It has been a while, but I think I know now about an idea to solve this problem. I really appreciate all the help I got from your responses.
I wrote a document that explains it here: https://www.newtolife.net/the-trusted-supernode-and-distributed-banking.html Abstract: The Trusted Supernode is an abstract idea for a distributed secure and efficient banking system. This system allows payment operations that disturb only small amount of participants. It overcomes adversarial attacks by applying a useful proof of work, combined with node mixing. The Trusted Supernode bank system relies at its core on a special form of trusted entity called the supernode. In addition to its ability to manage payments, the supernode should allow to securely exchange computation and storage services for money. real. ---------- Forwarded message ---------- From: realcr <rea...@gmail.com> Date: Wed, Jan 7, 2015 at 5:40 PM Subject: The Wandering Music Band To: cryptography@randombit.net Hi, I am looking for some crypto primitive to solve a problem I have. Assume that I meet a group of people. call it S. I get to talk to them a bit, and then they are gone. This group of people walk together in the world. Sometimes they add a person to their group, and sometimes they remove one person. (You can assume it's a music band, then it all makes sense). Generally, though, you may assume that they have at least k people in the group at all times. Assume that I meet the resulting group at some time in the future, after many members were added or removed. How can the new group S' prove to me that they are the descendants of the original group S? I include here some of my thoughts about this. 1. Naive Solution: Remembering lots of signatures. Every person in the world will have a key pair (of some asymmetric crypto) to represent his identity. When I first meet the group S, I collect all their public keys and keep them. Whenever a new member x is added to the group S, all the current members of S sign over the new list: S U {x}. Whenever a member x is removed from the group S, all the current members of S sign over the new list S \ {x}. The group members always have to carry with them all the signatures since the beginning of time. When I meet the group at some point in the future, I can just ask them to prove their current public keys, and also to show me all the signatures since the beginning. My issue with this solution is that the group has to remember more and more signatures as time goes by. I wonder if there is a more efficient way. 2. Using "Transitive Signatures" I have seen two articles about a concept called Transitive Signatures. Shortly: Given a signature of x over y, and of y over z, any participant will be able to generate a signature where x signs over z. http://people.csail.mit.edu/rivest/MicaliRivest-TransitiveSignatureSchemes.pdf https://eprint.iacr.org/2004/215.pdf I didn't manage to apply this method to my problem though. I will appreciate any idea or hint about how to solve this. Regards, real.
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