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One-time public-private key pairs are used. The next public-private key pair to be used, is recorded with a proof c = sha3(nextPublicKey).

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    $\begingroup$ I see at most a commitment for the next public key. I do not see a signature scheme! $\endgroup$ – cypherfox Mar 17 '18 at 13:17
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No, Lamport signature is a particular one-time signature scheme prescribing a particular method of verifying signatures, generating key pairs, and generating signatures. You could use that technique to turn a one-time signature scheme such as Lamport's into a tremendously awkward stateful many-time signature scheme.

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