So I'm reading over the Yaksha Security System and see it is based on the RSA cryptosystem and a centralized server, easy enough. What I'm slightly confused on is the math behind the related keys.
nAlice - Alice(some user) modulus
dAliceA - First private key only known to Alice
dAliceY - Second Private key only known to Yaksha server
eAlice - Alice's public key
The keys are related by the following:
dAliceA*dAliceY mod phi(mod nAlice) = dAlice
It states that the server sends Alice:
Calice = (Ksession) ^ dAliceY * eAlice mod nAlice
And Alice can determine the session key as:
(Calice) ^ dAliceA mod nAlice = Ksession
My question is, Can Alice obtain the session key due to the multiplicative properties of the modulus function and the basis of which RSA is built on? Or am I missing something here?
Edit: Also, is
dAlice just the combined private key of the server and Alice to verify that the keys are correct?