From 59ea57ef9a8aba514f8d76f2dc73e2ed6a88f219 Mon Sep 17 00:00:00 2001
From: Joey Yandle <xoloki@gmail.com>
Date: Mon, 9 Dec 2024 12:54:23 -0500
Subject: [PATCH] add elgamal encryption to utils; add pvss module; check that
 the secp256k1 group order is prime, and also (order - 1)/2 which is sadly not

---
 Cargo.toml  |  2 ++
 src/lib.rs  |  2 ++
 src/pvss.rs | 38 ++++++++++++++++++++++++++++++++++++++
 src/util.rs | 49 +++++++++++++++++++++++++++++++++++++++++++++++--
 4 files changed, 89 insertions(+), 2 deletions(-)
 create mode 100644 src/pvss.rs

diff --git a/Cargo.toml b/Cargo.toml
index af374bc5..a231ed8a 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -19,6 +19,8 @@ aes-gcm = "0.10"
 bs58 = "0.5"
 hashbrown = { version = "0.14", features = ["serde"] }
 hex = "0.4.3"
+is_prime =  { git = "https://github.com/xoloki/is_prime.git" }
+num-bigint = "0.4"
 num-traits = "0.2"
 polynomial = { version = "0.2.5", features = ["serde"] }
 primitive-types = "0.12"
diff --git a/src/lib.rs b/src/lib.rs
index 12f846d8..3d622e42 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,6 +1,8 @@
 #![deny(missing_docs)]
 #![doc = include_str!("../README.md")]
 
+/// PVSS
+pub mod PVSS;
 /// Types which are common to both v1 and v2
 #[allow(clippy::op_ref)]
 pub mod common;
diff --git a/src/pvss.rs b/src/pvss.rs
new file mode 100644
index 00000000..1e93cf28
--- /dev/null
+++ b/src/pvss.rs
@@ -0,0 +1,38 @@
+use is_prime;
+use rand_core::{CryptoRng, RngCore};
+
+use crate::curve::scalar::Scalar;
+
+/// A publicly verifiable secret share algorithm
+pub struct PVSS {
+    R: Vec<Scalar>,
+    c: Scalar,
+}
+
+impl PVSS {
+    /// Construct a random polynomial of the passed degree `n`
+    pub fn new<RNG: RngCore + CryptoRng>(rng: &mut RNG) -> PVSS {
+        let R = Vec::new();
+        let c = Scalar::random(rng);
+        PVSS { R, c }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+    use crate::curve::{point::Point, scalar::Scalar};
+
+    use num_bigint::BigUint;
+
+    #[test]
+    fn is_p_minus_1_over_2_prime() {
+        let p = BigUint::from_bytes_be(crate::curve::point::N.as_slice());
+
+        assert!(is_prime::is_biguint_prime(p.clone()));
+
+        let p12 = (p - 1u32) / 2u32;
+
+        assert!(is_prime::is_biguint_prime(p12.clone()));
+    }
+}
diff --git a/src/util.rs b/src/util.rs
index 402e2e7b..974cffd4 100644
--- a/src/util.rs
+++ b/src/util.rs
@@ -82,6 +82,34 @@ pub fn decrypt(key: &[u8; 32], data: &[u8]) -> Result<Vec<u8>, AesGcmError> {
     cipher.decrypt(nonce, cipher_vec.as_ref())
 }
 
+/// An El-Gamal encryption packet
+struct ElGamal {
+    c1: Scalar,
+    c2: Scalar,
+}
+
+/// encrypt using a scalar based El-Gamal
+pub fn encrypt_elgamal<RNG: RngCore + CryptoRng>(
+    generator: Scalar,
+    message: Scalar,
+    public_key: Scalar,
+    rng: &mut RNG,
+) -> Result<ElGamal, String> {
+    // ephemeral key
+    let k = Scalar::random(rng);
+
+    let c1 = generator ^ k;
+    let c2 = (message.invert()) * (public_key ^ k);
+
+    Ok(ElGamal { c1, c2 })
+}
+
+/// encrypt using a scalar based El-Gamal
+pub fn decrypt_elgamal(elgamal: &ElGamal, private_key: Scalar) -> Result<Scalar, String> {
+    let message = (elgamal.c1 ^ private_key) * (elgamal.c2.invert());
+    Ok(message)
+}
+
 /// Creates a new random number generator.
 pub fn create_rng() -> impl RngCore + CryptoRng {
     OsRng
@@ -94,7 +122,7 @@ mod test {
 
     #[test]
     #[allow(non_snake_case)]
-    fn test_shared_secret() {
+    fn shared_secret() {
         let mut rng = create_rng();
 
         let x = Scalar::random(&mut rng);
@@ -111,7 +139,7 @@ mod test {
 
     #[test]
     #[allow(non_snake_case)]
-    fn test_encrypt_decrypt() {
+    fn encrypt_decrypt() {
         let mut rng = create_rng();
         let msg = "It was many and many a year ago, in a kingdom by the sea...";
 
@@ -129,4 +157,21 @@ mod test {
 
         assert_eq!(msg.as_bytes(), &plain);
     }
+
+    #[test]
+    fn elgamal() {
+        let mut rng = create_rng();
+        let generator = Scalar::random(&mut rng);
+        let private_key = Scalar::random(&mut rng);
+        let public_key = generator ^ private_key;
+        let message = Scalar::random(&mut rng);
+
+        let elgamal = encrypt_elgamal(generator, message, public_key, &mut rng).unwrap();
+        let decrypted_message = decrypt_elgamal(&elgamal, private_key).unwrap();
+
+        assert_eq!(message, decrypted_message);
+    }
+
+    #[test]
+    fn pvss() {}
 }