diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index 9a1eab14..c6680623 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -14,9 +14,8 @@ jobs:
       matrix:
         rust: [
           1.31.0, # 2018!
-          1.32.0, # rand
           1.34.0, # quickcheck, has_try_from
-          1.36.0, # alloc
+          1.36.0, # alloc, rand
           stable,
           beta,
           nightly
diff --git a/Cargo.toml b/Cargo.toml
index 76c374cc..6e54ee32 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -8,12 +8,17 @@ categories = [ "algorithms", "data-structures", "science" ]
 license = "MIT OR Apache-2.0"
 name = "num-bigint"
 repository = "https://github.com/rust-num/num-bigint"
-version = "0.3.2"
+version = "0.4.0-pre"
+publish = false
 readme = "README.md"
 build = "build.rs"
 exclude = ["/bors.toml", "/ci/*", "/.github/*"]
 edition = "2018"
 
+[features]
+default = ["std"]
+std = ["num-integer/std", "num-traits/std"]
+
 [package.metadata.docs.rs]
 features = ["std", "serde", "rand", "quickcheck", "arbitrary"]
 
@@ -47,7 +52,7 @@ features = ["i128"]
 
 [dependencies.rand]
 optional = true
-version = "0.7"
+version = "0.8"
 default-features = false
 
 [dependencies.serde]
@@ -65,9 +70,5 @@ optional = true
 version = "0.4"
 default-features = false
 
-[features]
-default = ["std"]
-std = ["num-integer/std", "num-traits/std"]
-
 [build-dependencies]
 autocfg = "1"
diff --git a/README.md b/README.md
index d9df19bc..3311b7a8 100644
--- a/README.md
+++ b/README.md
@@ -29,12 +29,12 @@ if your compiler is not new enough.
 feature is enabled. To enable it include rand as
 
 ```toml
-rand = "0.7"
+rand = "0.8"
 num-bigint = { version = "0.3", features = ["rand"] }
 ```
 
 Note that you must use the version of `rand` that `num-bigint` is compatible
-with: `0.7`.
+with: `0.8`.
 
 ## Releases
 
diff --git a/benches/bigint.rs b/benches/bigint.rs
index c2f7bd4d..b7f5fd21 100644
--- a/benches/bigint.rs
+++ b/benches/bigint.rs
@@ -5,18 +5,11 @@ extern crate test;
 
 use num_bigint::{BigInt, BigUint, RandBigInt};
 use num_traits::{FromPrimitive, Num, One, Zero};
-use rand::rngs::StdRng;
-use rand::SeedableRng;
 use std::mem::replace;
 use test::Bencher;
 
-fn get_rng() -> StdRng {
-    let mut seed = [0; 32];
-    for i in 1..32 {
-        seed[usize::from(i)] = i;
-    }
-    SeedableRng::from_seed(seed)
-}
+mod rng;
+use rng::get_rng;
 
 fn multiply_bench(b: &mut Bencher, xbits: u64, ybits: u64) {
     let mut rng = get_rng();
diff --git a/benches/gcd.rs b/benches/gcd.rs
index 1a65654c..c211b6ef 100644
--- a/benches/gcd.rs
+++ b/benches/gcd.rs
@@ -6,17 +6,10 @@ extern crate test;
 use num_bigint::{BigUint, RandBigInt};
 use num_integer::Integer;
 use num_traits::Zero;
-use rand::rngs::StdRng;
-use rand::SeedableRng;
 use test::Bencher;
 
-fn get_rng() -> StdRng {
-    let mut seed = [0; 32];
-    for i in 1..32 {
-        seed[usize::from(i)] = i;
-    }
-    SeedableRng::from_seed(seed)
-}
+mod rng;
+use rng::get_rng;
 
 fn bench(b: &mut Bencher, bits: u64, gcd: fn(&BigUint, &BigUint) -> BigUint) {
     let mut rng = get_rng();
diff --git a/benches/rng/mod.rs b/benches/rng/mod.rs
new file mode 100644
index 00000000..33e4f0fa
--- /dev/null
+++ b/benches/rng/mod.rs
@@ -0,0 +1,38 @@
+use rand::RngCore;
+
+pub(crate) fn get_rng() -> impl RngCore {
+    XorShiftStar {
+        a: 0x0123_4567_89AB_CDEF,
+    }
+}
+
+/// Simple `Rng` for benchmarking without additional dependencies
+struct XorShiftStar {
+    a: u64,
+}
+
+impl RngCore for XorShiftStar {
+    fn next_u32(&mut self) -> u32 {
+        self.next_u64() as u32
+    }
+
+    fn next_u64(&mut self) -> u64 {
+        // https://en.wikipedia.org/wiki/Xorshift#xorshift*
+        self.a ^= self.a >> 12;
+        self.a ^= self.a << 25;
+        self.a ^= self.a >> 27;
+        self.a.wrapping_mul(0x2545_F491_4F6C_DD1D)
+    }
+
+    fn fill_bytes(&mut self, dest: &mut [u8]) {
+        for chunk in dest.chunks_mut(8) {
+            let bytes = self.next_u64().to_le_bytes();
+            let slice = &bytes[..chunk.len()];
+            chunk.copy_from_slice(slice)
+        }
+    }
+
+    fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), rand::Error> {
+        Ok(self.fill_bytes(dest))
+    }
+}
diff --git a/benches/roots.rs b/benches/roots.rs
index 2433cf0a..7afc4f76 100644
--- a/benches/roots.rs
+++ b/benches/roots.rs
@@ -4,10 +4,11 @@
 extern crate test;
 
 use num_bigint::{BigUint, RandBigInt};
-use rand::rngs::StdRng;
-use rand::SeedableRng;
 use test::Bencher;
 
+mod rng;
+use rng::get_rng;
+
 // The `big64` cases demonstrate the speed of cases where the value
 // can be converted to a `u64` primitive for faster calculation.
 //
@@ -16,14 +17,6 @@ use test::Bencher;
 //
 // The `big2k` and `big4k` cases are too big for `f64`, and use a simpler guess.
 
