Solving prime-field ECDLPs on GPUs with OpenCL

Erik Boss
Radboud University, Nijmegen
Radboud University, 2015

   title={Solving prime-field ECDLPs on GPUs with OpenCL},

   author={Boss, Erik and Schwabe, Peter and Batina, Lejla},



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The intractability of the ECDLP is part of what makes many cryptographic application work. As such, viewing this problem from as many angles as possible is worthwhile. In this thesis, we explore the angle of creating a GPU ECDLP solver using OpenCL. In the process, we discuss the many issues, limitations and solutions we encounter. The main result is that, on our testing setup, we can construct a solver that computes a 112-bit ECDLP in 18.5 years but which can also scale up to 114-bit ECDLPs without a relative loss of performance, i.e., we solve a 114-bit ECDLP in approximately 37 years. This nature of the problem is such that, when we scale over many GPUs, we can decrease this number linearly by number of GPUs available.
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