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Is there a hierarchical key construction algorithm that achieves forward/backward privacy with any (unlimited) leakage of private non-master keys?

What I mean is that if there's an unbounded number of generated keys where their private key is revealed, the master private information is still safe.

The paper "Hierarchical deterministic Bitcoin wallets that tolerate key leakage" is only safe up to k keys, and takes O(k) space to share the public key generation information.

Has there been anyone getting k -> infinity with O(1) space?

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