1. A system comprising: a memory; a blockchain stored within the memory, the blockchain comprising: a selected block comprising original data; and a specific block comprising an integrity output, the integrity output determined from the original data as an input; communication interface circuitry configured to: perform a key secret exchange operation to receive portions of a key secret, the portions received on behalf of multiple individually untrusted parties; receive a command coordinated with the key secret exchange operation, the command specifying to overwrite the original data with altered data; and rewrite circuitry in data communication with the communication interface circuitry, the rewrite circuitry configured to: obtain a portion combination from the portions of the key secret; determine whether a count of the portions exceeds a rewriting threshold for rewrite privileges; and when the count of the portions exceeds the rewriting threshold for rewrite privileges: compute collision data that includes the altered data, where: the collision data is coding-consistent with the integrity output, where overwriting the original data with the collision data does not introduce coding-inconsistency with the integrity output thereby preserving validity of the blockchain; and the collision data is algorithmically determined from the portion combination and the altered data as inputs; and responsive to the command, overwrite the original data with the collision data.