How can I use RusTLS to encrypt a byte slice using a known public key and PKCS1 padding?

In order to create GitHub releases from Travis CI, you need to use public keys they provide to encrypt secrets which can be checked into a project.

I've successfully managed to do this using the openssl crate (v0.10.11):

extern crate base64;
extern crate openssl;

use openssl::rsa::{Padding, Rsa};
use std::{error, fs};

fn main() -> Result<(), Box<dyn error::Error>> {
  let data = b"some data";

  let pub_key = fs::read_to_string("./key.pem")?; // Read the public key.
  let rsa = Rsa::public_key_from_pem(pub_key.as_bytes())?;

  let mut res = vec![0; rsa.size() as usize];
  rsa.public_encrypt(data, &mut res, Padding::PKCS1)?;

  let encrypted = base64::encode(&res);
  println!("Encrypted Data: \n{}", encrypted);
  Ok(())
}

link to repro

However, using OpenSSL comes with a few tradeoffs. Most notably: getting cross platform builds to work requires some work.

I've been looking at rustls as an alternative, and was wondering what the equivalent of the code above is.