Problem: I'm thinking about a lightweight solution to provide source authentication (only one source) to multiple receivers (multicast message).

Context: Taking the problem to ground, we can think of use cases like firmware update (one to many), or a command to turn on several lights 'on' (that command can be sent by one and only one source). In all cases I don't want to send many times the same message, but only once (multicast), and that the receivers can authenticate that comes from an authorised-trusted source (one-way authentication).

The scenario is similar to the one described on: https://tools.ietf.org/html/draft-somaraju-ace-multicast-00 But there they have many senders, they use symmetric crypto, any member of the security group (same symmetric key) can send message to the other members of the group.

I know that with asymmetric cryptography the problem can be easily solved: Digital Signatures.

But I was wondering:

Is there any established symmetric-cryptography-only solution to this problem?

To my (not extensive) knowledge I'm inclined to say No (due to the symmetric characteristics of.. symmetric crypto), but maybe there is a smart symmetric cryptosystem that can achieve source-authentication.

ps: this question is simmilar Digital Signature using symmetric key cryptography but not the same (and the answers do not provide a categoric answer)