I maintain a series of WordPress sites.

One of them recently started throwing up an error whenever I tried to update the core or a plugin.  All I got was the not very helpful message:

Download failed. error:0D0890A1:asn1 encoding routines:func(137):reason(161)

As this meant that every update had to be downloaded locally and then FTP'd up to the site I was anxious to find a fix.

I found this simple piece of code (courtesy of Damien Carbery over at the WordPress Forums)

<?php
/*
Plugin Name: Skip SSL Verify
Plugin URI: http://www.damiencarbery.com
Description: Skip SSL verify in curl downloads - fixes: Download failed. error:0D0890A1:asn1 encoding routines:func(137):reason(161).
Author: Damien Carbery
Version: 0.1

$Id:  $
*/

function ssv_skip_ssl_verify($ssl_verify) {
    return false;
}
add_filter('https_ssl_verify', 'ssv_skip_ssl_verify');
add_filter('https_local_ssl_verify', 'ssv_skip_ssl_verify');

I saved this into a text file which I named Skip_SSL_Verify.php, copied it up into the site's plugin directory and activated it.

Problem solved.  The site now updates normally.