feat: rsa 1-2 ot

src/encryption/asymmetric/rsa/mod.rs

@@ -17,56 +17,88 @@ const fn mod_inverse(e: u64, totient: u64) -> u64 {
   }
   d
 }
-/// RSAKey struct
-pub struct RSA {
-  /// pub key (e,n)
-  pub private_key: PrivateKey,
-  /// priv key (d,n)
-  pub public_key:  PublicKey,
-}
 
 /// private key
 pub struct PrivateKey {
-  /// gcd(e, totient) = 1
-  e: usize,
+  /// d x e mod totient = 1
+  d:     usize,
   /// modulus
-  n: usize,
+  pub n: usize,
 }
 
 /// public key
 pub struct PublicKey {
-  /// d x e mod totient = 1
-  d: usize,
+  /// gcd(e, totient) = 1
+  e:     usize,
   /// modulus
-  n: usize,
+  pub n: usize,
 }
 
-impl RSA {
-  /// Encrypts a message using the RSA algorithm
-  #[allow(dead_code)]
+/// RSA encryption
+pub struct RSAEncryption {
+  /// RSA public key
+  pub public_key: PublicKey,
+}
+
+/// RSA decryption
+pub struct RSADecryption {
+  /// RSA private key
+  pub private_key: PrivateKey,
+}
+
+impl RSAEncryption {
   /// Encrypts a message using the RSA algorithm
   /// C = P^e mod n
-  const fn encrypt(&self, message: u32) -> u32 {
-    message.pow(self.private_key.e as u32) % self.private_key.n as u32
+  pub const fn encrypt(&self, plaintext: u32) -> u32 {
+    let mut plaintext = plaintext;
+    let mut res = 1;
+    let mut exp = self.public_key.e as u32;
+
+    while exp > 0 {
+      if exp % 2 == 1 {
+        res = ((res as u64 * plaintext as u64) % self.public_key.n as u64) as u32;
+      }
+      plaintext = ((plaintext as u64).pow(2) % self.public_key.n as u64) as u32;
+      exp >>= 1;
+    }
+
+    res
   }
+}
 
-  #[allow(dead_code)]
+impl RSADecryption {
   /// Decrypts a cipher using the RSA algorithm
   /// P = C^d mod n
-  const fn decrypt(&self, cipher: u32) -> u32 {
-    cipher.pow(self.public_key.d as u32) % self.public_key.n as u32
+  pub const fn decrypt(&self, ciphertext: u32) -> u32 {
+    let mut res = 1;
+    let mut ciphertext = ciphertext;
+    let mut exp = self.private_key.d as u32;
+
+    while exp > 0 {
+      if exp % 2 == 1 {
+        res = ((res as u64 * ciphertext as u64) % self.private_key.n as u64) as u32;
+      }
+      ciphertext = ((ciphertext as u64).pow(2) % self.private_key.n as u64) as u32;
+      exp >>= 1;
+    }
+
+    res
+    // ((ciphertext as u64).pow(self.private_key.d as u32) % self.private_key.n as u64) as u32
   }
 }
+
 /// Key generation for the RSA algorithm
 /// TODO: Implement a secure key generation algorithm using miller rabin primality test
-pub fn rsa_key_gen(p: usize, q: usize) -> RSA {
+pub fn rsa_key_gen(p: usize, q: usize) -> (RSAEncryption, RSADecryption) {
   assert!(is_prime(p));
   assert!(is_prime(q));
   let n = p * q;
   let e = generate_e(p, q);
   let totient = euler_totient(p as u64, q as u64);
   let d = mod_inverse(e, totient);
-  RSA { private_key: PrivateKey { e: e as usize, n }, public_key: PublicKey { d: d as usize, n } }
+  (RSAEncryption { public_key: PublicKey { e: e as usize, n } }, RSADecryption {
+    private_key: PrivateKey { d: d as usize, n },
+  })
 }
 
 /// Generates e value for the RSA algorithm
@@ -86,10 +118,10 @@ const fn generate_e(p: usize, q: usize) -> u64 {
   panic!("Failed to find coprime e; totient should be greater than 1")
 }
 
