A principal vulnerability of a proof-of-work ("PoW") blockchain is that an attacker can re-write the history of transactions by forking a previously published block and build a new chain segment containing a different sequence of transactions. If the attacker’s chain has the most cumulative mining puzzle difficulty, nodes will recognize it as canonical. We propose a modification to PoW protocols, called ADESS, that contains two novel features. The first modification enables a node to identify the attacker chain by comparing the temporal sequence of blocks on competing chains. The second modification penalizes the attacker by requiring it to apply exponentially increasing hashrate in order to make its chain canonical. We demonstrate two things; (i) the expected cost of carrying out a double-spend attack is weakly higher under ADESS compared to the current PoW protocols and (ii) for any value of transaction, there is a penalty setting in ADESS that renders the expected profit of a double-spend attack negative.