Example of a problem for which Zero-Knowledge proof is not sequentially composable There are notions that a Zero-knowledge proof with auxiliary input is necessary for sequential composition. However, the authors here give a very convoluted example of a system which is not sequentially composable under the original ZK definition. Could you please give me an example where the original definition by Goldwasser et al. is not enough for sequential composability?
The paper you cited gives that exact example. It shows that zero-knowledge that is NOT zero-knowledge for auxiliary input is not strong enough. The fact is that most known zero-knowledge proofs are secure for auxiliary input and thus are secure under sequential composition.