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We propose a new cryptographic primitive, a *seekable sequential key generator* (SSKG), that combines these two properties and has direct application in secure logging. We rigorously formalize the required security properties and give a provably-secure construction based on the integer factorization problem. We further optimize the scheme in various ways, preparing it for real-world deployment. As a byproduct, we develop the notion of a *shortcut one-way permutation* (SCP), which might be of independent interest.
Our work is highly relevant in practice. Indeed, our SSKG implementation has become part of the logging service of the systemd system manager, a core component of many modern commercial Linux-based operating systems.