Дослідження методів та алгоритмів для рішення проблеми дискретного логарифмування в контексті криптографії біткоїну

Abstract

This work investigates methods and algorithms for solving the discrete logarithm problem in the context of the cryptographic security of Bitcoin. Bitcoin cryptographic security depends on the difficulty of recovering a private key from a public key. The work analyzes classical approaches such as the Baby-step Giant-step and Pollard Rho algorithms, with attention to the Bernstein-Lange optimizations. The work also examines the use of GPU acceleration to increase the performance of cryptanalytic algorithms through large-scale parallelism. The results indicate that, despite algorithmic improvements and hardware acceleration, solving the discrete logarithm problem for Bitcoin parameters remains computationally infeasible with current technologies.