diff --git a/src/utils.ts b/src/utils.ts
index f04a3f3..1f5c97f 100644
--- a/src/utils.ts
+++ b/src/utils.ts
@@ -17,11 +17,14 @@ export function randomFq(): Fq {
 }
 
 export function randomFr(): Fr {
-    return new Fr(randomBigIntModP(31, R))
+    return new Fr(randomBigIntModP(32, R))
 }
 
 export function randomBigIntModP(bytes: number, p: bigint): bigint {
     const randUpperBound = 2n ** BigInt(bytes * 8)
+    if (randUpperBound < p) {
+        throw new Error(`Insufficient bytes for modulus ${p}`)
+    }
     const upperBound = randUpperBound - (randUpperBound % p)
     let rand: bigint
     while ((rand = randomBigInt(bytes)) >= upperBound) {}
diff --git a/test/ff.spec.ts b/test/ff.spec.ts
index 1eeb016..6f0baf1 100644
--- a/test/ff.spec.ts
+++ b/test/ff.spec.ts
@@ -2,6 +2,7 @@ import { expect } from 'chai'
 import fs from 'node:fs/promises'
 import path from 'node:path'
 import { Fq, Fq12, Fq2, Fq6, Fr } from '../src/ff'
+import { randomFr } from '../src/utils'
 
 async function readTestVectors<S, P>(
     name: string,
@@ -98,6 +99,11 @@ const reviveFq12 = ([x, y, z]: SFq12[]): PFq12Vector => [
 
 describe('finite fields', () => {
     describe('Fr', () => {
+        it('random', () => {
+            const r = randomFr()
+            expect(r.value).to.not.equal(0n)
+        })
+
         it('inv', () => {
             const expected: [Fr, Fr][] = [
                 [1n, 1n],