-/// Generates a random prime number bigger than 1_000_000
-pub fn random_prime(first_prime: usize) -> usize {
-  let mut n = 1_000_000;
-  while !is_prime(n) && n != first_prime {
+/// Generates a random prime number bigger than `begin`
+pub fn random_prime(begin: usize) -> usize {
+  let mut n = begin;
+  while !is_prime(n) {
     n += 1;
   }
   n

src/encryption/asymmetric/rsa/tests.rs

@@ -13,17 +13,26 @@ fn test_euler_totient() {
 
 #[test]
 fn key_gen() {
-  let key = rsa_key_gen(PRIME_1, PRIME_2);
-  assert_eq!(key.public_key.n, PRIME_1 * PRIME_2);
-  assert_eq!(gcd(key.private_key.e as u64, euler_totient(PRIME_1 as u64, PRIME_2 as u64)), 1);
-
-  let key = rsa_key_gen(PRIME_2, PRIME_3);
-  assert_eq!(key.public_key.n, PRIME_2 * PRIME_3);
-  assert_eq!(gcd(key.private_key.e as u64, euler_totient(PRIME_2 as u64, PRIME_3 as u64)), 1);
-
-  let key = rsa_key_gen(PRIME_3, PRIME_1);
-  assert_eq!(key.public_key.n, PRIME_3 * PRIME_1);
-  assert_eq!(gcd(key.private_key.e as u64, euler_totient(PRIME_3 as u64, PRIME_1 as u64)), 1);
+  let (rsa_encrypt, rsa_decrypt) = rsa_key_gen(PRIME_1, PRIME_2);
+  assert_eq!(rsa_encrypt.public_key.n, PRIME_1 * PRIME_2);
+  assert_eq!(
+    gcd(rsa_decrypt.private_key.d as u64, euler_totient(PRIME_1 as u64, PRIME_2 as u64)),
+    1
+  );
+
+  let (rsa_encrypt, rsa_decrypt) = rsa_key_gen(PRIME_2, PRIME_3);
+  assert_eq!(rsa_encrypt.public_key.n, PRIME_2 * PRIME_3);
+  assert_eq!(
+    gcd(rsa_decrypt.private_key.d as u64, euler_totient(PRIME_2 as u64, PRIME_3 as u64)),
+    1
+  );
+
+  let (rsa_encrypt, rsa_decrypt) = rsa_key_gen(PRIME_3, PRIME_1);
+  assert_eq!(rsa_encrypt.public_key.n, PRIME_3 * PRIME_1);
+  assert_eq!(
+    gcd(rsa_decrypt.private_key.d as u64, euler_totient(PRIME_3 as u64, PRIME_1 as u64)),
+    1
+  );
 }
 
 #[test]
@@ -58,33 +67,32 @@ fn test_mod_inverse() {
 #[test]
 fn test_encrypt_decrypt() {
   let message = 10;
-  let key = rsa_key_gen(PRIME_1, PRIME_2);
-  let cipher = key.encrypt(message);
-  let decrypted = key.decrypt(cipher);
+  let (rsa_encrypt, rsa_decrypt) = rsa_key_gen(PRIME_1, PRIME_2);
+  let cipher = rsa_encrypt.encrypt(message);
+  let decrypted = rsa_decrypt.decrypt(cipher);
   assert_eq!(decrypted, message);
 
-  let key = rsa_key_gen(PRIME_2, PRIME_3);
-  let cipher = key.encrypt(message);
-  let decrypted = key.decrypt(cipher);
+  let (rsa_encrypt, rsa_decrypt) = rsa_key_gen(PRIME_2, PRIME_3);
+  let cipher = rsa_encrypt.encrypt(message);
+  let decrypted = rsa_decrypt.decrypt(cipher);
   assert_eq!(decrypted, message);
 
   let message = 10;
-  let key = rsa_key_gen(PRIME_3, PRIME_1);
-  let cipher = key.encrypt(message);
-  let decrypted = key.decrypt(cipher);
+  let (rsa_encrypt, rsa_decrypt) = rsa_key_gen(PRIME_3, PRIME_1);
+  let cipher = rsa_encrypt.encrypt(message);
+  let decrypted = rsa_decrypt.decrypt(cipher);
   assert_eq!(decrypted, message);
-}
 
-#[test]
-fn test_random_prime() {
-  let prime = random_prime(2);
-  assert!(is_prime(prime));
-  assert!(prime >= 1_000_000);
+  let message = u16::MAX as u32;
+  let (rsa_encrypt, rsa_decrypt) = rsa_key_gen(10007, 49999);
+  let cipher = rsa_encrypt.encrypt(message);
+  let decrypted = rsa_decrypt.decrypt(cipher);
+  assert_eq!(decrypted, message);
 }
 
