diff --git a/core/src/hash.rs b/core/src/hash.rs
new file mode 100644
index 0000000..7442e87
--- /dev/null
+++ b/core/src/hash.rs
@@ -0,0 +1,17 @@
+//! FNV-1a hashing for state checksums.
+//!
+//! The hash only has to reveal accidental divergence between peers. It is
+//! not meant to resist tampering.
+
+const FNV_OFFSET_BASIS: u64 = 0xcbf2_9ce4_8422_2325;
+const FNV_PRIME: u64 = 0x0000_0100_0000_01b3;
+
+/// Returns the 64-bit FNV-1a hash of `bytes`.
+pub fn fnv1a64(bytes: &[u8]) -> u64 {
+    let mut hash = FNV_OFFSET_BASIS;
+    for &byte in bytes {
+        hash ^= u64::from(byte);
+        hash = hash.wrapping_mul(FNV_PRIME);
+    }
+    hash
+}
diff --git a/core/src/lib.rs b/core/src/lib.rs
index 127e8a1..b640c90 100644
--- a/core/src/lib.rs
+++ b/core/src/lib.rs
@@ -7,3 +7,5 @@
 //! world and exchange nothing but commands.
 
 pub mod codec;
+pub mod hash;
+pub mod rng;
diff --git a/core/src/rng.rs b/core/src/rng.rs
new file mode 100644
index 0000000..53e269f
--- /dev/null
+++ b/core/src/rng.rs
@@ -0,0 +1,34 @@
+//! Repeatable pseudo random numbers (SplitMix64).
+//!
+//! The core never uses any other source of randomness. The same seed always
+//! gives the same sequence, on every machine.
+
+/// Pseudo random number generator with 64 bits of state.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct Rng {
+    state: u64,
+}
+
+impl Rng {
+    pub fn new(seed: u64) -> Self {
+        Self { state: seed }
+    }
+
+    /// Returns the next value of the sequence.
+    pub fn next_u64(&mut self) -> u64 {
+        self.state = self.state.wrapping_add(0x9E37_79B9_7F4A_7C15);
+        let mut z = self.state;
+        z = (z ^ (z >> 30)).wrapping_mul(0xBF58_476D_1CE4_E5B9);
+        z = (z ^ (z >> 27)).wrapping_mul(0x94D0_49BB_1331_11EB);
+        z ^ (z >> 31)
+    }
+
+    /// Returns a value in `0..bound`.
+    ///
+    /// # Panics
+    /// Panics if `bound` is zero.
+    pub fn below(&mut self, bound: u32) -> u32 {
+        assert!(bound > 0, "bound must be greater than zero");
+        ((u128::from(self.next_u64()) * u128::from(bound)) >> 64) as u32
+    }
+}
diff --git a/core/tests/hash.rs b/core/tests/hash.rs
new file mode 100644
index 0000000..96784db
--- /dev/null
+++ b/core/tests/hash.rs
@@ -0,0 +1,13 @@
+use grovewright_core::hash::fnv1a64;
+
+#[test]
+fn matches_the_published_fnv1a_test_vectors() {
+    assert_eq!(fnv1a64(b""), 0xcbf2_9ce4_8422_2325);
+    assert_eq!(fnv1a64(b"a"), 0xaf63_dc4c_8601_ec8c);
+    assert_eq!(fnv1a64(b"foobar"), 0x8594_4171_f739_67e8);
+}
+
+#[test]
+fn the_order_of_bytes_matters() {
+    assert_ne!(fnv1a64(&[0, 1]), fnv1a64(&[1, 0]));
+}
diff --git a/core/tests/rng.rs b/core/tests/rng.rs
new file mode 100644
index 0000000..4060e80
--- /dev/null
+++ b/core/tests/rng.rs
@@ -0,0 +1,49 @@
+use grovewright_core::rng::Rng;
+
+#[test]
+fn matches_the_splitmix64_reference_values() {
+    let mut rng = Rng::new(0);
+    assert_eq!(rng.next_u64(), 0xE220_A839_7B1D_CDAF);
+    assert_eq!(rng.next_u64(), 0x6E78_9E6A_A1B9_65F4);
+    assert_eq!(rng.next_u64(), 0x06C4_5D18_8009_454F);
+}
+
+#[test]
+fn the_same_seed_gives_the_same_sequence() {
+    let mut a = Rng::new(2026);
+    let mut b = Rng::new(2026);
+    for _ in 0..1_000 {
+        assert_eq!(a.next_u64(), b.next_u64());
+    }
+}
+
+#[test]
+fn different_seeds_give_different_sequences() {
+    assert_ne!(Rng::new(1).next_u64(), Rng::new(2).next_u64());
+}
+
+#[test]
+fn below_stays_inside_the_bound() {
+    let mut rng = Rng::new(7);
+    for bound in [1u32, 2, 3, 10, 100, 1_000_000, u32::MAX] {
+        for _ in 0..1_000 {
+            assert!(rng.below(bound) < bound);
+        }
+    }
+}
+
+#[test]
+fn below_reaches_every_value_of_a_small_bound() {
+    let mut rng = Rng::new(99);
+    let mut seen = [false; 6];
+    for _ in 0..1_000 {
+        seen[rng.below(6) as usize] = true;
+    }
+    assert_eq!(seen, [true; 6]);
+}
+
+#[test]
+#[should_panic(expected = "bound must be greater than zero")]
+fn below_refuses_a_bound_of_zero() {
+    Rng::new(1).below(0);
+}