I was asked about this question by a friend.
He considers that Alice and Bob share a secret key
So why isn't it considered a symmentric-key scheme?
According to Wikipedia:
Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext. The keys may be identical or there may be a simple transformation to go between the two keys.
I observe that the shared
s is quite easy to compute by Alice and Bob.
I know there's misunderstanding, but I can't convince myself now.