 #[test]
-fn test_random_prime_generation() {
-  let prime = random_prime(2);
+fn test_random_prime() {
+  let prime = random_prime(1_000_000);
   assert!(is_prime(prime));
   assert!(prime >= 1_000_000);
 }

src/lib.rs

@@ -30,6 +30,7 @@ pub mod encryption;
 pub mod field;
 pub mod hashes;
 pub mod kzg;
+pub mod ot;
 pub mod polynomial;
 pub mod tree;
 

src/ot/mod.rs

@@ -0,0 +1,2 @@
+//! Contains implementation of oblivious transfer and various extensions.
+pub mod ot_rsa;

src/ot/ot_rsa.rs

@@ -0,0 +1,120 @@
+//! Contains implementation of 1-out-of-2 OT using RSA encryption.
+
+use rand::{thread_rng, Rng};
+
+use crate::encryption::asymmetric::rsa::{rsa_key_gen, RSADecryption, RSAEncryption};
+
+/// Sender that has two messages and wants to send one of it to [`OTReceiver`] without knowledge of
+/// which one.
+pub struct OTSender {
+  messages:        [usize; 2],
+  random_messages: [usize; 2],
+  rsa_decrypt:     RSADecryption,
+}
+
+/// Receiver wants to get access to one of the message that [`OTSender`] has without knowledge of
+/// the other.
+pub struct OTReceiver {
+  choice: bool,
+  key:    usize,
+}
+
+impl OTSender {
+  /// create a new [`OTSender`] object.
+  /// ## Arguments
+  /// - `messages`: message that sender has access to
+  /// - `primes`: [`RSAEncryption`] primes
+  pub fn new(messages: [usize; 2], primes: [usize; 2]) -> (Self, RSAEncryption, [usize; 2]) {
+    let (rsa_encrypt, rsa_decrypt) = rsa_key_gen(primes[0], primes[1]);
+
+    let random_messages: [usize; 2] = rand::random();
+    (OTSender { messages, rsa_decrypt, random_messages }, rsa_encrypt, random_messages)
+  }
+
+  /// Encrypt messages with receiver's choice
+  pub fn encrypt(&self, v: usize) -> [usize; 2] {
+    let k0 = if v < self.random_messages[0] {
+      v + self.rsa_decrypt.private_key.n
+        - (self.random_messages[0] % self.rsa_decrypt.private_key.n)
+    } else {
+      v - self.random_messages[0]
+    };
+    let k1 = if v < self.random_messages[1] {
+      v + self.rsa_decrypt.private_key.n
+        - (self.random_messages[1] % self.rsa_decrypt.private_key.n)
+    } else {
+      v - self.random_messages[1]
+    };
+
+    let k0 = self.rsa_decrypt.decrypt((k0) as u32);
+    let k1 = self.rsa_decrypt.decrypt((k1) as u32);
+
+    println!("k0: {}, k1: {}", k0, k1);
+
+    let m0 = (self.messages[0] + k0 as usize) % self.rsa_decrypt.private_key.n;
+    let m1 = (self.messages[1] + k1 as usize) % self.rsa_decrypt.private_key.n;
+
+    [m0, m1]
+  }
+}
+
+impl OTReceiver {
+  /// create new [`OTReceiver`] object
+  /// ## Arguments
+  /// - `choice`: receiver message choice
+  pub fn new(choice: bool) -> Self {
+    let mut rng = thread_rng();
+    Self { choice, key: rng.gen::<u32>() as usize }
+  }
+
+  /// Encrypts receiver's choice out of sender's messages.
+  ///
+  /// v = (x_b + k^e) mod N
+  pub fn encrypt(&self, rsa_encrypt: RSAEncryption, sender_messages: [usize; 2]) -> usize {
+    println!("key: {}", self.key % rsa_encrypt.public_key.n);
+    (rsa_encrypt.encrypt(self.key as u32) as usize + sender_messages[self.choice as usize])
+      % rsa_encrypt.public_key.n
+  }
+
+  /// Decrypts sender's encrypted message
+  ///
+  /// m_b = (m'_b - k) mod N
+  /// ## Arguments:
+  /// - `messages`: sender's encrypted messages: m'_0, m'_1
+  /// - `modulus`: RSA modulus
+  pub fn decrypt(&self, messages: [usize; 2], modulus: usize) -> usize {
+    if messages[self.choice as usize] < self.key {
+      (messages[self.choice as usize] + modulus - (self.key % modulus)) % modulus
+    } else {
+      (messages[self.choice as usize] - self.key) % modulus
+    }
+  }
+}
+
+#[cfg(test)]
+mod tests {
+
+  use super::*;
+
+  #[test]
+  fn ot_rsa() {
+    let mut rng = thread_rng();
+    let messages = [10, 2];
+    let random_primes = [19, 13];
+
+    let (ot_sender, rsa_encrypt, random_messages) = OTSender::new(messages, random_primes);
+
+    let modulus = rsa_encrypt.public_key.n;
+
+    let bit = rng.gen::<bool>();
+    let ot_receiver = OTReceiver::new(bit);
+
+    let v = ot_receiver.encrypt(rsa_encrypt, random_messages);
+
+    let encrypted_messages = ot_sender.encrypt(v);
+
+    let message = ot_receiver.decrypt(encrypted_messages, modulus);
+
+    assert_eq!(message, messages[bit as usize]);
+  }
+}