What are the problems with symmetric cryptographic algorithms?

It is suitable for a closed system, in which users are interrelated and trust each other, and we should guard against external attacks. With the increasingly prominent security problems in the open network environment, the traditional symmetric cipher has encountered many difficulties: the key needs to be replaced after a period of use, and the key transmission needs a reliable channel; In the communication network, if all users use the same key, it loses the meaning of confidentiality; If n people use different keys, they need N(N- 1)/2 keys, which makes key management difficult. Can not meet the confidentiality requirements of private conversations between strangers. The symmetric key is shared by at least two people, and it has no personal characteristics, so it cannot be digitally signed.