We identify two attacks on the Network Time Protocol (NTP)'s cryptographically-authenticated broadcast mode. First, we present a replay attack that allows an on-path attacker to indefinitely stick a broadcast client to a specific time. Second, we present a denial-of-service (DoS) attack that allows an off-path attacker to prevent a broadcast client from ever updating its system clock; to do this, the attacker sends the client a single malformed broadcast packet per query interval. Our DoS attack also applies to all other NTP modes that are `ephemeral' or `preemptable' (including manycast, pool, etc). We then use network measurements to give evidence that NTP's broadcast and other ephemeral/preemptable modes are being used in the wild. We conclude by discussing why NTP's current implementation of symmetric-key cryptographic authentication does not provide security in broadcast mode, and make some recommendations to improve the current state of affairs.