[crypto]添加素数相关的算法和验证示例

crypto/crypto_util/src/lib.rs

@@ -1,2 +1,3 @@
 pub mod base_compute;
 pub mod point;
+mod prime;

crypto/crypto_util/src/prime.rs

@@ -0,0 +1,85 @@
+// 统计范围[2，n）内有多少个质数
+fn count_prime_up_to(n: usize) -> usize {
+    (2..n).filter(|x| is_prime(*x)).count()
+}
+
+fn is_prime(n: usize) -> bool {
+    if n <= 1 {
+        return false;
+    }
+    if n <= 3 {
+        return true;
+    }
+    if n % 2 == 0 || n % 3 == 0 {
+        return false;
+    }
+    let mut i = 5;
+    while i * i <= n {
+        if n % i == 0 || n % (i + 2) == 0 {
+            return false;
+        }
+        i += 6;
+    }
+    return true;
+}
+
+// 确定性素性判断：[埃拉托斯特尼筛法](https://zh.wikipedia.org/wiki/%E5%9F%83%E6%8B%89%E6%89%98%E6%96%AF%E7%89%B9%E5%B0%BC%E7%AD%9B%E6%B3%95)
+fn sieve_of_eratosthenes(n: usize) -> Vec<usize> {
+    let mut is_primes = vec![true; n + 1];
+    let mut primes = Vec::new();
+    // 0和1不是素数
+    is_primes[0] = false;
+    is_primes[1] = false;
+    // 基础原理
+    /*    for p in 2..n {
+        if is_primes[p] {
+            primes.push(p);
+            let mut multiple = p * p;
+            while multiple <= n {
+                is_primes[multiple] = false;
+                multiple += p;
+            }
+        }
+    }*/
+    // 优化标记空间到sqrt(n)
+    for p in 2..=((n as f64).sqrt() as usize) {
+        if is_primes[p] {
+            let mut multiple = p * p;
+            while multiple <= n {
+                is_primes[multiple] = false;
+                multiple += p;
+            }
+        }
+    }
+    for p in 2..=n {
+        if is_primes[p] {
+            primes.push(p);
+        }
+    }
+    primes
+}
+
+#[cfg(test)]
+mod test_prime {
+    use super::*;
+
+    #[test]
+    fn test_prime_theorem() {
+        let n = 1_000_000;
+        let prime_nums = count_prime_up_to(n);
+        let estimate_prime = (n as f64) / (n as f64).ln();
+        println!(
+            "(0, {n}) primes nums: {prime_nums}, estimate prime nums {}",
+            estimate_prime
+        );
+    }
+
+    #[test]
+    fn test_sieve_of_eratosthenes() {
+        let primes = sieve_of_eratosthenes(50);
+        assert_eq!(
+            primes,
+            vec![2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
+        );
+    }
+}