crypt: Switch to using large unsigned integers

- The crate now uses crypto_bigint U128 ints instead of i32.
- OsRng instead of thread_rng(), (cryptographically more secure?).
- Modular arithmetic methods from crypto_bigint, no more overflows.
- Error code for invalid parameters.
- Simpler naming.

.gitignore

@@ -1 +1,2 @@
 /target
+Cargo.lock

Cargo.lock

@@ -1,109 +0,0 @@
-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-version = 3
-
-[[package]]
-name = "autocfg"
-version = "1.1.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d468802bab17cbc0cc575e9b053f41e72aa36bfa6b7f55e3529ffa43161b97fa"
-
-[[package]]
-name = "cfg-if"
-version = "1.0.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd"
-
-[[package]]
-name = "false-bottom"
-version = "0.1.0"
-dependencies = [
- "modinverse",
- "rand",
-]
-
-[[package]]
-name = "getrandom"
-version = "0.2.12"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "190092ea657667030ac6a35e305e62fc4dd69fd98ac98631e5d3a2b1575a12b5"
-dependencies = [
- "cfg-if",
- "libc",
- "wasi",
-]
-
-[[package]]
-name = "libc"
-version = "0.2.153"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9c198f91728a82281a64e1f4f9eeb25d82cb32a5de251c6bd1b5154d63a8e7bd"
-
-[[package]]
-name = "modinverse"
-version = "0.1.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "2f62f577f148cc1a9466e7065a22e59466a7d537cceba5e77e57181d0f706633"
-dependencies = [
- "num-integer",
-]
-
-[[package]]
-name = "num-integer"
-version = "0.1.46"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7969661fd2958a5cb096e56c8e1ad0444ac2bbcd0061bd28660485a44879858f"
-dependencies = [
- "num-traits",
-]
-
-[[package]]
-name = "num-traits"
-version = "0.2.18"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "da0df0e5185db44f69b44f26786fe401b6c293d1907744beaa7fa62b2e5a517a"
-dependencies = [
- "autocfg",
-]
-
-[[package]]
-name = "ppv-lite86"
-version = "0.2.17"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5b40af805b3121feab8a3c29f04d8ad262fa8e0561883e7653e024ae4479e6de"
-
-[[package]]
-name = "rand"
-version = "0.8.5"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "34af8d1a0e25924bc5b7c43c079c942339d8f0a8b57c39049bef581b46327404"
-dependencies = [
- "libc",
- "rand_chacha",
- "rand_core",
-]
-
-[[package]]
-name = "rand_chacha"
-version = "0.3.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
-dependencies = [
- "ppv-lite86",
- "rand_core",
-]
-
-[[package]]
-name = "rand_core"
-version = "0.6.4"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ec0be4795e2f6a28069bec0b5ff3e2ac9bafc99e6a9a7dc3547996c5c816922c"
-dependencies = [
- "getrandom",
-]
-
-[[package]]
-name = "wasi"
-version = "0.11.0+wasi-snapshot-preview1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9c8d87e72b64a3b4db28d11ce29237c246188f4f51057d65a7eab63b7987e423"

Cargo.toml

@@ -6,5 +6,5 @@ edition = "2021"
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
-rand = "^0.8.5"
+rand = "0.8.5"
-modinverse = "0.1.1"
+crypto-bigint = "0.5.5"

src/errors.rs

@@ -1,6 +1,7 @@
 #[derive(Debug)]
-pub enum FalseBottomError {
+pub enum FBError {
     IntegerTooLarge,
     NoModInverse,
     InvalidKey,
+    InvalidParams,
 }

src/lib.rs

@@ -1,80 +1,85 @@
 pub mod errors;
 
-use rand::Rng;
+use rand::{Rng, seq::IteratorRandom};
-use rand::seq::IteratorRandom;
+use crate::errors::FBError;
-use crate::errors::FalseBottomError;
+use crypto_bigint::{U128, RandomMod, NonZero, rand_core::OsRng, Limb};
-use modinverse::modinverse;
 
 #[derive(Debug)]
-pub struct FalseBottom {
+pub struct FBCrypt {
-    pub k: i32,
+    k: usize,
-    pub r: Vec<i32>,
+    r: Vec<U128>,
-    pub c: Vec<i32>,
+    c: Vec<U128>,
 }
 
 #[derive(Debug)]
-pub struct FalseBottomKey {
+pub struct FBKey {
-    pub key_indices: Vec<i32>,
+    r_i: Vec<usize>,
-    pub cipher_indices: Vec<i32>,
+    c_i: Vec<usize>,
 }
 
-const P: i32 = 9973;
+// Prime number value
+const P: U128 = U128::MAX.wrapping_sub(&U128::from_u32(159 - 1));
+// Our prime is at 159th position to the left of 2^128
+const P_POS: Limb = Limb::from_u32(159);
 
