CSAIL2019 Crypto-Puzzle Solver Architecture

Abstract

The CSAIL2019 time-lock puzzle is an unsolved cryptographic challenge introduced by Ron Rivest in 2019, replacing the solved LCS35 puzzle. Solving these types of puzzles requires large amounts of intrinsically sequential computations, with each iteration performing a very large (3072-bit for CSAIL2019) modular multiplication operation. The complexity of each iteration is several times greater than known FPGA implementations, and the number of iterations has been increased by about 1000x compared to LCS35. Because of the high complexity of this new puzzle, a number of intermediate, or milestone versions of the puzzle have been specified. In this article, we present several FPGA architectures for the CSAIL2019 solver, which we implement on a medium-sized Intel Agilex device. We develop a new multi-cycle modular multiplication method, which is flexible and can fit on a wide variety of sizes of current FPGAs. We introduce a class of multi-cycle squarer-based architectures that allow for better resource and area trade-offs. We also demonstrate a new approach for improving the fitting and timing closure of large, chip-filling arithmetic designs. We used the solver to compute the first 22 out of the 28 milestone solutions of the puzzle, which are the first reported results for this problem.