The race for post-quantum cryptographic signature primitives is in its final lap over at NIST, which recently announced DILITHIUM, FALCON and Rainbow as the three signature primitive finalists. But a paper recently published by KU Leuven researcher Ward Beullens claims to find serious weaknesses in the security of Rainbow, one of those three finalists. In fact, the paper claims that the weaknesses are so severe that Rainbow’s security parameters now fall short of the security requirements set out by the NIST post-quantum competition. But how does Rainbow work, and how do these weaknesses affect it? And why weren’t they spotted until now? We discuss this and more in this week’s episode of Cryptography FM. Links and papers discussed in the show: Improved Cryptanalysis of UOV and Rainbow SQISign: compact post-quantum signatures from quaternions and isogenies Music composed by Toby Fox and performed by Sean Schafianski. Special Guest: Ward Beullens.