ssh maimed on testing update

[rvclayton@acm.org]

I'm running

  $ lsb_release -a
  No LSB modules are available.
  Distributor ID: Debian
  Description:    Debian GNU/Linux testing-updates (sid)
  Release:        testing-updates
  Codename:       sid

  $ uname -a
  Linux BanjaLuka 4.3.0-1-686-pae #1 SMP Debian 4.3.3-2 (2015-12-17) i686 GNU/Linux

  $

and after the most recent (dist-)upgrade

  $ grep ssh 160103 
    mesa-vdpau-drivers multiarch-support nodejs openssh-client openssh-server
    openssh-sftp-server openssl p11-kit p11-kit-modules perl perl-base perl-doc
  Preparing to unpack .../openssh-sftp-server_1%3a7.1p1-5_i386.deb ...
  Unpacking openssh-sftp-server (1:7.1p1-5) over (1:6.9p1-3) ...
  Preparing to unpack .../openssh-server_1%3a7.1p1-5_i386.deb ...
  Unpacking openssh-server (1:7.1p1-5) over (1:6.9p1-3) ...
  Preparing to unpack .../openssh-client_1%3a7.1p1-5_i386.deb ...
  Unpacking openssh-client (1:7.1p1-5) over (1:6.9p1-3) ...
  Setting up openssh-client (1:7.1p1-5) ...
  Installing new version of config file /etc/ssh/moduli ...
  Setting up openssh-sftp-server (1:7.1p1-5) ...
  Setting up openssh-server (1:7.1p1-5) ...

  $

I find that I can no longer just ssh hostname into a system, I have to give a
password

  $ ssh burkinafaso
  rclayton@burkinafaso's password: ^C

  $ 

Before the upgrade, I used to ssh into a system without supplying a password.
I get the same behavior independent of the host on the other end (another
testing system, freebsd, or centos).  Re-installing the (unchanged) ssh key
via ssh-copy-id doesn't fix anything.

How do I recover the ssh behavior I had before the upgrade?