This article presents a new lossless compression algorithm based on a Finite Radon Transform. The baseline of this work consist in encoding the difference between several sim- ilar finite Radon projections. Two differential encoding tech- niques are needed to efficiently encode the Radon trans- formed data. An intra-projection encoding technique is first performed, this differential encoding process takes benefit of the redundancy present in such projections. The second step consists in encoding the similarities between Radon projections, this is the inter-projection encoding procedure. The used Finite Radon transform (called Mojette transform), allows to ensure both compression and data redundancy. The main novelty of this work is the use of a secure dis- tributed storage or transmission tool in a lossless compres- sion context.