-impl FalseBottom {
+impl FBCrypt {
-    pub fn init(k: i32) -> FalseBottom {
+
-	let mut rng = rand::thread_rng();
+    pub fn init(n: usize, k: usize) -> Result<FBCrypt, FBError> {
-	let mut r: Vec<i32> = Vec::new();
+	if n < k || k < 2 {
-	let mut c: Vec<i32> = Vec::new();
+	    return Err(FBError::InvalidParams)
-	for _ in 0..k {
-	    r.push(rng.gen_range(1..k));
-	    c.push(rng.gen_range(1..P));
 	}
-	FalseBottom {k, r, c}
+	const MODULUS: NonZero<U128> = NonZero::<U128>::const_new(P).0;
+	let r: Vec<U128> = (0..k)
+	    .map(|_| U128::random_mod(&mut OsRng, &MODULUS))
+	    .collect();
+	let c: Vec<U128> = (0..n)
+	    .map(|_| U128::random_mod(&mut OsRng, &MODULUS))
+	    .collect();
+	Ok(FBCrypt {k, r, c})
     }
 
-    pub fn add(&mut self, m: i32) ->
+    pub fn add(&mut self, m: &U128) -> Result<FBKey, FBError> {
-	Result<FalseBottomKey, FalseBottomError>
+	if m.ge(&P) {
-    {
+	    return Err(FBError::IntegerTooLarge);
-	if m > P as i32 {
-	    return Err(FalseBottomError::IntegerTooLarge)
 	}
-	let mut rng = rand::thread_rng();
+	let (r, c) = (&mut self.r, &mut self.c);
-	let n = rng.gen_range(2..=self.k);
+	let n = OsRng.gen_range(2..=self.k);
+	let mut c_i: Vec<usize> = (0..c.len())
+	    .choose_multiple(&mut OsRng, n-1);
+	let r_i: Vec<usize> = (0..self.k)
+	    .choose_multiple(&mut OsRng, n);
 
-	let mut cipher_indices: Vec<i32> = (0..self.c.len() as i32)
+	let mut sum: U128 = U128::ZERO;
-	    .choose_multiple(&mut rng, n as usize - 1);
+	for (&ci, &ri) in c_i.iter()
-	
+	    .zip(r_i.iter())
-	let key_indices: Vec<i32> = (0..self.k)
-	    .choose_multiple(&mut rng, n as usize);
-
-	let mut sum = 0;
-	for (j, rho) in cipher_indices.iter()
-	    .zip(key_indices.iter())
 	{
-	    sum += self.c[*j as usize] * self.r[*rho as usize];
+	    sum = sum.add_mod(
-	    sum %= P;
+		&c[ci].mul_mod_special(&r[ri], P_POS),
+		&P);
 	}
-
+	let r_last = *r_i.last().unwrap();
-	let key_last_el = *key_indices.last().unwrap() as usize;
+	let (mod_inv, inv_exists) = r[r_last].inv_mod(&P);
-	let mod_inv = modinverse(self.r[key_last_el], P)
+	let inv_exists: bool = inv_exists.into();
-	    .ok_or(FalseBottomError::NoModInverse)?;
+	if !inv_exists {
-	let cipher_new_element = ((m - sum) * mod_inv)
+	    return Err(FBError::NoModInverse);
-	    .rem_euclid(P);
+	}
-	self.c.push(cipher_new_element);
+	let c_new = m.sub_mod(&sum, &P)
-	cipher_indices.push(self.c.len() as i32 - 1);
+	    .mul_mod_special(&mod_inv, P_POS);
-	Ok(FalseBottomKey {key_indices, cipher_indices})
+	c.push(c_new);
+	c_i.push(c.len()-1);
+	Ok(FBKey {r_i, c_i})
     }
 
-    pub fn decrypt(&self, indices: &FalseBottomKey) -> Result<i32, FalseBottomError> {
+    pub fn decrypt(&self, indices: &FBKey) -> Result<U128, FBError> {
-	let keyi = &indices.key_indices;
+	let (r_i, c_i) = (&indices.r_i, &indices.c_i);
-	let cipheri = &indices.cipher_indices;
+	if r_i.len() > self.r.len() || c_i.len() > self.c.len() {
-	if keyi.len() > self.r.len() || cipheri.len() > self.c.len() {
+	    return Err(FBError::InvalidKey)
-	    return Err(FalseBottomError::InvalidKey)
 	}
-	let mut m: i32 = 0;
+	let mut m: U128 = U128::ZERO;
-	for (ki, ci) in keyi.iter().zip(cipheri.iter()) {
+	for (&ri, &ci) in r_i.iter().zip(c_i.iter()) {
-	    m += self.c[*ci as usize] * self.r[*ki as usize];
+	    m = m.add_mod(
-	    m %= P;
+		&self.c[ci].mul_mod_special(&self.r[ri], P_POS),
+		&P);
 	}
 	Ok(m)
     }
@@ -83,12 +88,20 @@ impl FalseBottom {
 #[cfg(test)]
 mod tests {
     use super::*;
+
     #[test]
     fn encrypt_decrypt_100() {
-	let msg = 100;
+	let msg: U128 = U128::from_u32(100);
-	let mut fb = FalseBottom::init(9);
+	let mut fb = FBCrypt::init(20, 12).unwrap();
-	let key = fb.add(msg).unwrap();
+	let key = fb.add(&msg).unwrap();
 	let decrypted = fb.decrypt(&key).unwrap();
-        assert_eq!(decrypted, msg);
+        assert_eq!(msg, decrypted);
+    }
+
+    #[test]
+    fn many_runs() {
+	for _ in 0..1000 {
+	    encrypt_decrypt_100();
+	}
     }
 }