Block withholding resilience

It has been known for some time that the Nakamoto consensus as implemented in the Bitcoin protocol is not totally aligned with the individual interests of the participants. More precisely, it has been shown that block withholding mining strategies can exploit the difficulty adjustment algorithm of the protocol and obtain an unfair advantage. However, we show that a modification of the difficulty adjustment formula taking into account orphan blocks makes honest mining the only optimal strategy. Surprinsingly, this is still true when orphan blocks are rewarded with an amount smaller to the official block reward. This gives an incentive to signal orphan blocks. The results are independent of the connectivity of the attacker.