Add CSIDH example

Author: rustaceanrob

Cargo.lock

@@ -6,3 +6,6 @@ edition = "2024"
 [dependencies]
 field = { path = "../field" }
 curve = { path = "../curve" }
+
+[dev-dependencies]
+rand = "0.10.1"

isogeny/Cargo.toml

@@ -0,0 +1,43 @@
+use curve::Curve;
+use isogeny::csidh;
+use rand::{RngExt, rng};
+
+const KEY_BOUND: usize = 74;
+
+fn random_private_key<R: RngExt>(rng: &mut R) -> [i8; csidh::PRIMES.len()] {
+    let mut key = [0i8; csidh::PRIMES.len()];
+    for slot in key.iter_mut().take(KEY_BOUND) {
+        *slot = (rng.random::<u8>() % 3) as i8 - 1;
+    }
+    key
+}
+
+fn main() {
+    let mut rng = rng();
+    let a_priv = random_private_key(&mut rng);
+    let b_priv = random_private_key(&mut rng);
+    let ells: Vec<u64> = csidh::PRIMES.iter().take(KEY_BOUND).copied().collect();
+    println!("Small primes in play: {:?}", ells);
+    println!("Alice's private:      {:?}", &a_priv[..KEY_BOUND]);
+    println!("Bob's private:        {:?}", &b_priv[..KEY_BOUND]);
+
+    let start = csidh::base_curve();
+
+    println!("\nDeriving public curves...");
+    let t = std::time::Instant::now();
+    let a_pub = csidh::action(&start, &a_priv, &mut || rng.random::<u64>());
+    let b_pub = csidh::action(&start, &b_priv, &mut || rng.random::<u64>());
+    println!("done in {:?}", t.elapsed());
+
+    println!("\nDeriving shared secrets...");
+    let t = std::time::Instant::now();
+    let a_shared = csidh::action(&b_pub, &a_priv, &mut || rng.random::<u64>());
+    let b_shared = csidh::action(&a_pub, &b_priv, &mut || rng.random::<u64>());
+    println!("done in {:?}", t.elapsed());
+
+    let j_a = a_shared.j_invariant();
+    let j_b = b_shared.j_invariant();
+    assert_eq!(j_a, j_b, "shared j-invariants disagreed");
+    println!("\nShared j-invariant: {:?}", j_a);
+    println!("CSIDH shared secret established.");
+}