International Association
for Cryptologic Research

In this short note we give another direct proof for the variant of the FO transform used by Kyber in the QROM. At PKC'23 Maram & Xagawa gave the first direct proof which does not require the indirection via FO with explicit rejection, thereby avoiding either a non-tight bound, or the necessity to analyze the failure probability in a new setting. However, on the downside their proof produces a bound that incurs an additive collision bound term. We explore a different approach for a direct proof, which results in a simpler argument closer to prior proofs, but a slightly worse bound.