Every actor can create a root node and delegate a right to add a child node. Every node contains name of its’ creator or who added it, and value S. Sum of all values S at the same level of the tree must be equal to the sum of all values of the parent level nodes which in turn is equal to the sum of S’s of their parent nodes and so on up to the root.

Original question: Resending an encrypted message so that it’s guaranteed from being changed and is visible only to final receivers

I faced the next rather theoretical problem. Sender sends a message (I, Ch, S), where I is the proper content of the message, Ch is chain of receivers/resenders and S is just a sum. By having received the message Receiver sees all the information (I, Ch and S), next he/she can either accept or decline the message. By accepting it he is in right to resend the message as many times as he wants, adding every time its’ name to Ch, but S of all the resent messages is equal to the S of the original message.

Example. Alice sends <“1st message”, Alice, 500> to Bob, Bob resends <“1st message”, (Alice, Bob), 500> to Daenerys. Daenerys resends <“1st message”, (Alice, Bob, Daenerys), 300> to Jon and <“1st message”, (Alice, Bob, Daenerys), 200> to Tyrion.

The message must be encrypted , firstly, with Bob’s public key, then decrypted with his private key, then encrypted by Daenerys’ public key. But Dany can’t be sure that the content isn’t changed. Jon and Tyrion can’t be sure that the sum of the received messages is equal to the sum of the original message.

  • $\begingroup$ Welcome to Computer Science! Are you asking two very different questions? The first question is in the title, how to "resend an encrypted message so that it’s guaranteed from being changed and is visible only to receivers". The second question is about, if I understand it correctly, how to perform and verify encrypted addition (homomorphic encryption). $\endgroup$ – John L. Jul 6 '19 at 19:36
  • $\begingroup$ "Dany can’t be sure that the content isn’t changed. " Please clarify what dany could have known beforehand. If Dany knows nothing about the original message, "1st message", then there is no way Dany can be sure that the content isn't changed. $\endgroup$ – John L. Jul 6 '19 at 19:40
  • $\begingroup$ "An encrypted message" "is visible only to receivers". Is Bod considered a receiver? Is Dany consider a receiver? Are Jon and Tyrion considered receivers? Or do you mean "final receivers"? $\endgroup$ – John L. Jul 7 '19 at 2:33
  • $\begingroup$ Dany only knows the content of the message she received (I, Ch, S). She’s not sure of it. Since she knows Ch, she can try to verify a message checking all the receivers/resenders up to the first sender/originator of the message. But then she can’t be sure if S is not altered. $\endgroup$ – nuwus Jul 7 '19 at 9:20
  • $\begingroup$ Also the problem with S rather reminds me the “double spending problem” in blockchains, although I’m not sure since know pretty much close to nothing about cryptocoins. $\endgroup$ – nuwus Jul 7 '19 at 9:22

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