diff --git a/src/math.rs b/src/math.rs
index 6ae678d..865f1cc 100644
--- a/src/math.rs
+++ b/src/math.rs
@@ -30,12 +30,12 @@ pub fn interpolate(shares: &[Share]) -> Vec<u8> {
         .collect()
 }
 
-// Generates `k` polynomial coefficients, being the last one `s` and the others randomly generated between `[1, 255]`.
+// Generates `k` polynomial coefficients, being the last one `s` and the others randomly generated between `[0, 255]`.
 // Coefficient degrees go from higher to lower in the returned vector order.
 pub fn random_polynomial<R: rand::Rng>(s: GF256, k: u8, rng: &mut R) -> Vec<GF256> {
     let k = k as usize;
     let mut poly = Vec::with_capacity(k);
-    let between = Uniform::new_inclusive(1, 255);
+    let between = Uniform::new_inclusive(0, 255);
 
     for _ in 1..k {
         poly.push(GF256(between.sample(rng)));