 Hello everyone, my name is Shan Shan Li, this is a short video abstract for our paper in Aethercripts 2022. The title of our paper is Towards Practical Topology Heading Computation. The main topic of this paper is Secure Multi-Party Computation. MPC allows N parties to securely compute some functions without leaking additional information about the inputs. Life cycle MPC assumes that either two parties can communicate directly, namely, the communication graph is complete. So what if the communication graph is incomplete and sensitive? Maran Adelaou and Dray Chawson formalized the concept of topology-hiding computation. In formally speaking, a THC protocol is an MPC protocol over incomplete graph, which does not give the parties any information about the graph topology. In the setting that the adversary may statically passively corrupt any number of parties, THC has been shown to be feasible on any graph. In fact, if there exists a topology-hiding graph broadcast for some graph class and a PKE scheme, then THC uses this for the same graph class. This is achieved by using THB and PKE to simulate point-to-point channels in an MPC protocol. Firstly, each party uses THB to broadcast its public key in a setup phase. Then to send a message X to BG, PI increments X using the public key of BG, and then uses THB to broadcast the resulting ciphertext. Finally, upon receiving the ciphertext, PG can decrypt it to get X. Other parties know nothing about X because they do not know the decryption key. Akevia, Louvaini, and Moran thought that THB is feasible over general graphs. This implies that any function can be topology-hidingly computed over any graph. Although THC has been shown to be feasible, exiting THC protocols are not practical. In this work, we improve several exiting THC protocols on circles and general graphs. For THC on circles, we consider three functionalities, including broadcast, sum, and general computation. The AM protocol is the state-of-the-art topology-hiding broadcast protocol for circles. Using the AM protocol, broadcasting 1-bit costs o n squared times cap-base. We optimize it such that the communication cost for broadcasting cap-base is o n squared times cap-base. The state-of-the-art topology-hiding sum and general topology-hiding computation protocols for circles are constructed by comparing blackboards from the AM protocol. By allowing the parties to know the exact value of n, we reduce the communication cost by a factor of o n times c kappa for both the sum and general computation functionalities. For THC on general graphs, the state-of-the-art topology-hiding broadcast protocol for general graphs is the ALM protocol. Using the ALM protocol, broadcasting 1-bit costs o the fifth power of n times cap-squared-base. We optimize it such that the communication cost for broadcasting cap-base is o the fifth power of n times cap-squared-base. Then we consider the LZM3T protocol, which is an FHE-based GTHC protocol with low-run complexity. This protocol requires the parties to communicate o the eighth power of n times cap-squared FHE self-test and o the fifth power of n times cap-fhe public case. We optimize this protocol such that the communication cost is reduced to o the sixth power of n times cap-fhe self-tests and o the fifth power of n times cap-fhe public case. This is a short presentation of our paper. Thanks for listening.