diff --git a/Cargo.toml b/Cargo.toml index ddbdc50..ed35a3e 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -20,10 +20,10 @@ travis-ci = { repository = "AtropineTears/num-primes", branch = "master" } [dependencies] # num num = { version = "0.4.0", default-features = false } -num-traits = "0.2.11" -num-bigint = { version = "0.2.6", features = ["rand"] } +num-traits = "0.2.14" +num-bigint = { version = "0.4.3", features = ["rand"] } # random -rand = "0.5.6" +rand = "0.8.4" # Logging log = "0.4.14" diff --git a/README.md b/README.md index 0519e12..99a66eb 100644 --- a/README.md +++ b/README.md @@ -11,10 +11,6 @@ It takes full advantage of the [num](https://crates.io/crates/num) crate on **st * Read the [License](#license) * Read the [Contribution](#contribution) -## Notice - -Please note there is a critical bug in this program that I cannot seem to fix where it marks some prime numbers as not prime. It is in the miller-rabin implementation and I cannot seem to fix it. If anyone is up to it, feel free to look through the issues tab for information about the bug and submit a PR if you find a fix. - ## Usage Add this to your `Cargo.toml`: @@ -24,10 +20,6 @@ Add this to your `Cargo.toml`: num-primes = "0.2.0" ``` -## Warning - -There is currently a major bug in `is_prime()` and `is_composite()` that makes some values return wrong. For example, a prime can sometimes be marked as composite unless it was generated as they use the same tests to test for primality. - ## How To Use There are three main structs that are included in this library @@ -98,10 +90,6 @@ fn main(){ } ``` -## Verification - -WARNING: There is currently a bug that makes verification of certain prime numbers fail. Be careful when using this feature. - ### Verify Composite Number This function will verify whether a `BigUint` type is a **composite** by returning a boolean value. diff --git a/src/lib.rs b/src/lib.rs index 7de7569..dbca7f1 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -8,8 +8,10 @@ extern crate num_bigint as bigint; use core::ops::Sub; +use core::convert::TryInto; +use num::integer::gcd; use num::Integer; -pub use bigint::{BigUint,RandBigInt}; +pub use bigint::{BigUint, BigInt, RandBigInt}; use num_traits::{Zero, One}; use num_traits::*; @@ -19,7 +21,7 @@ use log::info; // Settings // NIST recomends 5 rounds for miller rabin. This implementation does 8. Apple uses 16. Three iterations has a probability of 2^80 of failing -const MILLER_RABIN_ROUNDS: usize = 8usize; +const MILLER_RABIN_ROUNDS: usize = 64usize; /// # Generator @@ -97,11 +99,11 @@ impl Generator { /// ``` pub fn new_composite(n: usize) -> BigUint { let mut rng = rand::thread_rng(); + let n = n.try_into().unwrap(); + loop { - // Make mutable and set LSB and MSB - let candidate: BigUint = rng.gen_biguint(n); - //candidate.set_bit(0, true); - //candidate.set_bit((n-1) as u32, true); + let mut candidate: BigUint = rng.gen_biguint(n); + candidate.set_bit((n-1) as u64, true); if is_prime(&candidate) == false { return candidate; } @@ -123,7 +125,7 @@ impl Generator { /// ``` pub fn new_uint(n: usize) -> BigUint { let mut rng = rand::thread_rng(); - return rng.gen_biguint(n); + return rng.gen_biguint(n.try_into().unwrap()); } /// # Generate Prime Number @@ -146,13 +148,13 @@ impl Generator { /// ``` pub fn new_prime(n: usize) -> BigUint { let mut rng = rand::thread_rng(); - + let n = n.try_into().unwrap(); + loop { - // Make mutable and set LSB and MSB - let candidate: BigUint = rng.gen_biguint(n); - - //candidate.set_bit(0, true); - //candidate.set_bit((n-1) as u32, true); + let mut candidate: BigUint = rng.gen_biguint(n); + + candidate.set_bit(0, true); + candidate.set_bit((n-1) as u64, true); if is_prime(&candidate) == true { return candidate; @@ -172,11 +174,14 @@ impl Generator { /// ``` pub fn safe_prime(n: usize) -> BigUint { let mut rng = rand::thread_rng(); + let n = n.try_into().unwrap(); + loop { - // Make mutable and set LSB and MSB - let candidate: BigUint = rng.gen_biguint(n); - //candidate.set_bit(0, true); - //candidate.set_bit((n-1) as u32, true); + let mut candidate: BigUint = rng.gen_biguint(n); + + candidate.set_bit(0, true); + candidate.set_bit((n-1) as u64, true); + if is_prime(&candidate) == true { if is_safe_prime(&candidate) == true { // checks with (p-1/n) @@ -219,7 +224,7 @@ impl Verification { /// let x: BigUint = BigUint::from_u64(7u64).unwrap(); /// /// // Verify Its A Smooth Number - /// let result: bool = Verification::is_smooth_number(&x,31.0,5); + /// let result: bool = Verification::is_very_smooth_number(&x,31.0,5); /// /// println!("Is A {} Smooth Number: {}",x,result); /// } @@ -256,39 +261,85 @@ impl Factorization { return Some(n) } + let org = n.clone().try_into().unwrap(); + let mut n: BigInt = n.try_into().unwrap(); + + let mut f = BigInt::zero(); + + let one = BigInt::one(); + let two: BigInt = &one + &one; + + // This while loop will run until n is completely factorized, + // thus giving the largest factor. If you only care about A factor, + // this can be rewritten as below for much better performance. + + while n > one { + // while f == BigInt::zero() { + + + let mut x = two.clone(); + let mut y = two.clone(); + let mut d = one.clone(); + let n_int = n.clone().try_into().unwrap(); + + let g = |x: &BigInt| (x.modpow(&two, &n_int) + 1) % &n_int; + + while d == one { + x = g(&x); + y = g(&g(&y)); + d = gcd((&x - &y).abs(), &n_int - 0); + } + + if &d == &org { + return Some(brute_force_prime_factor(d.try_into().unwrap())); + } + + n /= &d; + + if &d > &f { + f = d; + } + } + + return Some(f.try_into().unwrap()); + } +} + +fn brute_force_prime_factor(mut n: BigUint) -> BigUint { + let one = BigUint::one(); let two = &one + &one; - + // STEP 1 | n divided by 2 while n.is_even() { n = n / &two; } - + // STEP 2 | 3..sqrt(n) | Divide i by n. On failure, add 2 to i let n_sqrt = n.sqrt().to_usize().unwrap(); - for mut i in 3..n_sqrt { - while n.divides(&BigUint::from(i)) { - n = n / BigUint::from(i); + for mut i in 3..n_sqrt + 1 { + let divisor = BigUint::from(i); + while n.divides(&divisor) { + n /= &divisor; } - i = i + 2usize; + i = i + 1usize; } - // Step 3 - if n > two { - return Some(n) - } - else { - return None - } + return if n == one { BigUint::from(n_sqrt) } else { n }; +} - } +#[derive(PartialEq)] +enum SmallPrimeResult { + Prime, + NotPrime, + MaybePrime } // if true, then is not prime // if false, then maybe prime -fn div_small_primes(numb: &BigUint) -> bool { +fn div_small_primes(numb: &BigUint) -> SmallPrimeResult { let zero: BigUint = Zero::zero(); let one: BigUint = One::one(); @@ -296,15 +347,19 @@ fn div_small_primes(numb: &BigUint) -> bool { static SMALL_PRIMES: [u32; 2048] = 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for p in SMALL_PRIMES.iter() { - if numb % &BigUint::from(*p) == zero { - return false + let prime = &BigUint::from(*p); + + if numb == prime { + return SmallPrimeResult::Prime; } - // Fixes part of Issue 1 but may slow down generation | https://github.com/AtropineTearz/num-primes/issues/1 - if numb / &BigUint::from(*p) == one { - return true + + // numb % prime == 0 and numb != prime => numb is not prime + if numb % prime == zero { + return SmallPrimeResult::NotPrime; } } - return