diff --git a/.travis.yml b/.travis.yml
index ce24cfcb..4a39a397 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,7 +2,7 @@ language: rust
 
 matrix:
   include:
-    - rust: 1.31.0
+    - rust: 1.36.0
     - rust: stable
     - rust: nightly
       env: TRAVIS_NIGHTLY=true
diff --git a/Cargo.toml b/Cargo.toml
index c8291560..9021dcab 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -12,18 +12,18 @@ categories = ["cryptography"]
 readme = "README.md"
 
 [dependencies]
-num-bigint = { version = "0.5", features = ["rand", "i128", "u64_digit", "prime", "zeroize"], package = "num-bigint-dig" }
+num-bigint = { version = "0.6", features = ["rand", "i128", "u64_digit", "prime", "zeroize"], package = "num-bigint-dig" }
 num-traits = "0.2.6"
 num-integer = "0.1.39"
 num-iter = "0.1.37"
 lazy_static = "1.3.0"
-rand = "0.6.5"
+rand = "0.7.0"
 byteorder = "1.3.1"
 failure = "0.1.5"
 subtle = "2.0.0"
 
 [dependencies.zeroize]
-version = "0.10.1"
+version = "1.1.0"
 features = ["alloc", "zeroize_derive"]
 
 [dependencies.serde]
@@ -33,11 +33,12 @@ default-features = false
 features = ["std", "derive"]
 
 [dev-dependencies]
-base64 = "0.10.1"
+base64 = "0.11.0"
 sha-1 = "0.8.1"
 sha2 = "0.8.0"
 hex = "0.4.0"
 serde_test = "1.0.89"
+rand_xorshift = "0.2.0"
 
 
 [[bench]]
diff --git a/README.md b/README.md
index 4156b327..c88eb99d 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,6 @@
 # RSA
 [![crates.io](https://img.shields.io/crates/v/rsa.svg)](https://crates.io/crates/rsa) [![Documentation](https://docs.rs/rsa/badge.svg)](https://docs.rs/rsa) [![Build Status](https://travis-ci.org/RustCrypto/RSA.svg?branch=master)](https://travis-ci.org/RustCrypto/RSA) [![dependency status](https://deps.rs/repo/github/RustCrypto/RSA/status.svg)](https://deps.rs/repo/github/RustCrypto/RSA)
+![minimum rustc 1.36](https://img.shields.io/badge/rustc-1.36+-red.svg)
 
 A portable RSA implementation in pure Rust.
 
@@ -14,7 +15,7 @@ extern crate rand;
 use rsa::{PublicKey, RSAPrivateKey, PaddingScheme};
 use rand::rngs::OsRng;
 
-let mut rng = OsRng::new().expect("no secure randomness available");
+let mut rng = OsRng;
 let bits = 2048;
 let key = RSAPrivateKey::new(&mut rng, bits).expect("failed to generate a key");
 
diff --git a/src/key.rs b/src/key.rs
index 636bbf46..fd39d3e9 100644
--- a/src/key.rs
+++ b/src/key.rs
@@ -578,7 +578,8 @@ mod tests {
     #[test]
     #[cfg(feature = "serde1")]
     fn test_serde() {
-        use rand::{SeedableRng, XorShiftRng};
+        use rand::SeedableRng;
+        use rand_xorshift::XorShiftRng;
         use serde_test::{assert_tokens, Token};
 
         let mut rng = XorShiftRng::from_seed([1; 16]);
diff --git a/src/lib.rs b/src/lib.rs
index 42799cd5..a96c2a5c 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -11,7 +11,7 @@
 //! use rsa::{PublicKey, RSAPrivateKey, PaddingScheme};
 //! use rand::rngs::OsRng;
 //!
-//! let mut rng = OsRng::new().expect("no secure randomness available");
+//! let mut rng = OsRng;
 //! let bits = 2048;
 //! let key = RSAPrivateKey::new(&mut rng, bits).expect("failed to generate a key");
 //!