Philip Maymin, Markets are Efficient if and Only if P = NP.
I prove that if markets are efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can “program” the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data availability confirms this prediction.
But if P = NP then that’s it for most of modern cryptography, especially public/private key encryption. We’ll have to send giant one-time pads to each other before we can have secure communications.
So it turns out (if this paper is correct) that the choice is not (national) security or privacy. It’s market efficiency or (data) security and privacy.
Then again, it’s hardly news that markets fail. Look outside your window.