true + + return SmallPrimeResult::MaybePrime; } @@ -316,9 +371,8 @@ fn fermat(candidate: &BigUint) -> bool { // p - 1 let exponent: BigUint = candidate.sub(BigUint::one()); - let result = random.modpow(&(exponent), candidate); + let result = random.modpow(&exponent, candidate); - //let result = random.pow_mod(&(candidate - One::one()), candidate); result == One::one() } @@ -327,61 +381,40 @@ fn miller_rabin(candidate: &BigUint, limit: usize) -> bool { let zero: BigUint = Zero::zero(); let one = BigUint::one(); let two: BigUint = &one + &one; - let two_2 = num_bigint::ToBigUint::to_biguint(&2).unwrap(); // Check Whether Candidate Is 2 (which is prime) - if candidate == &two_2 { + if candidate == &two { return true } - - // Check Whether Candidate Is Even - /* - if candidate.mod(two) { - return false - } - */ let (d,s) = rewrite(&candidate); let step = s.sub(&one).to_usize().unwrap(); + let one_usize = one.to_usize().unwrap(); + let zero_usize = zero.to_usize().unwrap(); + let c_minus_1 = candidate-&one; let mut rng = rand::thread_rng(); for _i in 0..limit { // Generate Random Number between [2,n-1) | Exclusive End Range; Uses (n-1), not (n-2) - let a = rng.gen_biguint_range(&two, &(candidate-&one)); - - // Reference Implementation - // Pretty sure `sample_range()` has an inclusive end - //let basis = Int::sample_range(&two, &(candidate-&two)); + let a = rng.gen_biguint_range(&two, &c_minus_1); // (a^d mod n) let mut x = a.modpow(&d, &candidate); - // Reference Implementation - //let mut y = Int::modpow(&basis, &d, candidate); - - if x == one || x == (candidate - &one) { + if x == one || x == c_minus_1 { continue - // return true } else { - // Convert To Usizes For Loop - // step = (s - 1) - let one_usize = one.to_usize().unwrap(); - let zero_usize = zero.to_usize().unwrap(); - let mut break_early = false; // Issue #1 | Changed one_usize to zero_usize; step (s-1) was equal to iterations-1 and therefore needed an extra iteration for _ in zero_usize..step { x = x.modpow(&two,candidate); - // Reference Implementation - //y = Int::modpow(&y, &two, candidate); - if x == one { return false } - else if x == (candidate - BigUint::one()) { + else if x == c_minus_1 { break_early = true; break; } @@ -433,9 +466,11 @@ fn is_prime(candidate: &BigUint) -> bool { return false } - // First, simple trial divide - if div_small_primes(candidate) == false { - return false + + let p = div_small_primes(candidate); + + if p != SmallPrimeResult::MaybePrime { + return p == SmallPrimeResult::Prime; } // Second, Fermat's little theo test on the candidate @@ -450,7 +485,6 @@ fn is_prime(candidate: &BigUint) -> bool { else { return true } - return true } // p = 2q + 1 diff --git a/tests/factorization.rs b/tests/factorization.rs index 59dcd30..ca2eba3 100644 --- a/tests/factorization.rs +++ b/tests/factorization.rs @@ -2,18 +2,17 @@ use num_primes::{Generator,Factorization}; #[test] fn factor_uint(){ - // Generate a Large Unsigned Integer of 32 bits - let x = Generator::new_uint(32); - - println!("Number: {}",x); + // Generate a Unsigned Integer of 16 bits + let p = Generator::new_prime(16); + let q = Generator::new_prime(16); + let f = &p * &q; // Factor The Largest Prime of x - let prime_factor = Factorization::prime_factor(x); + let prime_factor = Factorization::prime_factor(f).unwrap(); - // Print Out The Statements - match prime_factor { - Some(prime_factor) => println!("Prime Factor: {}",prime_factor), - None => println!("There are no prime factors") + if &p > &q { + assert_eq!(prime_factor, p); + } else { + assert_eq!(prime_factor, q); } - } \ No newline at end of file