The quadratic hashing issue appears in the verification of all pre-segwit transaction formats. It stems from the method of verifying the input scripts.
For each input the transaction has, all the other inputs are stripped from the transaction to check that remaining input against the output it spends as wells as the corresponding signature. As the effort of stripping the transaction is linearly dependent on the number inputs and the stripping is repeated for each input, we do n-times work that scales linearly with n:
O(n)*O(n) = O(n²), the cost grows quadratically with the number of inputs. This means that with twice the number of inputs, the computational effort for the verification quadruples.
Rusty Russell explained the conundrum in his blog when he analyzed 'The Megatransaction: Why Does It Take 25 Seconds?'.