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Distribution of national SessionKeys

The following steps must be executed to create Alice's SessionKey to Bob :

1. Alice asks the TA for a SessionKey giving the ID-numbers of the sender (herself) and the receiver
2. based on these information, the TA constructs a stamp (ID sender + ID receiver)
3. the TA encrypt this stamp with his PrivateKey to generate the SessionKey from Alice to Bob, K_ses
4. the TA reconstructs the PrivateKeys (and inverse ones) of Alice and Bob : K_Alice, K^-1_Alice, K_Bob, K^-1_Bob
5. the TA computes the SessionKeys (direct, inverse, inverse complementary, and inverse of the inverse complementary) : K_ses, K^-1_ses , K_comp (=[11...1] XOR K^-1_ses) and K^-1_comp
6. the TA sends 4 different encrypted blocks to Alice :
   • the first block contains the SessionKey from Alice to Bob, K_ses, encrypted with the inverse PrivateKey of Alice, K^-1_Alice (*)
   • the second block contains the stamp (ID of sender + ID of receiver) encrypted with the inverse SessionKey
   • the third block contains the inverse SessionKey from Alice to Bob, K^-1_ses, encrypted first with the inverse PrivateKey of Bob, K^-1_Bob, and then with the inverse PrivateKey of Alice, K^-1_Alice.
   • the last block contains the stamp first encrypted with the inverse of the complementary inverse SessionKey, K^-1_comp, and then with the inverse SessionKey, K^-1_ses.

(*) Of course, knowing the ID-number of an end-user, the TA is able to reconstruct his PrivateKeys (direct and inverse keys). This is done internally in a way that they are not accessible to humans.

What are these 4 blocs for ?

• The first block permits Alice to reconstruct the SessionKey whenever she sends a message to Bob. The SessionKey is NOT recorded by Alice...
• The second block permits Alice to verify that the received blocks concern the SessionKey between herself and Bob.
• The third and fourth blocks will be included in all the messages that Alice will send to Bob.
• The third block permits to Bob to decipher all the messages sent by Alice.
• With the last block, Bob is sure that the SessionKey was generated by the TA.