Digital signature with Big Brother

I have read digital signature with Big Brother but don't understand the sequence.

One approach to digital signatures is to have a central authority that knows everything and whom everyone trusts, say Big Brother $$(BB).$$Each user then chooses a secret key and carries it by hand to $$BB$$'s office. Thus, only Alice and $$BB$$ know Alice's secret key, $$K_A$$, and so on.

When Alice wants to send a signed plaintext message, $$P$$, to her banker, Bob, she generates $$K_A(B, R_A, t, P)$$, where $$B$$ is Bob's identity, $$R_A$$ is a random number chosen by Alice, $$t$$ is a timestamp to ensure freshness, and $$K_A(B, R_A, t, P)$$ is the message encrypted with her key, $$K_A.$$

After then I don't understand how the following sequence works because there is nothing explained. Can anyone please explain in detail?

• When quoting from a source, please cite the source. Sep 27 '21 at 17:20

Alice - knowing $$K_A$$ - sends $$K_A(B, R_A, t, P)$$ to $$BB$$.

$$BB$$ - knowing $$K_A$$ - decrypts $$K_A(B, R_A, t, P)$$, obtaining $$(B, R_A, t, P)$$.

$$BB$$ - knowing $$K_B$$ and $$K_{BB}$$ - sends $$K_B(A, R_A, t, P, K_{BB}(A, t, P))$$ to Bob.

Bob - knowing $$K_B$$ - decrypts $$K_B(A, R_A, t, P, K_{BB}(A, t, P))$$, obtaining $$(A, R_A, t, P, K_{BB}(A, t, P))$$.

At this point you can go on reading.

• could you explain little, I don't understand what is happening here.. Sep 27 '21 at 18:57
• Maybe you don't understand the notation: $K_A(M)$ means encrypting the message $M$ using the key $K_A$. I usually write it as $Enc(M,K_A)$. Sep 27 '21 at 19:00
• all things are understood. But in last paragraph "Trudy replaying either message "-- what does mean by replaying message? Sep 27 '21 at 19:39
• It means trying to impersonate Alice by sending to Bob copies of messages sent by Alice to Bob. Sep 28 '21 at 6:47
• @Riccardo here middle in attack is impossible because everything is encrypted? Sep 28 '21 at 8:32