; | |
| const B: i64 = 3; | |
| /// Represents a point on the elliptic curve. | |
| /// The point is (x, y). The identity point (Point at Infinity) is represented | |
| /// by (0, 0) since the point (0, 0) is not on this curve (0^2 != 0^3 + 2*0 + 3 mod 17). |
| use std::f64::consts::PI; | |
| /// Calculates an approximation of Pi using Viète's formula. | |
| /// | |
| /// The formula is based on an infinite product of terms involving nested square roots. | |
| /// This function approximates the product up to a given number of iterations. | |
| /// | |
| /// # Arguments | |
| /// | |
| /// * `iterations` - The number of terms to include in the product. More iterations |
| fn main() { | |
| // The Golden Ratio is (1 + sqrt(5)) / 2 | |
| let five = 5.0f64; | |
| // --- Floating-Point Types (Accurate Representation) --- | |
| // f64: Double-precision floating point (default and most precise) | |
| let phi_f64: f64 = (1.0 + five.sqrt()) / 2.0; | |
| // f32: Single-precision floating point (less precision) | |
| let phi_f32: f32 = (1.0f32 + (5.0f32).sqrt()) / 2.0f32; |
| //#![no_std] | |
| extern crate alloc; | |
| use alloc::vec::Vec; | |
| /// Placeholder for the real SHA-256 function. | |
| /// It only uses the length of the data to generate a predictable output. | |
| fn sha256_placeholder(data: &[u8]) -> [u8; 32] { | |
| let mut hash = [0u8; 32]; | |
| let len_bytes = (data.len() as u32).to_le_bytes(); | |
| hash[0..4].copy_from_slice(&len_bytes); |
| //#![no_std] | |
| fn sha256_placeholder(data: &[u8]) -> [u8; 32] { | |
| let mut hash = [0u8; 32]; | |
| let len_bytes = (data.len() as u32).to_le_bytes(); | |
| hash[0..4].copy_from_slice(&len_bytes); | |
| hash | |
| } | |
| const SHA256_BLOCK_SIZE: usize = 64; |