  Automated certificate authorities (CAs) have expanded the reach of public key
infrastructure on the web and for software signing. The certificates that these
CAs issue attest to proof of control of some digital identity. Some of these
automated CAs issue certificates in response to client authentication using
OpenID Connect (OIDC, an extension of OAuth 2.0). This places these CAs in a
position to impersonate any identity. Mitigations for this risk, like
certificate transparency and signature thresholds, have emerged, but these
mitigations only detect or raise the difficulty of compromise. Researchers have
proposed alternatives to CAs in this setting, but many of these alternatives
would require prohibitive changes to deployed authentication protocols.
  In this work, we propose a cryptographic technique for reducing trust in
these automated CAs. When issuing a certificate, the CAs embed a proof of
authentication from the subject of the certificate -- but without enabling
replay attacks. We explain multiple methods for achieving this with tradeoffs
between user privacy, performance, and changes to existing infrastructure. We
implement a proof of concept for a method using Guillou-Quisquater signatures
that works out-of-the-box with existing OIDC deployments for the open-source
Sigstore CA, finding that minimal modifications are required.
