I wonder if you'd run into some sort of energy problem. Like, this time machine would require some sort of energy and incur some amount of wear and tear on during each pass. The amount of possible solutions to today's cryptography might make this brute force level of effort, even with a time machine, infeasible. I feel like nasty old thermodynamics may preserve our world still. :)

Granted, I'm way way out of my depth here. I have a Ph.D. in physics but I studied nonlinear oscillators, relating them to problems in neuroscience.