-fn get_rng() -> StdRng {
-    let mut seed = [0; 32];
-    for i in 1..32 {
-        seed[usize::from(i)] = i;
-    }
-    SeedableRng::from_seed(seed)
-}
-
 fn check(x: &BigUint, n: u32) {
     let root = x.nth_root(n);
     if n == 2 {
diff --git a/bors.toml b/bors.toml
index 5ef58889..1a5421b0 100644
--- a/bors.toml
+++ b/bors.toml
@@ -1,6 +1,5 @@
 status = [
   "Test (1.31.0)",
-  "Test (1.32.0)",
   "Test (1.34.0)",
   "Test (1.36.0)",
   "Test (stable)",
diff --git a/ci/big_rand/Cargo.toml b/ci/big_rand/Cargo.toml
index 199c022e..d2bfe353 100644
--- a/ci/big_rand/Cargo.toml
+++ b/ci/big_rand/Cargo.toml
@@ -6,14 +6,11 @@ edition = "2018"
 
 [dependencies]
 num-traits = "0.2.11"
-rand_chacha = "0.2"
-rand_isaac = "0.2"
-rand_xorshift = "0.2"
+rand = "0.8"
+rand_chacha = "0.3"
+rand_isaac = "0.3"
+rand_xorshift = "0.3"
 
 [dependencies.num-bigint]
 features = ["rand"]
 path = "../.."
-
-[dependencies.rand]
-features = ["small_rng"]
-version = "0.7"
diff --git a/ci/big_rand/src/lib.rs b/ci/big_rand/src/lib.rs
index 1bea5750..69728777 100644
--- a/ci/big_rand/src/lib.rs
+++ b/ci/big_rand/src/lib.rs
@@ -11,7 +11,7 @@ mod torture;
 mod biguint {
     use num_bigint::{BigUint, RandBigInt, RandomBits};
     use num_traits::Zero;
-    use rand::distributions::Uniform;
+    use rand::distributions::{Distribution, Uniform};
     use rand::thread_rng;
     use rand::{Rng, SeedableRng};
 
@@ -192,7 +192,7 @@ mod biguint {
 
         let mut rng = thread_rng();
         let bit_range = Uniform::new(0, 2048);
-        let sample_bits: Vec<_> = rng.sample_iter(&bit_range).take(100).collect();
+        let sample_bits: Vec<_> = bit_range.sample_iter(&mut rng).take(100).collect();
         for bits in sample_bits {
             let x = rng.gen_biguint(bits);
             for n in 2..11 {
diff --git a/ci/big_rand/src/torture.rs b/ci/big_rand/src/torture.rs
index 746128de..72059ef2 100644
--- a/ci/big_rand/src/torture.rs
+++ b/ci/big_rand/src/torture.rs
@@ -1,11 +1,10 @@
 use num_bigint::RandBigInt;
 use num_traits::Zero;
 use rand::prelude::*;
-use rand::rngs::SmallRng;
+use rand_xorshift::XorShiftRng;
 
-fn get_rng() -> SmallRng {
-    let seed = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16];
-    SmallRng::from_seed(seed)
+fn get_rng() -> XorShiftRng {
+    XorShiftRng::seed_from_u64(0x1234_5678_9abc_def0)
 }
 
 fn test_mul_divide_torture_count(count: usize) {
@@ -14,8 +13,8 @@ fn test_mul_divide_torture_count(count: usize) {
 
     for _ in 0..count {
         // Test with numbers of random sizes:
-        let xbits = rng.gen_range(0, bits_max);
-        let ybits = rng.gen_range(0, bits_max);
+        let xbits = rng.gen_range(0..bits_max);
+        let ybits = rng.gen_range(0..bits_max);
 
         let x = rng.gen_biguint(xbits);
         let y = rng.gen_biguint(ybits);
diff --git a/ci/rustup.sh b/ci/rustup.sh
index ad98c34a..ef75c700 100755
--- a/ci/rustup.sh
+++ b/ci/rustup.sh
@@ -5,6 +5,6 @@
 set -ex
 
 ci=$(dirname $0)
-for version in 1.31.0 1.32.0 1.34.0 1.36.0 stable beta nightly; do
+for version in 1.31.0 1.34.0 1.36.0 stable beta nightly; do
     rustup run "$version" "$ci/test_full.sh"
 done
diff --git a/ci/test_full.sh b/ci/test_full.sh
index 3b3b472d..c3e2785f 100755
--- a/ci/test_full.sh
+++ b/ci/test_full.sh
@@ -28,8 +28,8 @@ if ! check_version $MSRV ; then
 fi
 
 STD_FEATURES=(serde)
-check_version 1.32 && STD_FEATURES+=(rand)
 check_version 1.34 && STD_FEATURES+=(quickcheck)
+check_version 1.36 && STD_FEATURES+=(rand)
 check_version 1.36 && NO_STD_FEATURES=(serde rand)
 check_version 1.40 && STD_FEATURES+=(arbitrary)
 echo "Testing supported features: ${STD_FEATURES[*]}"