Abderrahim Siam2024-03-132024-03-132023-04-27http://dspace.univ-khenchela.dz:4000/handle/123456789/4240Broadcast abstractions are among the most important concepts in the field of fault tolerant distributed computing. These abstractions are used by consensus algorithms as a fundamental building block for ensuring that all correct processes in the system decide the same value. The Timely Provable Reliable Send primitive is among these broadcast abstractions with which we guarantee that messages are delivered correctly and in a timely manner, even in the presence of faulty processes. In this paper, we present an authenticated algorithm implementing provable reliable send primitive with very few eventually synchronous links. In other words, this algorithm assumes that there is a ⋄〈t + 1〉-sink in the system. A ⋄〈t + 1〉- sink is a correct process where the number of incoming eventually timely links that connecting it with correct processes is (t + 1) (including itself). We also show that a ⋄〈t + 1〉-sink is the minimal synchrony assumption for implementing this primitive in a Byzantine system where an authentication mechanism is available.enArticle