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In a non-interactive proxy re-encryption scheme, Alice, with the key pair $(pk_a, sk_a)$, needs to issue a re-encryption key $re_{a\rightarrow b}$ once she wants to share her secret message with Bob, with key pair $(pk_b, sk_b)$.

In other words, Alice does: $re_{a\rightarrow b} = rekey(sk_a, pk_b)$.

Let's say Alice wants to issue re-encryption keys automatically, maye because she has been notified she has received a payment from Bob that entitles him to see the secret message. She would then need a program/server that issues new re-encryption keys when certain conditions are met.

How would she proceed? Without any encryption scheme modifications, she may either:

  • run her own private server
  • trust a third party to run that server

Let's say both cases are not feasable: Alice neither has resources to run her own server, nor she wants to reveal her secret key to a third party.

Can Alice delegate re-encryption keys issuance without revealing her secret key?

What really Alice wants to achieve is sharing a secret with an unknown number of Bobs under certain conditions, so any solutions wich may even involve changing encryption scheme will be accepted.

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