With the goal of improving the security of Internet protocols, we seek faster, semi-automatic methods to discover new vulnerabilities in protocols such as DNS, BGP, and others. To this end, we introduce the LLM-Assisted Protocol Attack Discovery (LAPRAD) methodology, enabling security researchers with some DNS knowledge to efficiently uncover vulnerabilities that would otherwise be hard to detect. LAPRAD follows a three-stage process. In the first, we consult an LLM (GPT-o1) that has been trained on a broad corpus of DNS-related sources and previous DDoS attacks to identify potential exploits. In the second stage, a different LLM automatically constructs the corresponding attack configurations using the ReACT approach implemented via LangChain (DNS zone file generation). Finally, in the third stage, we validate the attack's functionality and effectiveness. Using LAPRAD, we uncovered three new DDoS attacks on the DNS protocol and rediscovered two recently reported ones that were not included in the LLM's training data. The first new attack employs a bait-and-switch technique to trick resolvers into caching large, bogus DNSSEC RRSIGs, reducing their serving capacity to as little as 6%. The second exploits large DNSSEC encryption algorithms (RSA-4096) with multiple keys, thereby bypassing a recently implemented default RRSet limit. The third leverages ANY-type responses to produce a similar effect. These variations of a cache-flushing DDoS attack, called SigCacheFlush, circumvent existing patches, severely degrade resolver query capacity, and impact the latest versions of major DNS resolver implementations.