I more or less understand how an attacker (with less than 50%+1 of the hashing power) can artificially lower the block difficulty by messing with timestamps. I also understand how such an attacker could, on his own chain, at one point "ramp up" the difficulty of his last blocks to match the current chain's difficulty (I've read the other questions containing the time-warp-attack tag). What I don't understand is how at one point his chain, with less total chainwork, can be accepted by the network.
Say we're at block 100 on the honest chain and an attacker crafted a fake chain starting from block 50. He's now at block 105 and his block 105 has the same difficulty (that he ramped up) as the honest's chain 's block 100. He decides to broadcast his chain and he "wins" because he succeeded with his time warp attack (the question here is not about the feasability, budget-wise, of pulling such an attack today on the Bitcoin network: it's about the technical aspect of the attack).
What I don't get is that the honest chain has more total chainwork from block 50 to 100 than the total chainwork on the attacker's chain from block 50 to 105. The attacker, in the case of a time warp attack, has less than 50%+1 of the hashrate. So it's impossible for him to come up with x blocks that have more total PoW than the y blocks that the honest majority have mined meanwhile (even if he has more blocks, without 50%+1 he simply cannot have more chainwork than the honest majority).
So how comes that this re-org is accepted by the clients? When there's a re-org of the chain of several blocks, ain't the total chainwork of both chains compared?
