From question 3 in a project titled Blockchain: CSI (in what looks like a very cool class, run by University of Virginia!):
Problem 3. The Heuristic 1 (Section 4.3) used to detemine sets of public addresses owned by the same entity is based on the assumption that all inputs to a bitcoin transaction are controlled by the same entity. According to the paper, “the sender in the transaction must know the private signing key belonging to each public key used as an input, so it is unlikely that the collection of public keys are controlled by multiple entities (as these entities would need to reveal their private keys to each other).” Explain why this is not actually true. (A good answer will consider in more detail what is needed in the unlocking script to spend each input.)
How is this a flawed assumption?