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Extending the functionality and overcoming the performance limitation underwhich QKD can operate requires either quantum repeaters or new security models.Investigating the latter option, we introduce the \textit{Quantum ComputationalHybrid} (QCH) security model, where we assume that computationally secureencryption may only be broken after time much longer than the coherence time ofavailable quantum memories. We propose an explicit $d$-dimensional keydistribution protocol, that we call MUB-\textit{Quantum Computational Timelock}(MUB-QCT) where one bit is encoded on a qudit state chosen among $d+1$ mutuallyunbiased bases (MUBs). Short-term-secure encryption is used to share the basisinformation with legitimate users while keeping it unknown from Eve until afterher quantum memory decoheres. This allows reducing Eve's optimal attack to animmediate measurement followed by post-measurement decoding. \par Wedemonstrate that MUB-QCT enables everlasting secure key distribution with inputstates containing up to $O(\sqrt{d})$ photons. This leads to a series ofimportant improvements when compared to QKD: on the functional side, theability to operate securely between one sender and many receivers, whoseimplementation can moreover be untrusted; significant performance increase,characterized by a $O(\sqrt{d})$ multiplication of key rates and an extensionby $25 {\rm} km \times \log(d)$ of the attainable distance over fiber.Implementable with a large number of modes with current or near-term multimodephotonics technologies, the MUB-QCT construction has the potential to provide aradical shift to the performance and practicality of quantum key distribution.

Everlasting Secure Key Agreement with performance beyond QKD in a Quantum Computational Hybrid security model