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This paper introduces a parallelized variant of the Random Sample Matching (RANSAM) approach, which is a very time and memory efficient enhancement of the common Random Sample Consensus (RANSAC). RANSAM exploits the theory of the birthday attack whose mathematical background is known from cryptography. The RANSAM technique can be applied to various fields of application such as mobile robotics, computer vision, and medical robotics. Since standard computers feature multi-core processors nowadays, a considerable speedup can be obtained by distributing selected subtasks of RANSAM among the available cores. First of all this paper addresses the parallelization of the RANSAM approach. Several important characteristics are derived from a probabilistic point of view. Moreover, we apply a fuzzy criterion to compute the matching quality, which is an important step towards real-time capability. The algorithm has been implemented for Windows and for the QNX RTOS. In an experimental section the performance of both implementations is compared and our theoretical results are validated.