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**2023/1836**

**Title:**

An Incremental PoSW for General Weight Distributions

**Authors:**
Hamza Abusalah, Valerio Cini

**Abstract:**

A proof of sequential work (PoSW) scheme allows the prover to convince a verifier that it computed a certain number of computational steps sequentially.

Very recently, graph-labeling PoSW schemes, found applications in light-client blockchain protocols, most notably bootstrapping. A bootstrapping protocol allows a light client, with minimal information about the blockchain, to hold a commitment to its stable prefix. An incremental PoSW (iPoSW) scheme allows the prover to non-trivially increment proofs: given \chi,\pi_1 and integers N_1,N_2 such that \pi_1 is a valid proof for N_1, it generates a valid proof \pi for N_1+N_2.

In this work, we construct an iPoSW scheme based on the skiplist-based PoSW scheme of Abusalah et al. and prove its security in the random oracle model by employing the powerful on-the-fly sampling technique of Döttling et al. Moreover, unlike the iPoSW scheme of Döttling et al., ours is the first iPoSW scheme which is suitable for constructing incremental non-interactive arguments of chain knowledge (SNACK) schemes, which are at the heart of space and time efficient blockchain light-client protocols. In particular, our scheme works for general weight distributions, which we characterize as incrementally sampleable distributions. Our general treatment recovers the distribution underlying the scheme of Döttling et al. as well as the distribution underlying SNACK-enabled bootstrapping application as special cases. In realizing our general construction, we develop a new on-the-fly sampling technique.

**ePrint:**
https://eprint.iacr.org/2023/1836

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